Radio Study of Galactic Supernova

Remnants and the Interstellar Medium

A Thesis submitted for the degree of

Doctor of Philosophy

(in PHYSICS) to the

UNIVERSITY OF PUNE

by

SANJAY BHATNAGAR

National Centre for Radio Astrophysics Tata Institute of Fundamental Research

Pune - 411 007 July 2001

Contents

i ii CONTENTS

List of Figures

iii iv LIST OF FIGURES

List of Tables

v vi LIST OF TABLES

Acknowledgments

It has been a long trek - at least longer than what I imagined it would be. On the trek, I am fortunate to have come in touch with a variety of people. Some of them have become close at a personal level too. This is an attempt to convey to the reader, my appreciation for these people who directly or indirectly affected the course of this trek.

Apart from the usual stuff, I was taught by Prof. H. S. Mani, at IIT Kanpur, that ”research is not just another profession, it is a way of life”. I also remember Prof. A.P.Shukla who, in his inimitable way, sparked in his students a desire for learning. I owe my presence in the National Centre for Radio Astrophysics (NCRA) to Prof. Mani, and to Prof. Shukla for making learning interesting, and motivating me into the pursuit of research. I express my deep respectful thanks to them.

Once at NCRA, stepping into that ”way of life”, the fascination of thinking big while keeping one’s feet firmly on ground came with Prof. Govind Swarup, and others at the NCRA. Prof. Swarup’s description, sometimes past midnight, of the design of some mechanical structure (which, I later realized was the GMRT antenna), how to do quick arithmetic (where I was made to play the role akin to that of temporary register of a computer CPU), his introducing me to Fourier Transforms, Aperture Synthesis, and Radio Astronomy in general are the first few steps into that ”way of life” I fondly remember. His later demand that I be able to give quick answers to questions that he ”might throw at me while passing by in the corridors” helped me in many ways. His enthusiasm is even now a source of inspiration. Over the years I have interacted with him a lot. He became the source of guidance, consultations and advice and sometimes even a sink for my outbursts due to problems in personal and professional life. I am all the more thankful to him for this, and hope to continue this relationship in future.

For my thesis, I slowly gravitated towards A. Pramesh Rao probably because of his approach to work and his style of thinking and his scientific interests. He gradually became my unofficial guide at NCRA. During the early stages of the GMRT (and to some extent even now), I learnt from him the tricks of the trade, and thoroughly enjoyed that phase of my thesis and GMRT debugging and I am very thankful to him for that. All along he encouraged me to be independent. Partly because of this, I was able to do large parts of my work independently. Even for work where he was not directly involved or interested, he was and continues to remain an excellent person to bounce off ideas - and I sometimes even receive healthy criticism with equanimity.

Another scientist from whom I learnt a good deal is T.J.Cornwell. The time I spent working with him was very satisfying in terms of work in hand, and in future, as well as in terms of learning directly from someone whose work I admire a lot. I could not pursue that line of work due to limitations of my domestic and professional problems. I may have disappointed him there. However, I continue to find in him a very understanding, supportive and inspiring senior colleague. Tim - my heartfelt thanks to you for everything. I look forward to working together again sometime. The possibility to finally go forward from where we left gives an inviting and positive hue to the future.

I am very grateful to D.J.Saikia (a.k.a. Sykes) for agreeing to become my Official Guide. Besides reading my thesis and providing useful comments/criticisms and contributing his all important signatures to my thesis, his contribution in the role of a more experienced friend and well-wisher was a great support. I remember long sessions where he would patiently listen to my diatribe that I would pour out. His counsel at various points of time, his assistance, and discussions were of great help. His legendary wholehearted laughter (which often reached me in my office with minimal attenuation) and his one-liner punch-lines kept the environment cheerful (though I must add that he is now trying to extort something useful out of me as a ”fee” for his signatures!). Sykes, I am indeed grateful to you for all you have done.

Interaction with Rajaram Nityananda towards the concluding stages of my work, started with what was to become Chapter 7 of my thesis. It has been a very rewarding and fruitful experience. Working with him has been sheer joy, and I hope to do more fruitful work with him in future. I continue to learn from his very broad spectrum of interests. I am grateful to him for his indulgence in often going out of his way to help me out in facing problems on various fronts of life.

I also spent sometime working with K.R. Anantharamaiah of the Raman Research Institute, Bangalore and it was such a pleasure. Although, finally, that work did not go into my thesis, I hope to pursue that line of work with him in the near future. He and Namir Kassim of the Naval Research Labs. became the target for bouncing off many of my ideas.

Thank you both for tolerating and helping me.

I wish to also thank S. Ananthkrishnan, Gopal-Krishna, C.R. Subrahmanya, V.K. Kulkarni, M. Vivekananda, and K. Subramaniya, for all the help, cheer and fun they brought in life.

Many thanks to my friend Prem Kumar, who helped at various stages with some drawings, and in printing and binding the thesis.

My close friends Sulekha and Goutam Chattopadhyay contributed towards this effort in ways I find difficult to describe - in any case I wish not to attract severe penalties they would impose on expressing formal ”thanks”. Nonetheless, I would say this much – without my family and them I would not have made it. I also found an excellent companion in Divya Oberoi (”Div”) and Jaishree Oberoi. At Pune, I fondly remember long sessions of discussions on just any thing under the Sun, interspersed with generous helpings of aalooparanthas at their home adding spice to our discussions.

Rajiv Singh (RK), Ajit Kulkarni, V.M. Tatke (Maharaj), Ramana Athreya, Nissim Kanekar, Sanjay Upreti, Niraj Upadyay, Ajith Kumar (Ajithum), Hemant Lohkhande - all with their own inimitable and unique personalities, helped eliminate drudgery from work and life in general. Late night strolls, tea/coffee/milk sessions (and lately, sessions of Nissim’s own invention of “Turmeric milk”, in the inviting company of potential new members of this gang) followed by “profound” discussions, hikes in the Sahyadris (particularly the Bhimashankar hike), catching snakes in the NCRA campus and photographing them from distances otherwise considered unsafe, and the music sessions were the activities with all these friends which helped me keep tempo of work and made life enjoyable. My thanks to all of them.

I also wish to thank the entire GMRT staff without whose cooperation and help this work would not have been possible. My special thanks to all the telescope operators (Anirudh, Mangesh, Sanjay, Manisha, Manish, Jayprakash and Jitendra) for all help during observations and keeping the GMRT control room environs cheerful (though again I must remind Mangesh that my investment in the music CD that I contributed to the GMRT Control Room did not give the expected dividends).

I enjoy a very special relationship with my youngest Chacha/Chachi - Mr. Anand Shankar / Ms. Mamta Shankar. I find in them a friend, an elder, a patient listener, concerned counselor/critic and a determined well-wisher who invariably make me feel comfortable and stable in life. Also my brothers-in-law and sisters were great sources of inspiration. My special thanks to them all for all they have done.

I always had, and to some extent still have, faith in the basic goodness of all humans and in the beauty of human relationships. During this trek, I came close to some people whose approach to life and relationships however leaves a nagging doubt in the mind. I am sure that what nature does to us must be handled with care, humility, compassion and love - but sometimes people, even in normal circumstances, can become completely insensitive and prefer going for easier solutions in life. I do not know if some of such people have contributed towards this work - positively or negatively. But I will remember them all - some of them even fondly - for a long time.

I am truly amazed by the patience and determination to constantly show the brighter side of life that my family, particularly my parents showed. Past few years have by far been the roughest patch in life I have walked and I have no doubt that without their patience and faith in me, I would have gone down that slippery path which I had begun to walk. There was nothing to look forward on that path, certainly not a thesis. I dedicate my thesis to them and I hope I have made them happier.

I would like to thank the NCSA Astronomy Digital Image Library (ADIL) for providing some of the images used for the purpose of illustration in this thesis.

The NASA’s Astrophysics Data System was extensively used during the course of this work for locating data, other references available on the web and for building the bibliography database for this thesis.

Most of the work which required computers was done using computers running the GNU/Linux operating system. The software I used was almost entirely from the Open Source movement and I am convinced that without the excellent work of all those GNUians out there, my life would have been more difficult. I wish to thank all those anonymous contributors to the Open Source movement and hope to become part of it by contributing something substantial someday. xi xii ACKNOWLEDGMENTS

Declaration

CERTIFIED that the work incorporated in this thesis entitled “Study of Galactic Supernova Remnants and Interstellar Medium at low frequencies” submitted by Sanjay Bhatnagar was carried out by the candidate under my supervision. Such material as has been obtained from other sources has been duly acknowledged in the thesis.

Place : Pune July , 2001 Prof. D. J. Saikia Thesis Supervisor

xiv DECLARATION

Abstract

This dissertation presents a study of Galactic Supernova Remnants (SNRs), using the newly available Giant Metrewave Radio Telescope (GMRT) at a frequency of 327 MHz. Extensive debugging and calibration of the telescope parameters was required before the above could be carried out; this is also presented here.

Towards the end of their evolution, stars with masses greater than about 8M_{⊙} explode, producing one of the most energetic observable events in the Galaxy. These explosions of massive stars are referred to as Supernovae (SNe). The shock wave traveling outwards, initially interacts with the circumstellar material of the progenitor star, giving the initial radiation detected in the x-ray, optical and radio bands. After crossing the circumstellar envelope, it continues to interact with the interstellar medium (ISM), sweeping up ISM material, and producing objects with extended emission; these are identified as Supernova Remnants (SNRs). When the mass of material swept up by this expanding blast wave becomes much greater than the ejected mass and the age of the SNR is comparable to the radiative cooling time, the shock wave decelerates, increasing the compression ratios by a large amount and setting up instabilities. Re-accelerated electrons in a thin shell, moving in the presence of a compressed (and hence amplified) magnetic field, produce non-thermal (synchrotron) radiation with a negative spectral index α (S ∝ ν^{α}) which can be detected for up to ∼ few ×10^{4} years.

The circumstellar environment of the progenitor star and the properties of the local ISM produce varied SNR morphologies. Morphological studies of a large number of SNRs have allowed their classification into various categories essentially based on the radio morphology. About 80% of the known SNRs show a shell-type morphology. Other morphologies include flat spectrum filled-center (or ‘crab-like’), composite, barrel-shaped, and bi-annular.

Galactic objects have usually been identified as candidate SNRs based on morphological evidence and the lack of thermal emission (excess over the expected synchrotron emission at high frequencies). Extended emission with no associated thermal component, and showing one of the typical SNR morphologies, would be considered to be a good candidate SNR. However, reliable deciphering of the morphology requires observations with angular resolution several times higher than the extent of the emission. Further, morphological evidence alone is often insufficient for an unambiguous identification of Galactic objects as SNRs. Detection of a negative spectral index, which indicates the presence of non-thermal emission, is also used in combination with morphological evidence to identify SNRs. This, of course, requires multi-frequency observations, especially at low frequencies, to provide clear evidence of the presence or absence of an SNR. Morphology and non-thermal emission are thus the primary signatures used for the identification of SNRs in the galaxy.

Apart from providing the crucial primary morphological signature for the identification of SNRs, high resolution observations of such objects also provide valuable information about the ISM. Morphology of a given class of SNRs is believed to be the result of a similar circumstellar and ISM environment. Detailed morphological studies of SNRs therefore provide information about the local ISM and the progenitor star. With SNRs distributed all over the Galaxy, such studies provide information about the large scale distribution and structure of the ISM. Angular resolutions better than ∼ 1 arcmin are often necessary to decipher the morphology of typical SNRs and a spatially separate SNRs from other sources of extended emission in the Galaxy, as well as to study their interaction with the ISM, .

Measurements of continuum radio spectra also provide other valuable information about SNRs. The shape of the continuum spectrum (and the spectral index) is also an indirect measure of the spectrum of relativistic electron energies. Simple Fermi shock acceleration theory predicts a spectral index of −0.5. While this is consistent with the spectral indices of many shell-type SNRs, substantially higher values of the spectral index have also been seen in a few SNRs (it should be noted that reliable measurements of spectral index exist only for a small number of SNRs). Models invoking self-consistent non-linear shock models of first-order Fermi acceleration can account for higher values of spectral index, but require reliable determination of the shape of the spectrum, particularly at low radio frequencies. However, for about 35% of the SNRs in current SNR catalogues, the spectral index is poorly determined or, in some cases, completely unknown. The quality of the low frequency observations in the past has also been poor due to the lower resolutions and sensitivities of various low frequency telescopes up to the present time.

To meet the dual requirements of high resolution and sensitivity for extended nonthermal emission, many Galactic plane observations have, till recently, been done using single dish telescopes at 2 − 5 GHz with a resolution of 2 − 4 arcmin. However, at a resolution of a several arcmin, these observations are insufficient for detailed morphological studies of the SNRs. Single dish observations at these high frequencies also suffer from the problem of confusing extended thermal emission, abundantly present in the Galaxy. High resolution observations of SNRs at a number of frequencies below ∼ 1 GHz, to reliably determine the spectrum and morphology, are therefore crucial for correct identification and morphological studies, as well as for studies of the effects of the interaction with the ISM and radiation mechanism in the SNR shells.

This dissertation contains work done towards a low frequency study of Galactic SNRs using the GMRT at a frequency of 327 MHz. The sensitivity of the GMRT to large angular scales with high resolution offers a crucial advantage in mapping the Galactic plane where the emission field is usually very complex. These features of the GMRT were exploited to study a sample of nine fields containing new candidate Galactic SNRs in the southern part of the Galactic plane at 327 MHz. This sample of fields was chosen from recent surveys done using the Molonglo Synthesis Telescope (MOST) at 843 MHz and the Parkes 64m dish at 2.4 GHz (note that the two surveys had no overlapping fields of view). The RMS noise of these survey observations was typically ∼ 20 mJy/beam. Further, many of these fields are in complicated regions with strong extended emission from other sources. Substantial thermal emission at these high frequencies as well as confusing emission from nearby strong sources severely limited the image fidelity. Finally, with information available only at single frequencies for most of the objects in this sample, their identification has remained inconclusive until the present work.

Full synthesis GMRT observations were carried out at 327 MHz for this sample of fields. These observations constitute the most sensitive and highest resolution images of these fields. Our observations confirmed most of these candidates as SNRs. Six fields show well resolved shell-type and two fields show barrel-shaped objects with non-thermal emission. IRAS 60–μm images of all these fields were also examined to look for any associated thermal emission. In one of the fields designated as G004.2 + 0.0, significant thermal emission was detected. Radio flux density at 327 MHz is consistent with a flat spectrum source suggesting that it may be a compact thermal source.

Apart from the target SNRs in the fields, images of all the nine fields provide useful information about many other objects in the field of view. The 327 MHz images, each with a field of view of ∼ 1.4^{∘}, reveal a number of compact as well as extended sources of emission. Flux densities of the compact sources were measured at 327 MHz from the GMRT images and at 1420 MHz from the literature. The extended emission in one of the fields coincides with the location of previously identified as Ultra Compact HII (UC H II) regions. Recently, extended emission has been detected around many UC H II and the extended emission seen in this image may have the same origin. However, the true nature of the extended emission and the mechanism to sustain extended emission at such large scales to such low frequencies is not yet well understood. Similarly, the linear structure seen in another field is not clear. Such linear structures have been reported earlier as well. High resolution observations at other frequencies will be necessary for further study and to determine the nature of such objects.

Another compact source, G003.6 − 0.1, classified as an HII region from earlier higher frequency observations, showed significant structure and emission at 327 MHz. The GMRT observations reveal a shell-type morphology. Images at 5 GHz (from data acquired from the VLA archives) and 1.4 GHz (from the literature), at comparable resolution, provide resolved images of this object at these frequencies; two compact sources can be identified in these images, with extended emission around them. The spectrum of the extended emission is found to be non-thermal while emission from a strong compact source in the region shows a thermal signature. The current data on these components suggest that one of the components may be a radio star with a spectral index of ∼ 0.5. The cometary morphology of the extended emission is similar to that seen in high resolution images of a number of UC H IIregions.

HI absorption profiles against Galactic objects provide information about the intervening ISM. These can be used to estimate distances to the objects using models for the distribution and velocity of the Galactic ISM. HI distance estimates for three morphologically distinct components in the above field were obtained from GMRT 1420 MHz HI absorption observations against these components.

The usefulness of observations such as the ones presented in this dissertation and future directions of research in this area are also discussed. This dissertation is expected to be the first step in a longer term campaign for a Galactic plane survey at a number of GMRT frequency bands. Such a survey will be very useful in the identification of new SNRs. Current SNR catalogues are known to be incomplete for small sized SNRs. Such a survey will separate thermal and non-thermal radiation effectively and allow the identification of compact, SNRs in the Galaxy.

The GMRT has only recently come to a stage where enough antennas are available in the interferometric mode to attempt the imaging of extended sources. A substantial fraction of the work done for this dissertation involved the debugging and calibration of the telescope, to enable the observations discussed above to be carried out. Further, large amounts of software were required to be written, both to carry out debugging activity as well as to enable flagging and calibration of telescope data in a semi-automated fashion. This aspect of the thesis work is discussed below.

Monitoring the data quality, the health of the system using the complex visibility function measured by an interferometer like the GMRT, identifying sources of data corruption, general debugging of the instrument, etc. all require sophisticated and efficient software for data analysis, browsing, and display. Extensive software was developed for this purpose in the form of general purpose object oriented libraries as well as programs for on-line and off-line data processing and display.

This GMRT data analysis software system was developed with the longer term goal of providing a software environment which could be used by other users of the telescope, as well for developing new data analysis and calibration techniques. A general purpose user interface library was also developed to make the application programs user-friendly. Using these libraries, programs for data editing, semi-automatic data flagging, on-line monitoring of the data, computation for antenna-based complex gains, amplitude and phase calibration, etc. were also developed. All this software was extensively used during the course of this dissertation. These libraries and programs have also been used by other researchers in the group, both to develop new software as well as for data analysis purposes.

For the purpose of imaging, it is necessary to measure the precise location of the antennas on the ground to an accuracy of a fraction of the wavelength. Further, one must also measure the time delay suffered by the signals from various antennas. The software discussed in the preceding paragraph was extensively used for the calibration of various instrumental parameters, including antenna positions and time delays. These measurements were used in a program for off-line phasing in the initial stages of this work and are now used for the on-line phasing of the telescope.

The complex visibility function, V, depends on a number of telescope parameters like the system temperature, sensitivity, antenna fixed delays, antenna positions, etc. During debugging, it was frequently required to view this data in various representations (e.g., Cartesian versus polar representation of complex numbers). Since the complex visibilities are a function of a multitude of parameters, and different debugging purposes require viewing V with respect to various quantities, it was necessary to develop a compact macro language parser to extract and display the data in a flexible and programmable manner.

Inteferometry at low frequencies poses new challenges in data calibration and analysis, which are interesting in their own right. Mapping here requires the use of different (and computationally intensive algorithms), compared to those used for mapping at higher frequencies. These algorithms are discussed in detail in this dissertation. Further, the volume of data for a typical GMRT observation is exceedingly large with varied sources of data corruption. Manual identification and flagging of bad data is therefore tedious, time consuming and fraught with human errors. During the course of this dissertation, procedures were evolved for the editing, calibration and mapping of low frequency data. New algorithms were developed to identify and flag bad data in a semi-automatic fashion. These algorithms were extensively used for the data analysis, substantially reducing the time required for data editing, as well as improving the quality of the edited data used for mapping purposes. These procedures and algorithms for the analysis of GMRT data, for the purpose of continuum imaging studies, are also discussed in this dissertation.

Algorithms for phase calibration, available in standard data reduction packages, are very sensitive to the presence of severely corrupted data. The problem of computation of antenna-based complex gains was formulated using complex calculus and the algorithm implemented as a general purpose program. This allowed insights into the working of this algorithm, and enabled devising of the variants which are robust in the presence of bad data. This was done by (1) automatically eliminating out-lying points, (2) doing two passes to eliminate dead/bad antennas. This algorithm was also used to identify and flag corrupted data in a semi-automatic fashion. It was extensively used for measuring antenna pointing offsets, on-line monitoring of the instrumental phase, closure errors in the telescope, as well as for antenna position and time delay calibration.

Techniques used to minimize polarization leakage in the system have not yet been realized for the GMRT. This leakage is a significant source of noise at 150 MHz and also contributes noise at all other bands, albeit at a lower level. An algorithm was developed to measure the leakage using only the co-polar visibilities currently produced by the GMRT correlator. This work also enabled us to understand the various sources of non-antenna based errors; this technique can now be used for better calibration of GMRT data.

New and robust algorithms for automatic data editing and better calibration are necessary for the analysis of data from any large scale observational project at low frequencies (such as the suggested multi-frequency Galactic plane survey). New software for on-line data monitoring and display as well as for generating flagging information during observations is also required to improve the data quality. Further, algorithms and associated software are also crucially necessary to detect RFI and possibly eliminate RFI affected data. Possibilities of future research in these directions is also discussed in this dissertation. xxii ABSTRACT

Chapter 1

Introduction

Towards the end of their evolution, stars with masses greater than about 8M_{⊙} explode, producing one of the most energetic observable events in our Galaxy and external galaxies. The generally accepted sequence of events leading to this outcome is as follows. A star is said to have formed when a self-gravitating cloud of gas (mostly hydrogen) collapses under its own gravity to densities and temperatures at which, hydrogen burning begins. Under the action of gravity, the centre gets denser and hotter resulting into a well defined series of nuclear reactions. These reactions, starting from hydrogen burning and going all the way to the formation of iron, start at the centre and feed on the products of earlier reactions, which continue to occur further out. With time, a series of concentric shells are formed around the core, consisting of various elements produced in the these reactions. This model is usually referred to as the “onion-skin model” with a core of iron surrounded by shells of lighter elements with the outer most shell consisting of hydrogen (and possibly some He, Ne, O, N and C). Simulations show that, depending upon the initial masses, some stars complete the full sequence of nuclear reactions while for others this sequence is interrupted (??, and references therein). Single stars with initial masses greater than about 8M_{⊙}, explode producing Type II supernovae (SNe) which are characterized by the presence of hydrogen lines in their spectra and are usually found in the spiral arms for spiral galaxies. Type I SNe on the other hand are produced due to a white dwarf reaching the critical mass due to accretion from a companion star in a binary system. These SNe are devoid of hydrogen lines in their spectra and occur in all types of galaxies. The star is completely disrupted in the case of Type I SNe and no compact core remains (?). The central part of the iron core in Type II SNe, however, is compressed to nuclear densities and is left behind as a spinning degenerate neutron star, which is, in some cases, detected as a pulsar.

After the core collapse, the rest of the material which is still in-falling, rebounds (since the neutron core cannot be further compressed) creating a powerful shock wave which ploughs though the the outer layers of the star and finally emerges out of the circumstellar material. The core collapse releases 10^{53} erg of gravitational energy in the form of neutrinos which, along with the blast wave, couple with the outer layers and eject them at high speeds. The explosion in both types of SNe releases ∼ 10^{51} erg of kinetic energy, which produces a shock wave travelling outwards. The cores of massive stars with initial masses in the range of 18 − 30M_{⊙} can also first explode as SNe and then collapse into low mass black holes (?). In such an event, a heavy star collapses into a black hole without returning matter to the galaxy. The empirical value of ΔY/ΔZ (the relative helium to metal enrichment) implies a maximum mass of the star, after which the nucleosynthesis must cut off (i.e., stars more massive than this limit cannot contribute higher metals to the galaxy). This maximum mass limit derived from the value of ΔY/ΔZ and that derived from the computation by ? are in good agreement.

The interaction of the above shock wave with the in-falling circumstellar material produces the initial radiation, which announces the onset of the explosive event to observers on Earth. The shape of the initial optical light curve and the spectra at the peak of optical emission can be used to differentiate between the Type I and Type II SNe (?). Type-I SNe are characterized by the absence of hydrogen lines in their peak optical spectra while Type-II exhibit hydrogen lines in their spectra. Based on further finer details of the light curve, SNe are further sub-divided into Type Ia, Ib, II-L (linear) and II-P (plateau). However, initial radio emission has been detected from Type-Ia SNe. The optical light curve of Type II-L decreases monotonically in intensity after reaching a peak value while that of Type II-P, on the other hand goes through a flat plateau before starting to decay further. The peak absolute blue magnitude of Type Ia SNe has been found to be remarkably constant for different events; these can hence be used as ideal standard candles in the universe. Hubble constant can therefore be derived from the observations of extragalactic Type Ia SNe light curves. It is this property of Type Ia SNe which is responsible for the currently thriving industry of Supernova Cosmology (?, and references therein).

Typically, radio emission is first detected at higher frequencies, and later, at successively lower frequencies due to changes in the optical depth for external free-free absorption (?). A typical example of radio light curve for a Type II-L SN is shown in Fig. ??. The shape and spectral behavior of this initial radio light curve is thought to be typical of the class. Radio emission is detected significantly after the optical light is detected. The spectral Figure 1.1: Initial radio light curves at 6 and 20 cm of a Type II-L SNe SN1980k taken from ?. Such light curves are thought to be typical of the class. The data points marked by crosses and filled circles are measured flux densities while the solid curves are the best fit theoretical curves. Emission at 6 cm starts and peaks earlier than at 20 cm. The emission initially increases rapidly, reaches a maximum value and then monotonically decays at both the frequencies.

index α (S_{ν} ∝ ν^{α}) evolves from a value of ∼ 1 to a relatively constant value of ∼ −0.7 when the emitting region becomes optically thin for radio photons (Fig. ??). Observations of SN1983N, a Type Ib SN, on the other hand, exhibited a far more rapid rise as well as decay in the flux density compared to that of Type II-L SN. This difference in the radio light curves of the two types have been interpreted as being due to significant differences between the environments of Type Ib and II-L SNe.

After the blast wave crosses the denser circumstellar envelope into the more tenuous interstellar medium (ISM), this initial radio emission ultimately dies down, over time scales of several weeks for Type I SNe to many years for Type II SNe. The evolution of the blast wave as it ploughs though the ISM can be roughly described in four distinct stages (?). This interaction of the blast wave with the ISM, at much later times, produces sources of synchrotron emission in the sky, called Supernova Remnants (SNRs). SNRs are visible at radio bands (and at optical and X-ray bands in regions where the obscuration by the Galactic plane is relatively low) for up to ∼ 10^{4} − 10^{6} years after the initial explosion. This dissertation is concerned with the observations of such Galactic SNRs at low radio frequencies.

Figure 1.2: Spectral index evolution between 6 and 20 cm for a Type II-L SNe SN1979c taken from ?. The solid curve corresponds the best fit curve derived from the flux densities measured at these wavelengths.

1.1 Synchrotron Radiation

A relativistic electron moving at a velocity v in the presence of magnetic field of strength B, moves in a helical path around the field line, and consequently emits synchrotron radiation (??, and references therein). A brief description of the synchrotron emission mechanism and the results which follow is taken from ?. If the angle between the v and B vectors (the pitch angle) is θ and the total energy of the electron is E = γmc^{2} where γ = 1/(1−v^{2}/c^{2})^{1/2} is the Lorentz factor, the frequency of gyration around the field lines is given by

ν_{g} = \frac{eB_{⊥}}{2πγmc} = \frac{ν_{∘}}{γ}  (1.1)

where B_{⊥} = B sin θ is the component of the magnetic field perpendicular to the electron path and ν_{∘} is the non-relativistic electron gyro-frequency. Due to relativistic effects, the radiation will be emitted in a narrow cone of half-angle of the order of 1/γ. In general, a detector will detect pulses of radiation from such a system every time the the cone of emission crosses the detector’s line of sight and the pulse shape will be defined by a cut across the cone of emission. The frequency of the pulses as seen by the detector will be the Doppler shifted gyration frequency given by

ν′_{g} ∼ \frac{ν_{g}}{sin^{2} θ}  (1.2)

while the pulse width is

Δt ∼ \frac{1}{2πν_{g}γ^{3}}  (1.3)

Since the width of the individual pulses will be narrow (at least for large values of γ), most of the emitted energy will be in harmonics of the fundamental frequency given by (2πΔt)^{−1} ∼ ν_{g}γ^{3}. For ultra-relativistic electron, these harmonics will be closely spaced and the resulting spectrum is essentially a continuum. The critical frequency at which the emission is maximum is given by

ν_{c} = \frac{3}{2}γ^{2}ν_{∘} = 16.08 × 10^{6}B_{⊥}E^{2} MHz  (1.4)

where E is the electron energy in GeV and B_{⊥} in gauss. The rate of loss of energy by the electron due to synchrotron radiation is given by

\frac{dE}{dt} = −119.7B_{⊥}^{2}E^{2} GeV/yr  (1.5)

This basic equation says that the most energetic electrons will lose energy at the fastest rate. With time, a high energy electron will lose energy and radiate for longer as a lower energy electron. For an ensemble of electrons with some initial energy distribution, with time time, more electrons will pile up at the lower energy end of the energy spectrum. This produces observable changes in the properties of the emission with time. This effect goes by the name of “ageing” in the literature.

For a homogeneous and isotropic ensemble of electrons with energy density distribution N(E)dE, the total intensity will be given by

I(ν) = ∫_{0}^{∞}N(E)P (ν)dE  (1.6)

where P (ν) is the spectrum of the electron with energy in the range between E and E +dE. For a power law energy spectrum given by N(E)dE = N_{∘}E^{−p}dE in a limited range E_{1} < E < E_{2}, I(ν) is given by

I(ν) = \frac{\sqrt{3}e^{3}L}{8πmc^{2}} (\frac{3e}{4πm^{3}c^{5}} )^{(p−1)/2} N_{∘}B_{⊥}^{(p+1)/2}ν^{(1−p)/2}a(p)  (1.7)

where a(p) is a slowly varying function of p and L is the spatial extent of the region with uniform magnetic field B. Clearly, for a power law distribution of initial energies, I(ν) ∝ ν^{α} where α is the spectral index and is related to p as α = (1 − p)/2. p is usually greater than unity; a negative spectral index is thus observational evidence for synchrotron emission.

Emission from a single electron will clearly be elliptically polarized with the electric field vector perpendicular to the projected magnetic field vector. However, for an ensemble of electrons with a random distribution of pitch angles, the observed radiation will be partially linearly polarized with the degree of polarization in a uniform magnetic field given by

Π = \frac{p + 1}{p + 7/3}  (1.8)

Linear polarization and a negative spectral index are the two defining characteristics used to identify sources of synchrotron emission, although either is usually sufficient to identify the emission mechanism. Radiation can however be depolarized due to a variety of reasons ranging from random orientations of the magnetic field vectors within the resolution element of the telescope or thermal material along the line of sight to Faraday rotation in the Earth’s ionosphere. Depolarization scales as λ^{2} and consequently measurement of polarization at low frequencies is usually difficult. Hence, while detection of linearly polarized emission is a strong proof of synchrotron emission, a lack of it cannot rule it out. A negative spectral index is therefore frequently used as a signature of synchrotron radiation.

1.2 Galactic Supernova Remnants

A large number of SNRs are radio sources with only less than 30% visible in optical and X-ray bands. The lack of optical and X-ray radiation is primarily due to obscuration by the Galactic disk. Out of the 225 Galactic SNRs listed in the catalogue of Galactic SNRs (?), about 80% are of shell-type morphology (see Section ??) with a median size of ∼ 30 arcmin. The emission is polarized (fractional polarization at 5 − 10% level for the shell-type SNRs and much higher for filled centre SNRs) with a negative spectral index and is therefore believed to be synchrotron radiation. These gross observed radio properties of the radio emission from SNRs can be understood by modeling the shock wave as a spherical supersonic piston propagating in a uniform medium (the ISM) sweeping up the ISM mass as it moves. Its evolution is described as four distinct stages (?, and references therein):

• Free expansion phase In this stage of the evolution, the ejected mass M_{∘} is much more than the mass sweptup by the shock front, i.e. M_{∘} ≫ 4πR_{s}^{3}ρ_{1}/3 where R_{s} is the shock radius and ρ_{1} the pre-shock density. The influence of the ISM on the dynamics of the ejecta in this stage is negligible and the initial properties of the explosion dominate the evolution. Consequently the blast wave freely expands into the medium.

• Sedov phase With time, the shock front sweeps up the ISM material and enters this phase when the swept-up ISM mass is comparable to that of the ejected mass. The shock is still strong and the pressure due to the swept-up mass is negligible. The expansion is essentially adiabatic (which is the other name this phase goes by) and the dynamical evolution is given by ? solution for the dynamics of a point explosion in a uniform medium. For a gas with the ratio of specific heats of 5/3, the shock radius and velocity (v_{s}) are given by

R_{s} = 1.17 (\frac{E_{∘}}{ρ_{1}} )^{1/5} t^{2/5}  (1.9)

v_{s} = 0.4R_{s}/t  (1.10)

where E_{∘} is the supernova energy. The ejecta begin to decelerate in this phase and a reverse shock develops which propagates into the ejecta, thus thermalizing it. The reverse shock propagating into the circumstellar material is thought to be responsible for the observed X-ray emission.

• Radiative phase Once the age of the remnant becomes comparable to the radiative cooling time scales near the shock, the blast wave enters the radiative phase. The deceleration becomes rapid and the shock compression becomes large. By this time, the dynamics and the resulting observed morphologies are significantly affected by the structure of the ISM, particularly the inhomogeneity of the ISM.

The time at which this phase begins and the shock velocity at this time is given by

t = 3.5 × 10^{4} (\frac{E_{∘}}{10^{51} erg}) n_{1}^{−9/17} yr  (1.11)

v = 230n_{1}^{2/17} (\frac{E_{∘}}{10^{51} erg})^{1/17} km s^{−1}  (1.12)

where n_{1} is the pre-shock number density.

• Dissipative phase Once the expansion velocity of the shock decreases below the local sound speed, it dissipates and merges with the ISM on time scales of 10^{5} − 10^{6} years.

This simple model of a shock wave propagating in a uniform medium, however, ignores a number of other effects such as dynamical effects of the magnetic field, pressure forces in the radiative phase and inhomogeneities in the ISM (?). Hydrodynamic calculations show that SNe produce ejecta with a uniform density towards the outer parts while the inner parts (close to the star) have a steep density profile (like ρ ∝ r^{−7}). A reasonable density profile for Type I SNe has a constant density ejecta for the inner four-sevenths of the mass, and the outer three-sevenths obeying ρ ∝ r^{−7}. Numerical simulations for Type I SNe with such a density profile modified the evolution of the shock radius to R_{s} ∝ t^{4/7} when the Sedov phase is reached, which is closer to the observed value of the exponent (e.g. for Tycho and SN 1006).

1.2.1 Nonthermal Emission from SNRs

As mentioned earlier, radio emission from SNRs is believed to be synchrotron radiation which requires understanding of the origin of the relativistic electrons and magnetic field. Broadly, the central pulsar is thought to be the source of both these quantities for Crab-like SNRs (see Section ??), while, for shell-type SNRs, both come from the ambient ISM. The inferred magnetic fields in SNRs, measured from the rotation measure measurements of background radio sources, X-ray observations and Zeeman splitting of OH maser lines (?), is however ∼ 2 − 3 order of magnitude higher than the ambient magnetic field, requiring magnetic field amplification mechanisms as well. Although it is easy to imagine amplification of the frozen-in magnetic field in the SNR shells, the observed brightness of young shell-type SNRs is often more than can be explained by magnetic field amplification due to compression by the shock alone (although, magnetic field strengths measured for a few SNRs using the Zeeman splitting of OH (1720 MHz) lines are consistent with the hypothesis that ambient molecular cloud magnetic fields are compressed via the SNR shock to the observed values (?)). The observationally deduced magnetic field for Cas A is far too high to be explained by magnetic field amplification by compression by a factor 4 compression. Similarly, the deduced magnetic field for the shell-type Kepler’s SNR (?) is too high to be produced by the amplification of the ambient field in the shock front. It is therefore believed that for shell-type SNRs, a combination of particle acceleration in the shock front (??) and magnetic field amplification as well as particle acceleration behind the shock (??) are responsible for the observed radio brightness. On the other hand, the observed properties and the evolution of Crab-type SNRs are believed to be dominated by rotational energy loss from the central pulsar (?).

Two classes of electron acceleration mechanisms have been used: turbulent acceleration at the unstable contact discontinuity and acceleration in the shock front itself. The first mechanism uses “second-order Fermi acceleration” and explains the morphology and emission from SNRs like Cas A. The latter mechanism uses the more efficient “first-order Fermi acceleration”. This has the added advantage that the inferred electron energy spectra is naturally a power law and explains the morphology and the spectra of typical shell-type SNRs (?). Mechanisms for magnetic field amplification are however far less well understood. Magnetic fields measured in a few SNRs are much too high to be explained by compression alone. Observed magnetic fields which are predominantly radial in young SNRs (?) also argue against the amplified field being the swept-up ambient field. Magnetic field amplification in the Rayleigh-Taylor instability due to the deceleration of the ejecta (???), is an attractive model, especially for clumpy ejecta and/or circulstellar medium in the sense that it can explain the mostly radial orientation of the magnetic field in the SNR shells. Their simulation also shows that such magnetic field amplification is dependent on the orientation of the field and can produce morphologies similar to those of “barrel-shaped” SNRs.

1.2.2 Continuum Radio Spectra

Although the details of the particle acceleration and magnetic field amplification mechanism are still not well understood, it is clear from the observed data that the radio emission from SNRs is synchrotron radiation. Radio emission from SNRs above ∼ 100 MHz has a non-thermal spectrum (Equation ??) and significant linear polarization (5 − 10% for shell-type SNRs and up to 30% for filled centre SNRs). Both these gross properties are considered to be defining properties of synchrotron emission. Integrated continuum radio spectra are therefore the primary signatures used to identify SNRs. As is also obvious, SNRs also produce sources of extended emission. Radio SNRs are classified into roughly four categories (see Section ??) based on the radio morphology. Radio morphology also provides information about the SNR type, its interaction with the ambient ISM as well as with the ambient magnetic field (?). Candidate SNRs are therefore often identified from single frequency observations based on the morphological evidence. However, H II regions in the Galaxy also exhibit extended radio emission easily detected at higher frequencies and, in some cases even exhibit morphologies similar to those of SNRs. Identifications of SNRs based on a single high frequency observation are therefore unreliable; observations at at least two frequencies are therefore usually required for proper identification of extended radio sources, to get a handle on the spectral index. Non-detection of thermal infrared emission, and where possible, lack of radio recombination lines (RRLs) are also used as supporting evidences to distinguish synchrotron sources from sources of thermal emission. However, RRL observations in the Galaxy are usually at coarse resolution and have a patchy coverage of the Galactic plane. High frequency observations in the Galactic plane also suffer from contaminating thermal emission (see Section ??), which has a relatively flat spectrum above ∼ 1 GHz. Below this frequency, typical thermal emission strongly turns over due to free-free absorption. Synchrotron emission on the other hand, has a negative spectral index for a large range of frequencies. As a result, the emission from SNRs is usually stronger at lower frequencies while the thermal emission is severely diminished. For these reasons, high resolution observations at low frequencies where the non-thermal emission is stronger than the thermal emission can identify SNRs unambiguously and also measure spatially resolved brightness variations. The latter provide crucial information about the interaction of the blast wave with the ISM as well about particle acceleration/magnetic field amplification.

The spectral index depends on the kinetic energy input mechanism (e.g. turbulence in the shells of shell-type SNRs and the central pulsar in Crab-type SNRs), localized particle acceleration mechanisms (e.g. interaction of the shock front with higher density ISM) and the properties of the intervening ISM (e.g. differential free-free absorption across SNRs). About 80% of the known Galactic SNRs are of shell-type (?) and exhibit a broad range of spectral indices (−0.2 < α < −0.8) with a mean value of ∼ −0.5. This implies a mean electron energy spectrum ∝ E^{−2}, close to what is expected from theoretical models for acceleration in strong shocks. Implied electron energy spectra corresponding to the lower range of α are explained by attributing them to weaker shocks while those corresponding to the higher range require the inclusion of non-linear effects. Data also suggests a trend in the spectral index with the remnant age (i.e. with diameter). Smaller diameter SNRs, considered to be younger, have α < −0.5 while older, larger diameter SNRs have flatter spectra. However it must also be kept in mind that the measured diameter is subject to (often large) errors in the distance estimate. Even if the distance is well known, the diameter of the SNR can be strongly influenced by the properties of the progenitor star and the local ISM and the inferred age may be quite different from the true age. Spectral indices for most SNRs have been obtained from measurements carried out with a variety of telescopes and techniques, resulting into uncertainties in flux density scales. As a result, the spectral indices are seldom known to accuracies better than ∼ 0.1.

Measurements of spatial and/or temporal variations in the radio spectra of SNRs are probably the best way to study the nature of electron acceleration mechanisms. Spatial spectral variations provide information about the local dynamics and require spatially resolved observations at at least at two frequencies. High resolution observations are usually done using interferometric telescopes. However, the set of the spatial frequencies measured by such instruments with fixed physical separation between the antennas are a function of the observing frequency. As a result the spatial frequencies sampled at two different frequencies are in general different and dividing the two images at different frequencies to obtain spectral index maps produces artifacts. In telescopes like the Very Large Array (VLA) this problem is solved by scaling the array in proportion to the observing frequency, but for most other interferometric telescopes, this remains a problem. Observations with interferometric telescopes also suffer from missing larger scale emission which in turn result into differences in flux density base-level. Similarly, single dish observations also suffer from base-level problems due to very large scale background emission within the field of view of the telescope. To minimize the errors in the measurement of spectral index due to these effects, ? used the so called “T-T plot” to measure the local gradient in the maps at two frequencies. This method is insensitive to large scale base-level variations in the two maps and gives a more reliable spatially resolved spectral index measurement. They find a spatial variation from −0.7 to −0.4 across a few, hopefully representative, SNRs. More recently ? used the method of spectral tomography to measure spectral variations within Tycho’s SNR. They identified a number of filaments with spectral index different from that of the smoother background. The filaments in the outer rim show a trend such that brighter filaments have a flatter spectral index which could be due to the interaction of the blast wave with a inhomogeneous ambient medium or due to inhomogeneities in the magnetic field.

Absorption by the low density ionized medium

Figure 1.3: Plot showing a typical continuum spectra for Galactic SNRs. The spectral index at frequencies > 100 MHz is clearly non-thermal. Below this frequency, the flux density decreases due to free-free absorption in the intervening low density ISM.

In their classic papers on the measurement of low-frequency continuum spectra of Galactic supernova remnants, ? reported spectral turnovers in several SNRs in the galactic plane at low frequencies. Such a turnover in the spectra of SNRs has since been confirmed by more extensive measurements at ∼ 31 MHz (?). The spectral index above ∼ 100 MHz is negative and is typical of most SNRs (Fig.??^{1}). The spectra however turns-over below this frequency due to absorption by low density ionized gas in the intervening ISM (?). The observed flux density at a frequency ν in the presence of absorbing foreground medium of free-free optical depth τ_{ν_{∘}} at a reference frequency ν_{∘} can be written as

I(ν) = I(ν_{∘}) (\frac{ν}{ν_{∘}} )^{α} e^{−τ_{ν∘}( \frac{ν}{ν∘} )^{−2.1}}  (1.13)

where I(ν) is in Jansky and the frequency ν is in MHz. τ_{ν_{∘}} is related to the emission measure EM(cm^{−6} pc^{−1}), and the electron temperature T_{e}(K) (?) by

τ_{ν} = 1.643 × 10^{5}a (T_{e}, ν) (ν^{−2.1}) (EM T_{e}^{−1.35})  (1.14)

1Taken from the catalogue of Galactic SNR spectra compiled by S. A. Trushkin and available on the web from http://www.ratan.sao.ru/_{}˜ cats

where a(T_{e}, ν) is the Gaunt factor, ∼ 1 for the relevant range of T_{e} and ν. The emission measure EM is defined as

EM = ∫_{L} n_{e}^{2}dl  (1.15)

where n_{e} is the thermal electron density in cm^{−3} and the L is the path length to the source in parsec. With an estimate of the distance to an SNR and assuming that the spectral index is same at the range of frequencies under consideration, these equations can be used to estimate the properties of the absorbing gas, namely τ_{ν} and n_{e}. The absence of a low frequency turn over towards distant SNRs places severe constraints on the thermal electron density of any widely distributed ionized medium: n_{e} ≤ 0.26 cm^{−3} for T_{e} = 8000 K and n_{e} ≤ 0.13 cm^{−3} for T_{e} = 3000 K. If the absorbing gas is the warm ionized medium, the obtained parameters, using the optical depth derived from the study of low frequency spectral turn over and a path length of 100 pc are: n_{e} ∼ 2.9 cm^{−3} for T_{e} = 3000 K and n_{e} ∼ 5.7 cm^{−3} for T_{e} = 8000 K. The fact that some of the distant SNR do not show low frequency absorption while some of the closer ones do demonstrates that this medium is patchy and localized (?).

Evidence for the existence of a widespread low-density ionized component in the inner Galaxy has come from observations of radio recombination lines (RRLs) near 1400 MHz (???) and near 327 MHz (??). These RRLs have been detected at almost every observed position in the inner Galaxy (with b = 0^{∘} and |l| ≤ 60^{∘}) including those positions where there are no discrete radio continuum sources (i.e. blank regions). This is believed to be the extended H II region envelopes (EHEs) (?). The parameters of the gas derived from the RRL observations are T_{e} ∼ 2000 − 8000 K, n_{e} ∼ 0.5 − 10.0 cm^{−3}, with a filling factor of < 3%. Based on the statistics of spectral turnovers in a number of SNRs and the properties of the low-density envelopes derived using RRL data, ? has argued in favor of a connection between the RRL-gas and the free-free-absorbing gas towards SNRs. The optical depth towards a few SNRs inferred from the low frequency spectral turn over and that from RRL observations agree well with each other, lending support to this suggestion. On the theoretical front, ? considered the luminosity function of OB associations in the Galaxy and found that about 65% of the ionizing photons emitted by O and B stars are absorbed outside the known HII regions. About 10% of these photons are needed to maintain the Warm Ionized Medium (WIM). The majority of the escaping photons can thus generate large HII envelopes. These HII envelopes are thus a reservoir of more than 50% of the ionizing photons emitted by all the O and B stars. An understanding of the properties of this ionized component is thus important in the galactic context. However the evidence remains circumstantial. The resolution of the low frequency RRL observations was too coarse to localize the source of RRL emission. High resolution RRL observation towards SNRs which do show spatially resolved low frequency absorption will provide a direct test for this. The Giant Meterwave Radio Telescope (GMRT) offers the right range of frequencies, resolution and sensitivity for these observations and is an ideal instrument for such a study.

1.2.3 Thermal emission

Apart from non-thermal emission, the Galactic plane, particularly at low Galactic latitudes, is also a sources of significant radio emission with a thermal spectrum. This emission is from H II regions and planetary nebulae in the Galaxy and is caused by the interaction between free charged particles, referred to as free-free or thermal bremsstrahlung emission.

The observed intensity from an emitting region of linear size L with a foreground radiation intensity of I_{fg} and background intensity of I_{bg} is given by

I = I_{bg}e^{−τ} + ∫_{0}^{τ} \frac{j}{κ}e^{−t}dt + I_{fg}  (1.16)

where j and κ are the emission and absorption coefficients, and τ is the optical depth.

A charged particle moving in the electric field of another charged particle undergoes a change in its direction of motion. This change of direction requires acceleration and as a result the particle emits electromagnetic radiation. In a realistic situation, however, there is a distribution of particle velocities and the total radiation is determined by integrating the emission during one interaction over the velocity distribution. To compute this, it is assumed (1) that the electric field in which the particle is moving is effective only over a finite distance,

(2) that the radiated energy is small compared to the kinetic energy of the moving particle (i.e. the encounter is adiabatic) and (3) the period of the emitted wave is small compared to the duration of the encounter. For a Maxwellian velocity distribution, j(ν)/κ(ν) = B_{ν}(T_{e}) where B_{ν}(T_{e}) is the Plank function. For hν < kT_{e}, this can be approximated by B_{ν} ≈ 2kT_{e}/λ^{2} - the usual Rayleigh-Jeans approximation. For a source of homogeneous density and temperature with I_{fg} = 0, and using the Rayleigh-Jeans approximation, Equation ?? can be written as

I = I_{bg}e^{−τ} + \frac{2kT_{e}ν^{2}}{c^{2}} (1 − e^{−τ})  (1.17)

The flux density S at a frequency ν is defined as

S = ∫_{source} I_{ν}dΩ ≈ \frac{2kν^{2}}{c^{2}} ∫ T_{source}dΩ  (1.18)

where Ω is the angular extent of the source and T_{source} is the source electron temperature. Equation ?? can then be transformed to an equation for the observed integrated flux density, assuming I_{bg} = 0, as

S_{ν} = S(1 − e^{−τ})  (1.19)

In the high frequency, optically thin regime (τ ≪ 1), S_{ν} ≈ Sτ and, since τ ∝ ν^{−2.1} and S ∝ ν^{2}, S_{ν} ∝ ν^{−0.1}. Thus, the spectra at high frequencies is a weak function of the frequency. On the other hand, in the optically thick regime of low frequencies, S_{ν} = S ∝ ν^{2}. Hence the spectral indices for radiation above and below the critical turnover frequency (typically 1 − 2 GHz) are markedly different (−0.1 and 2 respectively, see Fig. ??).

From the point of view of radio study of SNRs, the important point to note is that thermal emission progressively diminishes at frequencies below ∼ 1 GHz while the non-thermal emission progressively becomes stronger in this range of frequencies. Strong emission from H II regions has been observed all along the Galactic plane. High frequency observations close to or above this frequency are more sensitive to thermal emission and not well suited to the study of SNRs which emit non-thermal radiation at radio bands. On the other hand, at lower frequencies, thermal emission is diminished while non-thermal emission from SNRs progressively becomes stronger (see Fig. ??). Low frequency observations, where the contamination from thermal emission is minimized, are therefore more suited for the study of SNRs.

As mentioned above, angular resolution is important from the point of view of SNR identification and other detailed studies (particle acceleration, interaction with the local ISM, brightness variation as a function of galactic latitude, etc.). Since emission in the galactic plane occurs at all angular scales, it is also important that the observations be sensitive to large scale emission. To meet the requirement of high angular resolution with sensitivity to large scale emission, many observations of SNRs have been done at high frequencies either single dish instruments (????) or using interferometric telescopes (????). However the uv-coverage of these interferometric observations was not good resulting into severe artifacts in the images. Also, these observations often suffer from contamination by thermal emission, particularly for fields in the Galactic plane.

The GMRT, operating at 150, 233, 327, 610 and 1400 MHz provides frequency coverage where, typically, non-thermal emission is dominant. With a shortest physical antenna separation of ∼ 100 m and largest separation of ∼ 25 km, it also provides high angular resolution at these low frequencies (∼ 20 arcsec to ∼ 2 arcsec) while remaining sensitive to emission at large angular scales (∼ 1^{∘} to ∼ 10 arcmin). With a large collecting area, GMRT offers many advantages for the study of Galactic non-thermal emission in general and SNRs in particular. High resolution multi-frequency mapping of the galactic plane will also make it possible to identify compact sources of non-thermal emission (possibly compact SNRs) which may be confused with compact thermal sources in high frequency observations.

1.2.4 Radio morphology

The gross morphology of SNRs is largely governed by (1) properties of the progenitor and the pre-supernova circumstellar environment and (2) properties of the local interstellar medium and magnetic field. Traditionally, Galactic SNRs are classified in four different categories namely (1) shell-type, (2) filled centre (or Crab-type), (3) composite and (4) barrel shaped. About 80% of the SNRs in the Galactic SNR catalogue compiled and maintained by ? exhibit what is referred to as the shell-type morphology. This is expected from the generic model of an isotropic blast wave ploughing though the ISM and producing a bubble of emission after it slows down, having gathered enough ISM mass at the shock front. In projection, the bubble appears as a ring or shell of emission. On the other hand Crab-type SNRs exhibit a nebula of flat spectrum emission and is believed to be powered by the central neutron star. Variations of these basic morphologies are produced either due to a difference in the progenitor or in the local interstellar environment. The observed properties of these classes of SNRs are also therefore characteristic of the class and are briefly described below.

• Shell-type

As mentioned above, 80% of the known Galactic SNRs are of this type. Typical examples are Kepler’s and Tycho’s SNR, SN 1006 (Fig. ??). These SNRs are characterized by a ring of emission which is often incomplete. As the blast wave decelerates, it enters the radiative phase of its evolution. The contact discontinuity between the shock front and the shocked medium is unstable and produces a thin shell of turbulence. The turbulence in the shell is believed to be the source of particle acceleration within the shell and magnetic field amplification by turbulent mixing (?). A reverse shock develops just behind the shell and moves into the out-flowing ejecta, heating it to sufficiently high temperatures to produce the observed X-ray emission (?).

Figure 1.4: Image of a typical Galactic Shell-type SNR SN 1006 (courtesy of ADIL; image code 98.BG.01.07). This 8-GHz image was made using the Molonglo Synthesis Radio Telescope (MOST). The brightened shell of emission with a weaker emission projected against the center is clearly seen.

The typical average spectral index α along the shell ranges from −0.7 to −0.3. In some of the sensitive images of shell-type SNRs, weak emission (from the bubble) is sometimes seen in projection, filling the interior of the ring. The spectral index of this emission and the ring is, however the same, indicating that this corresponds to the bubble of emission seen projected at the centre of the shell. Substantial variation in the brightness across the shell of emission is often seen and may be due to the inhomogeneity of the local ISM with which the shock front interacts. This also produces spectral index variations in some cases (?) indicating sites of enhanced particle acceleration or magnetic field amplification. The emission from the shell is linearly polarized at 5 − 15% level and the inferred projected magnetic field is usually radial.

• Filled centre/Crab-like/Plerionic These types of SNRs are characterized by a flat spectrum plerionic emission (α ≥ −0.3) almost uniformly filling the emission region. Less than 10% of the known Galactic SNRs are of this type. Strong linear polarization up to 30% level has been Figure 1.5: Image of a typical Galactic plerionic SNR - The Crab nebula (courtesy of ADIL; image code 95.RP.02.01). This 327-MHz image was made using the VLA and is copyrighted by the NRAO^{2}(Observer: R.P.Perley). The compact source in the centre is the Crab pulsar.

observed from such SNRs. A typical example of this class of SNRs, not surprisingly, is the Crab SNR (Fig. ??) or 3C58. ? modeled a plerion as a spherical, homogeneous bubble of relativistic particles and magnetic field inflated by a central neutron star amidst uniformly expanding supernova ejecta. The plerionic emission is believed to be driven by the rotational energy losses of the central neutron star, which is seen as a pulsar at the centre of the Crab nebula. The central neutron star is believed to be the source of the magnetic field as well as of the energy which accelerates the electron in the medium thereby maintaining the flat spectrum of the emission. With the advent of high resolution X-ray telescopes, many plerionic SNRs have been found to be strong X-ray sources where the X-ray emission comes from the central region.

The blast wave should however produce a shell of emission outside such a nebula where it interacts with the ISM. The existence of a high-velocity, hydrogen-rich envelope corresponding to the initial blast wave is also required to account for the low total mass and kinetic energy of the observed nebula. No shell of emission has however been detected for such SNRs - at least not at radio frequencies. A deep search for the shell around the Crab nebula did not reveal any shell emission and this has been interpreted as being due to the blast wave expanding into a low density medium (?). The spectral index of the plerionic emission for the Crab nebula is ∼ −0.26. If the shell is close to the edge of the nebula, it can be distinguished from the nebula by the change in the spectral index from this value to close to ∼ −0.5, typical for shock accelerated shell emission. No evidence for a significant change in the spectral index was found by these authors. Similarly no such shell has been found in Hα and Xray emission (??). However, HST observations reveal a thin shell of [OIII] emission around the nebula (?) which is interpreted as a cooling region behind a radiative shock propagating at ∼ 150 km s^{−1} in a medium of density ∼ 10 cm^{−3}. Ironically, the Crab SNR may then no more be of the “crab-type” but may be re-classified as of the composite class (see below).

2The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Such shells have also not been detected for other plerionic SNRs. If the tenuous environment in which these SNRs are expanding is the reason for non-detection of the shell in radio continuum emission, it has been suggested that one must look for signs of interaction with the surrounding atomic or molecular gas (?). 21-cm neutral hydrogen observations of G074.9+1.2 (CTB87), which is a pulsar powered SNR with no outer shell, shows that this SNR lies within an expanding HI bubble (?). The radio continuum emission also shows signs of flattening at a point of apparent contact between the HI bubble and the SNR, lending further support to this model. However evidence for a shell of emission around other plerionic SNRs like 3C58 remains elusive.

Compact radio quiet thermal X-ray sources within SNRs have also been found in a few remnants (???). These compact objects may be radio quiet neutron stars in the SNRs and may thus explain the embarrassing lack of pulsar-SNR associations (?) in the sense that a non-pulsar neutron star or radio-quiet pulsar may be associated with many SNRs. The recent discovery of X-ray pulsations from some of these compact sources (??) lend support to the idea that for these compact objects are indeed the elusive radio quiet neutron stars which are thought to be produced by the explosion and hence associated with the SNRs.

• Composite Figure 1.6: Image of a typical Galactic composite/mixed morphology SNR G000.9+0.1 taken from ?. The shell and plerionic emission is clearly visible. The central compact source coincides with a compact thermal X-ray source.

This class of SNRs exhibit characteristics of both shell-type and plerionic SNRs (Fig. ??). These SNRs are characterized by flat spectrum emission from the central region with a steeper spectrum shell of emission. Typical examples of this class of SNRs are G000.9+0.1, CTB80, G326.3−1.8.

With high resolution imaging now possible in the X-ray band, this class has grown to include what are referred to as “centrally influenced” remnants; e.g. objects with shock powered radio shells with centrally enhanced X-ray emission. The X-ray radiation can be in the form of hard X-ray non-thermal emission from a compact nebula and/or extended soft thermal X-ray emission. ? term SNRs with thermal X-ray emission inside hollow radio shells as “mixed morphology” SNRs. The X-ray emission is proposed to come from the evaporation of clouds (of pre-explosion origin) by the reflected and reverse shocks. Many of the thermal X-ray composite SNRs are interacting with molecular clouds (conclusions drawn from molecular line and OH maser observations, e.g. W44, 3C391, W28, IC443) (????) and it has been suggested that

this may be a generic property of the class.

• Barrel shaped

Figure 1.7: Image of a typical Galactic barrel-type G003.7−0.2 (?) (image courtesy of ADIL; image code 98.BG.01.01). This 1.4-GHz VLA image shows the double arc structure with an axis of symmetry running right through the middle of the two brightened arcs of emission.

These remnants are characterized by a clear axis of symmetry with lower emission along the axis in between two brighter limbs (???) (Fig. ??). Proposed explanations for such a morphology are either on the lines of “extrinsic” effects relating to the ambient ISM and magnetic field and “intrinsic” effects relating to the progenitor and its circumstellar medium. Such morphologies can be produced if the ejecta expands inside an elongated cavity (?). Alternatively, ejecta expanding in a uniform magnetic field will preferentially compress where the shock normal is perpendicular to the field lines producing enhanced emission where the magnetic field is more compressed (?). On the other hand, such morphologies can be produced due to intrinsic reasons like toroidal distribution of ejecta (?) or due to initial high velocity of the progenitor (?) or intrinsic preferentially polar outflows from the central compact object (??). Analysis of highly resolved images of 17 barrel shaped SNRs done by ? show evidence of a statistically significant tendency for the bilateral axes to be aligned with the Galactic plane. This is interpreted as lending support for the extrinsic effects being the dominant cause for the observed morphology - namely the alignment of the magnetic field with the Galactic plane.

1.2.5 Galactic distribution

Figure 1.8: Distribution of known Galactic SNRs as a function of Galactic longitude. Most of the known SNRs are in the 1st and 4th quadrants. The number of SNRs in the 4th quadrant are however slightly less than that in the 1st quadrant. Significant lack of SNRs in the 3rd and 2nd quadrants is attributed to lack of star forming regions there.

Fig. ?? shows the distribution of the known Galactic SNRs as a function of Galactic longitude. Most of the known Galactic SNRs are in the 1st or the 4th quadrant. This bias towards the inner Galaxy is attributed to the fact that most of the star forming regions are in the Galactic arms which cover a larger fraction of the inner Galaxy. However, there appears to be a mild lack of SNRs in the 4th quadrant compared to the 1st quadrant which is most likely to be due to some selection effect, probably due to the use of different telescopes in these quadrants (?????????).

The incompleteness of the current Galactic SNR catalogue has been pointed out by ?. He noted that the catalogue is incomplete in very large low surface brightness as well compact small sized young SNRs. Low surface brightness SNRs may be missed due to sensitivity limits of the observations. Higher frequency observations may also miss them because they are also inherently weaker at high frequencies. Such SNRs will also be missed in interferometric observations which are not sensitive to emission at angular scales larger than a maximum value. Small sized compact SNRs may be missing because of confusion with compact source of thermal emission. Any statistical result based on the current SNR catalogue is therefore likely to be affected by these selection biases. This is reflected in about a factor of 2 − 3 error in the distance estimates for SNRs using the statistically derived Σ-D relation. ? also argues that the proposed Σ-D-z relation is not statistically significant.

Statistical studies of a complete sample of Galactic SNRs can help answer many question about the remnants themselves, their parent supernovae, their relation to pulsars and their interactions with the ISM and the ambient magnetic field. Observations to remove, if possible, the above mentioned biases in current catalogues are therefore important from the point of view of Galactic SNR research.

1.3 Effects of the ISM on the observed properties of SNRs

Most of the emission from SNRs is due to the interaction of the blast wave with the material into which it expands (the circumstellar envelope or the ISM). Low frequency spectral turnover, pulsar dispersion measures, HI absorption and brightness variations across SNRs, in particular along the shells of the shell-type SNRs suggest that the environments into which SNR expand are non-uniform. This is, however, hardly surprising since the structure and energetics of the ISM is largely dominated by star forming regions and supernova explosions, both of which are localized compared to the extent of the Galaxy. These density variations in the ISM are in-turn also expected to shape the morphologies of the SNRs. Interaction of the blast wave with higher density regions will result in stronger deceleration resulting in higher turbulence. This produces larger particle acceleration and consequently stronger synchrotron emission in such regions of interaction. On the other hand, the ejecta will expand at a more rapid rate in a lower density region and may even become radio loud at comparatively later times when the swept-up mass is enough to decelerate the blast wave. These effects are believed to give rise to the blow-out (G312.4−0.4), one-sided (G338.1+0.4) or irregular morphologies. The expanding blast also interacts with the ambient magnetic field and amplifies it via turbulent amplification or by simple compression of the frozen-in fields. This interaction of the blast wave with the magnetic field is believed to be responsible for the barrel shaped SNRs and it has been suggested that many intrinsically barrel shaped SNRs may not appear to be so due to projection effects (?).

Spatially resolved spectral index variations across SNRs trace changes in particle kinetic energies or magnetic field strengths or both. Both of these could also be due to the inhomogeneous nature of the medium into which the ejecta expands; reliable spatially resolved spectral index maps of SNRs thus give a handle on the scale of inhomogeneities in the ISM (??). Spectral index changes across SNRs probe scales smaller than the size of the remnants. If the intrinsic properties of the SNRs can be independently established, spectral index changes between widely separated SNRs will probe scales of the order of the separation between the remnants.

It has been shown recently that the OH (1720 MHz) emission is associated with SNRs while the other OH maser transitions are associated with HII regions (?). Both theoretical and observational evidence (???) suggests that the OH (1720 MHz) masers are associated with the C-type shocks and are collisionally pumped in molecular clouds at temperatures and densities of 50−125 K and 10^{5} −10^{6} cm^{−3} respectively (?, and references therein). OH masers at 1665, 1667 and 1612 MHz cannot be produced under these physical conditions and the absence of these lines along with the detection of OH (1720 MHz) emission favors this interpretation. The measurements of the post shock density and temperature for IC443 (?), W28, W44 and 3C391 (?) are in excellent agreement with these theoretical predictions. A solution to the problem of producing OH, which is not directly formed by shocks, are proposed by ?. They suggest that the molecular cloud is irradiated by the X-rays produced by the hot gas in the interior of the SNR. This leads to photo-dissociation of the H_{2}O molecules, which is produced by the shock wave in copious amounts, behind the C-type shock resulting in the required enhancement of OH just behind the shock. Indeed, such maser emission has been found in SNRs whose morphologies have long been suspected to be shaped by their interaction with nearby molecular clouds (???). The fact that OH (1720 MHz) emission is possible for a very narrow range of physical parameters of the gas and other OH transitions in this range do not produce maser emission provides a powerful tool to probe the interaction of SNRs with molecular clouds. Detection of extended OH (1720 MHz) emission along with compact maser spots, tracing the radio continuum emission is suggestive of the maser emission tracing the extended region of such an interaction (?).

1.4 Why low frequency?

As mentioned above, radio emission from SNRs is synchrotron radiation which has a nonthermal power law dependence on frequency with a negative spectral index α (S ∝ ν^{α}). This makes the emission progressively stronger at lower frequencies (see Section ??). Thermal emission from typical HII regions, on the other hand has a flat spectrum above ≈ 1 GHz. Below this frequency the optical depth is much greater than 1 and the spectrum turns over with a spectral index of 2. Continuum spectra of Galactic objects at low frequencies are therefore frequently used to distinguish between thermal and non-thermal sources of emission (???). Radio emission from SNRs is typically also extended, often with low surface brightness, with most of the remnants exhibiting easily identifiable morphologies. Detection of extended non-thermal emission in the Galaxy, with no thermal emission, has been the criterion used to identify Galactic sources as SNRs. Low frequency observations of SNRs also provide an added advantage in the sense that the surface brightness of typical SNRs increases at low frequencies, making it easier to detect and map them for detailed studies.

Interferometric telescopes are however insensitive to scales larger than those corresponding to the smallest projected baseline. Single dish telescopes, on the other hand, are sensitive to emission at all scales in the field. However, they provide the sensitivity and required resolution only at high frequencies. Many observations of SNRs till recently were therefore done using single dish instruments at high frequencies. However, apart from the contaminating thermal emission at these frequencies as well as inherently lower emission from SNRs, such observations are more prone to large scale confusing emission, which is abundantly present in the Galactic plane. The resolution of low frequency single dish observations is also not enough to resolve the extended emission.

Although high resolution interferometric observations of Galactic SNRs have been carried out, imaging at low frequencies using interferometers is also relatively tougher due to the problems arising from higher level of radio frequency interference (RFI), higher phase noise at low frequencies (due to various reasons ranging from cross talk to ionospheric phase corruption), non-co-planarity of arrays requiring much more complex software and higher computing power, etc. Hence, even interferometric observations have been typically done at frequencies > 1 GHz.

Sensitive low frequency observations which are also sensitive to extended emission are therefore most appropriate for SNR research. Aperture synthesis telescopes like the GMRT operating at relatively low frequencies are well suited for such observations.

1.5 Aperture synthesis at low frequencies

Low frequency aperture synthesis telescopes like the GMRT offer several unique advantages from the point of view of SNR research. The GMRT is best suited for SNR observations owing to its sensitivity, relatively high resolution as well as sensitivity to large scale emission at low frequencies. Observations done for this dissertation extensively used the GMRT which has only recently come to a stage where enough antennas are available in the interferometric mode to attempt the imaging of extended sources. Interferometry at low frequencies, however, poses new challenges in data calibration and analysis, which are interesting in their own right. A substantial fraction of the work done for this dissertation involved the debugging and calibration of the telescope, to enable the observations discussed above to be carried out. Further, large amounts of software were required to be written, both to carry out debugging activity as well as to enable flagging and calibration of telescope data in a semi-automated fashion. The origin of the problems in low frequency interferometry and the required on-line data monitoring and off-line data analysis are briefly described below.

1.5.1 Phase fluctuations

The plasma frequency of the ionosphere is ∼ 12 MHz. The only cosmic radio emission reaching the surface of the earth is at frequency significantly higher than this value. However radio observations at a few 100 MHz are still severely affected by the ionosphere. The ionosphere is modeled as a thin (compared to the distance from the observing plane) slab of inhomogeneous plasma. A plane wave incident on the ionosphere filled with plasma blobs will emerge with the plasma fluctuations imprinted on the phase of the wavefront (Fig.??). The amplitude of this wave front will remain largely unchanged but the phase is no longer constant. The RMS phase fluctuations of the visibility phase induced due to the Earth’s ionosphere can be written as (??, and references therein)

Δϕ = r_{e}λaΔN_{e}  (1.20)

where λ is the wavelength, ΔN_{e} is the fluctuation in the electron number density, r_{e} is the classical electron radius and a is the characteristic size of the blobs. Low frequency observations are therefore more severely affected by temporal and spatial fluctuations in the ionospheric electron content. The diurnal and seasonal temporal fluctuations in the ionospheric electron content induced by the Sun and Solar activity directly affect the phase measured by low frequency interferometers, which, if not corrected, affects the sensitivity of Figure 1.9: Schematic diagram showing the effect of the ionosphere. The incident plane wave above the ionosphere is shown with a constant phase. The ionosphere, modeled as a thin slab of inhomogeneous plasma, imprints the inhomogeneities on the phase of the emergent wave front. The emergent corrugated wave front is sampled at a various points on the observing plane by antennas separated in space. the observations. Spatial fluctuations in ΔN_{e} are at scales ranging from several kilometers up to hundreds of kilometers. The wave front emerging out of such a phase screen can be thought of as composed of a number of plane waves traveling in slightly different directions. Decomposing this resultant wave into an angular spectrum of plane waves arriving from a variety of angles, one can define a full width of the angular spectrum, θ_{s}. This can be estimated by imagining that the blobs refract the incident wave by the amount ±Δϕλ/2π over a distance a. Thus,

θ_{s} = \frac{1}{π} r_{e}λ^{2}ΔN_{e}\sqrt{L/a}  (1.21)

where L is the thickness of the ionospheric plasma screen. Let the correlation length of the ionospheric phase fluctuation be d. Phase corruption from two points in the ionosphere separated by more than this amount will be uncorrelated. Assume further that the joint probability distribution of these phases is Gaussian with a variance of Δϕ^{2} and a normalized correlation function given by ρ(d). For the sake of better understanding, let us also assume that

ρ(d) = e^{−d^{2}/2a^{2}}  (1.22)

It can then be shown that for d ≪ a, the expectation value of the measured visibility V_{m} is given by

⟨V_{m}⟩ = V e^{−Δϕ^{2}d^{2}/2a^{2}}  (1.23)

This limit samples the fluctuations in the phase due to fluctuations at length scales smaller than the typical blob size. Fluctuations at this scale induces small phase changes in the emerging wave front which can be treated as phase perturbations across the wavefront with the mean phase still preserved. Electron density fluctuations for d > a induces large changes in the mean phase equivalent to a much larger spread in the angular spectrum. Consequently, ⟨V_{m}⟩ rapidly decreases for d > a.

The result of the these fluctuations is that a point source is broadened into a gaussian of diameter given by

θ_{s} = \frac{\sqrt{2 ln 2}}{π}r_{e}λ^{2}ΔN_{e}\sqrt{L/a}  (1.24)

The final effect of phase fluctuations is therefore to effectively spread the power from a point source in the image (?). If the intrinsic resolution of the telescope is smaller than θ_{s}, its resolution will be limited by the fluctuations in the phase and will be defined by θ_{s}. A more realistic treatment involves a power-law spectrum of phase fluctuations, similar to the Kolmogorov model for turbulence in a neutral medium. With such a power-law model for phase fluctuations, it can be shown that θ_{s} ∝ λ^{2.2}.

Ionospheric electron density also changes as a function of time due to diurnal and seasonal changes in the position of the Sun and also due to the activity on the Sun. Since the induced phase fluctuations scale with the wavelength, the effect of ionosphere is more severe at low frequencies. These phase errors need to be calibrated before the measured visibilities can be used for mapping. Long term (several tens of minutes) variations in the phase of an interferometer can be measured by periodic observation of a source of known structure, usually referred to as the phase calibrator, using the self-cal algorithm which decomposes the visibility phases into antenna based phases (???). However for this, it is assumed that the variations in phase are small at angular scales smaller than the size of the primary beam of the antennas (iso-planatic case). At low frequencies, this assumption can break, at least for some fraction of time, and the derived phase corrections will not correct for the phase noise completely over the whole field. ? and ? have described methods to relax the iso-planatic assumption. However, such algorithms have never been tried in real life or demonstrated to work well. This remains a potential problem, at least for high dynamic range imaging at low frequencies.

1.5.2 Non-coplanar baselines

The calibrated visibility function measured by an aperture synthesis telescope is given by^{3}

V (u, v, w) = ∫∫ I(l, m)P (l, m)e^{−2πι(ul+vm+w(\sqrt{1−l^{2}−m^{2}}))} \frac{dldm}{\sqrt{1 − l^{2} − m^{2}}}  (1.25)

where (u, v, w) are the projected co-ordinates of the antennas, l, m, and n are the direction cosines in the uvw co-ordinates system, I(l, m) is the source brightness distribution (the image) and P (l, m) is the far field antenna reception pattern (the primary beam).

For a small field of view (l^{2} + m^{2} ≪ 1), V is related to the image by a 2D Fourier transform. However for θ_{P B}/\sqrt{θ_{r}} > 0.1^{rad} where θ_{P B} and θ_{r} are the widths of the primary beam and the telescope resolution element, the image plane can no longer be expressed as a 2D Fourier transform of the visibility function (?). The sky can no longer be approximated by a 2D plane and must be modeled as the surface of a sphere, referred to as the Celestial sphere. To continue to approximate Equation ?? as a 2D Fourier transform relation between the sky brightness distribution and the visibility will introduce severe distortions in the image away from the phase centre. The longest baseline for the GMRT at 327 MHz is ∼ 25 km. Imaging with the GMRT at 327 MHz using baselines longer than ∼ 2 − 3 km crosses the limit where the sky can be approximated, and a full 3D treatment of the problem is required to make distortion free images.

3The coefficient of w in the exponent for a fringe-stopped visibility (see Section ??) will be (\sqrt{1 − l^{2} − m^{2}}− 1). This will effectively only shift the “image–volume” along the n−axis by one unit. Since this has no bearing on the problem of imaging with non-coplanar baselines, the −1 in the coefficient has been dropped from this equation.

This problem can be handled by treating \sqrt{1 − l^{2} − m^{2}} as an independent co-ordinate. Re-writing Equation ?? as

V (u, v, w) = ∫∫∫ F (l, m, n)P (l, m)e^{−2πι(ul+vm+wn))}dldmdn  (1.26)

a full 3D Fourier transform of V can then be used to make what is referred to as “image volume”. I can be shown to be related to F as

F (l, m, n) = \frac{I(l, m)δ(\sqrt{1 − l^{2} − m^{2}} − n)}{\sqrt{1 − l^{2} − m^{2}}}  (1.27)

where δ is the Dirac delta function. The 2D sky brightness distribution can be recovered from this image volume (?). This method goes by the name of “3D inversion”. Alternatively, the sky can be approximated as a set of 2D tangent planes. Images can be made for points close to the tangent points of these planes using the 2D approximation. These images can then be properly combined to recover the full primary beam image of the sky. This method goes by the name of “polyhedron imaging”.

The Galactic plane at low frequencies exhibits complex emission all over the field of view. Hence, even if the source of interest is compact and close to the pointing centre, 2D imaging cannot be applied since the distortions of sources away from the pointing centre (which is assumed to be also the phase centre) will have unacceptable effects all over the image. It is therefore necessary to map the full field of view, even if the size of the source of interest is small compared to the primary beam. Polyhedron imaging is implemented in the Astronomical Image Processing System (AIPS) package and was extensively used for making full primary beam images this dissertation.

1.5.3 On-line and off-line data analysis

In these early days of the GMRT, apart from other sources of data corruption like radio frequency interference (RFI), ionospheric scintillation, etc., data was frequently corrupted due to the failure of various systems. Monitoring the data quality and the health of the system during the observations was therefore of paramount importance. Since there were many sources of data corruption and the manner in which they affected the data were varied, it is useful to develop techniques and software which can automatically identify as many of these problems as early on in the data analysis process as possible. Identifying sources of data corruption, general debugging of the instrument, etc. however require sophisticated and efficient software for data analysis, browsing, and display. Extensive software was developed for this purpose in the form of general purpose object oriented libraries as well as programs for on-line and off-line data processing and display.

The effort invested in software development is optimally used if the resultant software is easy to use at the user level and easy to extend at the programmer level. This is also almost necessary for software which is expected to be used by a relatively larger number of users. Development of a user interface which is easy to use as well designing the entire software such that it is easy to extend is therefore important. Also, a user interface which is not consistent with the functionality of the application programs to which it interfaces is unlikely to be useful. It is therefore desirable to develop a user interface which, as far as possible, automatically evolves with the application programs. The modern Object Oriented software design philosophy was adopted to achieve exactly this goal. Software designed in an Object oriented manner is highly modular and the modules are loosely coupled. The software is designed as set of “objects” which map closely to real-life objects in the problem being solved. Usually, these real-life objects do not change significantly over the software life time, but the coupling between various objects can drastically change. Such changes can be very easily incorporated in a big software system designed as set of objects. Apart from ease of maintenance, this also produces reliable software which is easy to debug.

A user interface, which becomes part of the compiled application programs (as against a user interface as an independent entity which loads and runs the applications programs) was developed in the form of a set of libraries. Such a user interface is referred to as an embedded user interface. Libraries which provide a high level, astronomically useful interface for manipulating the GMRT visibility database were also developed. Using these libraries, programs for data editing, semi-automatic data flagging, on-line monitoring of the data, computation for antenna-based complex gains, amplitude and phase calibration, etc. were also developed.

The visibility function V, depends on a number of telescope parameters like the system temperature (T^{sys}), antenna sensitivity, antenna fixed delays, antenna positions, etc. For debugging as well as for on-line data monitoring, it was frequently required to extract this data in various representations (e.g., Cartesian versus polar representation of complex numbers). Since the complex visibilities are a function of a multitude of parameters, and different debugging purposes require viewing V with respect to various quantities, it was necessary to develop a compact macro language parser to extract and display the data in a flexible and programmable manner. This macro language was implemented in the form of stand alone libraries as well as an application program which was extensively used for this dissertation.

The self-cal algorithm can be used to compute antenna based complex gains from the complex visibilities for a source of known structure. However, it is very sensitive to the presence of data from malfunctioning antennas or from a malfunctioning correlator. During the course of the observations, it was frequently the case that the data from a few antennas was unusable, at least for some fraction of the observing time. A large fraction of diagnosis of problems in the data/telescope is often done by examining the antenna based complex gains, which are computed using the self-cal algorithm which in turn required careful flagging of malfunctioning antennas/baselines. An algorithm was therefore implemented which was robust in such conditions and could identify bad baselines/antennas automatically. This was done by (1) automatically eliminating out-lying points, (2) doing two passes to eliminate dead/bad antennas. This algorithm was also used to identify and flag corrupted data in a semi-automatic fashion.

1.5.4 Instrumental polarization leakage

Signals from the two orthogonally polarized feeds are brought to the base of the antenna via co-axial cables, which run physically close to each other. These signals are then brought to the a central location via optical fibers where they are converted to baseband signals. The two orthogonally polarized signals can leak in each other at various points in the signal path resulting into polarization impurity. To minimize this leakage, the technique of Walsh switching (?, and references therein) is used wherein the two signals are multiplied by two orthogonal trains of square waves, called the Walsh functions. Later, before correlating the signals from different antennas, these Walsh switched signals are multiplied by the inverse Walsh functions to recover the original signals. Any leaked signal from one polarization channel to the other at time scales longer than the period of the Walsh functions then averages to zero.

The planned Walsh switching has not yet been implemented for the GMRT. In any case, polarization impurity introduced before the switching point will not be removed by Walsh switching. This leakage is a significant source of noise at 150 MHz and also contributes noise at all other bands, albeit at a lower level and manifests itself in the form of increased closure errors in the system (?). The current GMRT correlator computes only the copolar visibilities (i.e. RR and LL visibilities only). Even with the planned extension of the correlator where the cross-polar visibilities (i.e. RL and LR visibilities) will also be computed, one can think of observations which will be done using the higher frequency resolution provided by the GMRT correlator in the non-polar mode. All such data will then be affected by errors related to this polarization impurity related errors. ? pointed out in the context of the VLBA, that polarization leakage causes closure errors even in nominally co-polar visibilities. ? have carried out a detailed study of this effect for the telescopes of the European VLBI Network (EVN). The polarization leakage in some of the EVN antennas corrupts the co-polar visibilities at a level visible as a reduction in the dynamic range of the maps (???).

Non-polarimetric observations for imaging constitute a large fraction of observations done using interferometers where only the co-polar visibilities are recorded. The calibrators used for such observations are usually unpolarized. Since the above mentioned closure errors will affect such data adversely, a method to measure the polarization leakage using only the co-polar visibilites from an unpolarized calibrator to correct for these closure errors will be of use, particularly for high dynamic range imaging.

1.6 Organization of the thesis

Low frequency continuum spectra, radio morphology and, if possible polarization measurements are the key observables used to identify SNRs in the Galaxy. Spectra at frequencies greater than ∼ 1 GHz suffer from contaminating thermal emission. Therefore, although higher angular resolution observations can be done at high frequencies, low frequency radio observations are more suited for SNR research. However with the lower resolutions and sensitivities at low frequencies, identification of the morphology, particularly in regions with complicated emission becomes difficult. High resolution sensitive observations at low radio frequencies therefore appears to be the optimal observation expected to yield rich dividends for various aspects of SNR research. This thesis reports the work done on these lines using the GMRT.

The main thrust of the thesis is the study of Galactic SNRs taking advantage of the high sensitivity and resolution of the GMRT which has recently become available for scientific usage. Since this work was done in the early stages of the GMRT, a large fraction of time was also spent in debugging the instrument and in developing extensive software for data browsing, display and off-line analysis. New algorithms and techniques were also developed which were useful, in particular for the GMRT, and, in general, for low frequency interferometry.

While debugging the GMRT, need for a sophisticated software for data browsing, display and analysis was felt early on. As a result, large amounts of software (> 60 000 lines of code in C++, C and FORTRAN) was written with the goal of keeping it efficient and yet simple so that the turn around time between observations and results from data analysis is minimized. This software was also written in a modern object oriented fashion, with the hope that many more astronomers/engineers will find it useful to write useful application programs using the the underlying software libraries as well as to extend the software system.

The thesis is organized in the form of eight chapters and four appendices. The present chapter briefly describes the model for supernova explosions and introduces the theoretical concepts of radio synchrotron emission in Section ??. Particular emphasis is laid on the fact that low radio frequency observations for the purpose of identification of SNRs in the Galaxy provides a crucial advantage over high frequency observations. The various stages of the evolution of SNRs are described in Section ??. Proposed mechanisms to explain the observed non-thermal emission from SNRs are discussed in Section ?? and the information drawn from measured continuum spectra of SNRs is discussed in Section ??. At frequencies higher than ∼ 1 GHz, thermal emission from HII regions in the Galaxy is strong and sometimes even dominant. The spectral signatures and nature of thermal emission in the presence of absorbing foreground medium are discussed in Section ??. Various observed radio morphologies, distribution of SNRs in the Galaxy and the effects of the ISM on the observed properties of SNRs are discussed in Sections ??, ?? and ?? respectively.

Chapter ?? describes the GMRT from an astronomical point of view. The underlying principle of aperture synthesis is discussed in Section ??, with emphasis on the problems related to imaging at low frequencies. Section ?? briefly describes the parabolic dishes and the geometry of the array. Section ?? describes the signal path from the antennas feeds till the digital back-end correlator while Section ?? describes the astronomically relevant parameters of the telescope. Most of the observations included in this dissertation were done when the GMRT hardware as well software was in a state of being debugged. Consequently, a large fraction of the time was spent in debugging activities, which required understanding the details of the hardware - particularly of the GMRT FX-type correlator.

The GMRT correlator hardware and associated software is described in some detail in Section ??. Section ?? describes the algorithm used for accurate time stamping of the data in the data acquisition software. Precise location of the antennas on the ground as well as the fixed instrumental delay suffered by the signal from individual antennas before reaching the correlator are two important parameters of an aperture synthesis telescope. Before imaging could be attempted, these measurements were made for the GMRT. Details of the baseline and antenna fixed delay calibration and its results are described in Section ??.

Chapter ?? very briefly describes the design and implementation of the GMRT off-line data analysis software system, which was extensively used during the course of this work. Section ?? discusses the need for the development of such a software system. Section ?? describes the philosophy behind the design of this software system consisting of a set of generic libraries and a number of application programs. Data manipulation libraries are described briefly in Section ?? while the user interface system and a few selected application programs, most extensively used during the course of this work, are described in Sections ?? and ?? respectively.

Chapter ?? describes the 325-MHz GMRT observations of a sample of candidate SNR fields. Section ?? describes the parameters of these observations. Mapping in the Galactic plane at 325-MHz with the GMRT requires mapping of the entire field of view which in turn requires use of specialized imaging and deconvolution algorithms. Section ?? discusses the techniques used from imaging at low frequencies, which were used for mapping the GMRT data. Section ?? describes the observational procedure used for these observations including the use of off-line data analysis software for on-line monitoring of the system health and the data quality. The details of data analysis and calibration are described in Section ??. Section ?? discusses the details related to inversion of the visibility data and deconvolution of the images. Finally, Section ?? presents the full primary beam 325-MHz images of all the fields. Most of the SNRs studied in this dissertation are large in angular size (typically > 7 arcmin). Although these GMRT observations could provide typical resolution of ∼ 20 arcsec for these southern fields, the maps presented here are typically at arcmin resolution. The reason for this is two fold: (1) since many of the SNRs had low surface brightness, lower resolution maps show the morphology more clearly (2) large scale emission tend to “break-up” at the highest resolution due to a combination of problems of deconvolution of large sources as well as phase noise that could not be calibrated. For a few fields, where the angular size of the sources of interest was of the order of arcmin, high resolution images were used.

Full primary beam maps of almost all the fields at 325-MHz exhibit a number of sources of compact as well extended emission, particularly in the Galactic plane. The primary goal of these observations was the low frequency study of Galactic SNRs in the fields - many of which were not confirmed SNRs. Chapter ?? goes on to discuss the SNRs in these fields. Section ?? discusses the difference between low and high frequency observations of Galactic SNRs to bring forth the advantages offered by deep high resolution observations at low frequency. Section ?? then discusses the individual candidate SNRs in the fields. Some of the fields also contained other previously identified SNRs. For a few of them, these 325-MHz observations are the first observations at this frequency; in fact, these are also the first high resolution observations at this frequency for all these sources. These results are described and discussed in Section ??. Finally, Section ?? discusses these results in a broader perspective of Galactic SNR research.

Other sources in the field are discussed in Chapter ??. Section ?? briefly discusses the nature of other dominant sources of radio emission and Section ?? presents a list of point sources in the fields along with their measured flux densities at 325-MHz and, where possible, at 1400 MHz. Section ?? discusses the sources of extended emission in these fields, which are not SNRs. These high resolution observations at relatively low frequency are the first ever observations of these objects and the somewhat unexpected significant extended emission seen at this frequency is interesting from the point of view of better understanding of these sources (usually classified as “thermal”). Section ?? concludes the chapter with a summary of the results from these observations.

A technique for the computation of polarization leakage using only the co-polar visibilities is described in Chapter ??. Section ?? describes the motivation which led to the development of this technique. Section ?? mathematically describes the algorithm and also presents the results of the simulations done to test it. Section ?? presents the results of the tests done with real data acquired in a controlled experiment and the interpretation of the results in terms of the magnitude of the polarization leakage for various antennas. The Poincaré sphere is a convenient and possibly more intuitive representation of the polarization state of radiation. Interpretation of these results on the Poincaré sphere and the equivalence of the polarization leakage induced phase closure errors and the Pancharatanam phase is discussed in Section ??. Since only co-polar visibilities are used for the computation of polarization leakage, the solutions are not unique, but still provide useful information about the polarization properties of the antennas. This is discussed in Section ??.

Chapter ?? gives consolidated conclusions and results from this work. Section ?? describes the major results from the testing and debugging of the GMRT and the software developed for the purpose. Section ?? discusses the astronomical results from the observations of the candidate SNRs done for this dissertation. Section ?? discusses the inferences about other sources in the fields based on these low frequency observations. Section ?? proposes the future directions of research in the fields of Galactic SNRs, compact/Ultra compact H II regions as well as in the field of developing data analysis techniques for radio interferometry at low frequencies and related software development.

Details of the user interface for the off-line software is included as Appendix ??. A flexible mechanism was developed to allow easy extraction for any type of data from the GMRT visibility database. This was implemented in the form of a macro language; and the parser and complier for this language is implemented as a stand alone library and used in the program xtract. Details of all this work are included as Appendix ??. A flexible antenna and baseline naming convention is uniformly used in all off-line application programs. This convention is described in Appendix ??. Finally, Appendix ?? presents the formulation of the problem of computation of antenna based complex gains from the measured complex visibilities. The iterative equations are derived using complex calculus and the interpretation of these equations for better understanding of the algorithm is also presented.

38 CHAPTER 1. INTRODUCTION

The Giant Meterwave Radio

Telescope

The Giant Meterwave Radio Telescope (GMRT) (?), located 70 km North of Pune at a latitude of 19^{∘}05′ N and a longitude of 74^{∘}03′ E, is a connected element aperture synthesis radio telescope. It is optimized to run at meter wavelengths and currently operates at the 150, 233, 327, 610 and 1420-MHz bands. In addition to this, there are plans to put the 50 MHz feeds on few antennas to test the data quality since the major limitation is expected to come from Radio Frequency Interference (RFI) and ionospheric phase contamination. The 233 and 610 MHz feeds are co-axial which will ultimately allow simultaneous observations at these frequencies. This chapter describes the GMRT from an astronomical point of view, with emphasis on the 327-MHz band.

2.1 Principles of aperture synthesis

An aperture synthesis telescope, like the GMRT, consists of a number of antennas located on the ground and the resolution of such a telescope is proportional to the maximum projected separation between the antennas. The locations of the antennas are usually specified in the Earth-centred XY Z co-ordinate system. The Earth centred XY Z frame is related to the xyz location of the antennas on the ground by

[ \begin{matrix}X \\ Y \\ Z \end{matrix} ] = [ \begin{matrix}− sin L & cos L & 0 \\ 0 & 0 & 0 \\ sin L & cos L & 0 \end{matrix} ] [ \begin{matrix}x \\ y \\ z \end{matrix} ]  (2.1)

Figure 2.1: The right handed Cartesian co-ordinate system in which antenna positions are described is shown in the figure by the X,Y and Z-axis. The X and Y are in the plane parallel to earth’s equator with X-axis in the local meridian plane and Y-axis towards the east. The Z-axis points towards the north celestial pole (NCP). The w-axis of the uvw co-ordinate system, points towards the phase centre of the array at hour-angle H and declination δ. In terms of H and δ, X,Y and Z are measured towards (H = 0, δ = 0), (H = −6^{h}, δ = 0) and (δ = 90^{∘}). The uv-plane is parallel to the tangent plane at the phase centre on the celestial sphere and rotates with the rotation of the Earth.

where L is the nominal latitude of the telescope site. The x-axis points towards the geographical east, y-axis towards the north and z-axis towards the local zenith.

However, for the purpose of imaging, only the relative separation between the antennas is important. This separation between the antennas is usually referred to as the baseline and is measured in units of the wavelength λ of the incident radiation. For the purpose of the theory of synthesis imaging, the antenna positions are specified in the so called uvw frame. The geometric relationship between this XY Z frame and the uvw frame is shown in Fig. ?? and the co-ordinate transformation is given by

[ \begin{matrix}u \\ v \\ w \end{matrix} ] = [ \begin{matrix}sin H & cos H & 0 \\ − sin δ cos H & sin δ sin H & cos δ \\ cos δ cos H & − cos δ sin H & sin δ \end{matrix} ] [ \begin{matrix}X \\ Y \\ Z \end{matrix} ]  (2.2)

where H is the Hour Angle and δ the declination of the source.

The geometric relation between the observing plane represented by the uv-plane and the sky plane represented by the lm-plane is shown in Fig. ??. The lm-plane in the sky is parallel to the plane in which measurements are made (the uv-plane) and the separation between them is denoted by R. The w-axis points towards the origin of the lmn frame given by (l = 0,m = 0) and is parallel to the n-axis. The treatment of the theory of synthesis imaging given below follows that of ? and ?.

Let E(s⃗, b⃗_{1}, t) represent the electric field produced by an infinitesimal element in the sky in the direction s⃗ at point b⃗_{1} in the uvw frame (Fig. ??). The total electric field e(b⃗_{1}, t) measured at this point will be an integral of the signals from all the radiation elements and is given by

e(b⃗_{1}, t) = ∫_{P} E(s⃗, b⃗_{1}, t)ds⃗  (2.3)

b⃗_{1} is the vector denoting the point 1 in the uvw frame. Let R_{1} be the distance between point b⃗_{1} and the point in the source plane towards the direction given by the vector s⃗_{1}. E(s⃗_{1}, b⃗_{1}, t) can then be written as

E(s⃗_{1}, b⃗_{1}, t) = \frac{ξ(s⃗_{1}, t − τ_{1})}{R_{1}}e^{−2πιν(t−τ_{1})}  (2.4)

where ξ is the complex amplitude of the radiation at the source, ν is the frequency of the radiation, τ_{1} = R_{1}/c and c is the speed of light. τ_{1} represents the propagation delay for the radiation of complex amplitude ξ to travel the distance R_{1}.

The source coherence function, defined as

\begin{aligned}Γ(s⃗_{1}, s⃗_{2}, τ) & = lim_{T →∞} \frac{1}{2T} ∫_{−T}^{T} ξ(s⃗_{1}, t)ξ^{⋆}(s⃗_{2}, t − τ)dt \\ & = ⟨ξ(s⃗_{1}, t)ξ^{⋆}(s⃗_{2}, t − τ)⟩ \end{aligned}  (2.5)

is a measure of the coherence between radiation from two points on the source given by the directions s⃗_{1} and s⃗_{2} respectively. For a spatially incoherent source, radiation from two Figure 2.2: Figure showing the orientation of source co-ordinate reference frame and the observing plane. The 2D approximation of the Celestial sphere is shown as the tangent plane at the origin of the sky co-ordinate system.

points on the source will be uncorrelated. For such a source, Γ(s⃗_{1}, s⃗_{2}, τ) = δ(s⃗_{1} − s⃗_{2}) and equation ?? can be written as

Γ(s⃗, τ) = ⟨ξ(s⃗, t)ξ^{⋆}(s⃗, t − τ)⟩  (2.6)

This is the auto-correlation function of the radiation from the source Γ(s⃗, 0) is a measure of the average surface brightness of the radiation from the source.

The mutual coherence function, measured at two points b⃗_{1} and b⃗_{2} on the observing plane is defined as

\begin{aligned}γ(b⃗_{1}, b⃗_{2}, τ) & = lim_{T →∞} \frac{1}{2T} ∫_{−T}^{T} e(b⃗_{1}, t)e^{⋆}(b⃗_{2}, t − τ)dt \\ & = ⟨e(b⃗_{1}, t)e^{⋆}(b⃗_{2}, t − τ)⟩ \end{aligned}  (2.7)

Using Equations ?? and ?? and the equivalent equations for the point b⃗_{2}, the above equation can be written as

\begin{aligned}γ(b⃗_{1}, b⃗_{2}, 0) & = ∫ ⟨E(s⃗, b⃗_{1}, t)E^{⋆}(s⃗, b⃗_{2}, t)⟩ds⃗ \\ & = ∫ ⟨ξ(s⃗, t − τ_{1})ξ^{⋆}(s⃗, t − τ_{2})⟩e^{−2πιν(τ_{2}−τ_{1})} \frac{ds⃗}{R_{1}R_{2}} \\ & = ∫ ⟨ξ(s⃗, t)ξ^{⋆}(s⃗, t − τ_{t})⟩e^{−2πιντ_{t}} \frac{ds⃗}{R_{1}R_{2}} \end{aligned}  (2.8)

where τ_{t} = τ_{2} − τ_{1} = (R_{2} − R_{1})/c is the relative delay between the signals measured at the points b⃗_{1} and b⃗_{2} respectively.

In the above equation, the dependence on b⃗_{1} and b⃗_{2} is implicitly via τ_{t}. For a plane wavefront from a direction s⃗ in the sky, τ_{t} = b⃗_{12} · s⃗/c where b⃗_{12} is the vector separating the two antennas. It is therefore clear that γ depends only on the relative separation between the antenna positions given by b⃗_{1} and b⃗_{2} and can be written as

γ(b⃗_{1}, b⃗_{2}, 0) = γ(b⃗_{1} − b⃗_{2}, 0) = γ(b⃗_{12}, 0)  (2.9)

The components of b⃗_{12} will be given by (u_{12}, v_{12}, w_{12})=(u_{2} − u_{1}, v_{2} − v_{1}, w_{2} − w_{1}). Using direction cosines of s⃗ as the (l, m, n) co-ordinates of a point in the sky, we get

τ_{t} = \frac{b⃗_{12} · s⃗}{c} = \frac{u_{12}l + v_{12}m + w_{12}n}{c}  (2.10)

Let the antenna located at point b⃗_{1} track a direction given by the unit vector s⃗ in the sky. Due to the separation between the antennas on the ground, to track the same point in the sky, a second antenna located at point b⃗_{2} will need to point in a slightly different direction given by s⃗_{2}. The angle between s⃗ and s⃗_{2} is given by tan^{−1}(|b⃗_{2}−b⃗_{1}|/R). This difference in the pointing directions results in an extra relative delay between the signal arriving at the two antennas from a point in the sky. As a result, one of the antennas samples a slightly delayed version of the wave front. If, however, R ≫ |b⃗_{2} − b⃗_{1}|/λ where λ is the wavelength of the radiation, the same wavefront will be sampled by the two antennas (tan^{−1}(|b⃗_{2} −b⃗_{1}|/R) ≈ 0).

This corresponds to the usual plane wavefront approximation. This approximation is used in the rest of the treatment.

In the limit of the plane wave front approximation, the denominator in Equation ?? can be adequately represented by R^{2} and ds⃗/R^{2} = dldm/\sqrt{1 − l^{2} − m^{2}}. The phase of the mutual coherence function in Equation ??, for a spatially incoherent source, therefore, depends only on the relative separation between the points of measurement in the far field of the radiation.

Let s⃗_{∘} represent the unit vector along the w-axis pointing towards (l = 0, m = 0). The components of s⃗_{∘} in the uvw frame will be (0,0,1). The relative delay between the signals received at the two antennas from a point source in this direction will be τ_{g} = s⃗_{∘} · b⃗_{12}/c = w_{12}/c. Treating s⃗_{∘} as the reference direction towards the origin of the source co-ordinate system, the instantaneous phase of γ(b⃗_{12}) can be measured with respect to this direction, without losing any information about the sky brightness distribution. This can be done by rotating the phase of γ by −2πνw_{12}/c. The point in the sky in the direction s⃗_{∘} is referred to as the phase centre and τ_{g} is referred to as the geometrical delay. The Phase centre direction defines the origin of the source co-ordinate system. Since s⃗_{∘} is an arbitrary vector, the phase centre can be chosen at any convenient point in the sky. Usually, this is coincident with the antenna pointing centre.

The visibility phase for a point source at the phase centre, after correcting for the geometrical phase is equal to zero. With this correction, the visibility is said to be ‘phased’ for the phase centre. An interferometer phased for this reference direction will remain phased for all points on the surface of a sphere of unit radius passing through the point (l = 0, m = 0), centred at (u = 0, v = 0) and described by the equation l^{2} + m^{2} + n^{2} = 1. Under ideal conditions (i.e., with no other source of phase errors), any residual phase would be due to the relative separation between the phase centre and a source of emission located on such a sphere. In that sense, the visibility phase from a ‘phased’ interferometer provides information about the distribution of the sky brightness, relative to the phase centre. Moving one of the antennas to the origin of the uvw frame, the (u_{12}, v_{12}, w_{12}) co-ordinates are just the co-ordinates of the other antenna and the subscript ‘12’ can be dropped from Equation ??.

The length of time for which a signal remains coherent is given by the inverse of the bandwidth Δν. After correcting for the geometrical delay, the relative delay between the signals is τ_{c} = τ_{t}−τ_{g}. Replacing τ_{t} by τ_{c} in Equation ?? corresponds to the geometrical delay corrected version of this equation. If τ_{c} ≪ Δν^{−1}, two versions of a time series displaced with respect to each other in time by τ_{c} will remain coherent. In the limit of the validity of the assumption that τ_{c} ≪ Δν^{−1}, ⟨ξ(s⃗, t)ξ^{⋆}(s⃗, t − τ_{c})⟩ in Equation ?? can be replaced by ⟨ξ(s⃗, t)ξ^{⋆}(s⃗, t)⟩ = ⟨|ξ(s⃗)|^{2}⟩. This is the same as the source auto-correlation function at zero lag, Γ(s⃗, 0) (Equation ??) and is equal to the two dimensional source surface brightness, denoted by I(l, m)

Therefore, under the approximation that:

• the observing plane is in the far field of the radiation ( R ≫ |b⃗_{2} − b⃗_{1}|/λ)

• the total delay between the signals received at the two points on the observing plane is much less than the signal coherence time (τ ≪ Δν^{−1})

using the relation between l, m, n in Equation ?? and the above mentioned phase rotation, Equation ?? can be re-written as

γ(u, v, w) = ∫∫ I(l, m)e^{−2πι(ul+vm+w(\sqrt{1−l^{2}−m^{2}}−1))} \frac{dldm}{\sqrt{1 − l^{2} − m^{2}}}  (2.11)

where u, v and w are now the co-ordinates in the uvw frame measured in units of the wavelength. γ is usually referred to as the visibility function and denoted by V (u, v, w).

The integrals in the above equation are over the entire sky (limits of the integral from −1 to 1). However, the antenna primary beam limits the part of the sky from which the antenna can receive radiation to ∼ λ/D, where D is the diameter of a circular aperture. Assuming that the response close to the centre of the primary beam is ≈ 1, with an additional approximation that the field of view is small (l^{2} + m^{2} ≪ 1), Equation ?? can be written as

γ(u, v) = ∫∫ I(l, m)e^{−2πι(ul+vm)}dldm  (2.12)

This is a 2D Fourier transform relation between the mutual coherence function (visibility) and the source surface brightness. This statement is referred to as the van Cittert-Zernike theorem (??) and forms the basis of imaging with interferometric radio telescopes.

The source surface brightness I(l, m) is described in the lm-plane while u and v are the equivalent conjugate variables in Fourier space. u and v can therefore be interpreted as the spatial frequencies and the visibility function as the spatial frequency spectrum of the source surface brightness distribution. Synthesis radio telescopes like the GMRT measure the visibility function at several points in the uvw frame using an array of N antennas which instantaneously produce N(N − 1)/2 pairs of interferometers. Due to the rotation of the earth, the projected separations between the antennas change as the antennas track a source in the sky. Over time, each antenna pair therefore measures the visibility at several points in the uvw frame. As a result, over time, the array of antennas partially covers the uvw volume, up to a maximum projected antenna separation of B_{max} corresponding to a spatial resolution of 1/B_{max}. Also, an interferometric array does not measure V for baselines smaller than a minimum value. Just as the maximum baseline length for which V is measured corresponds to the highest spatial resolution the telescope can provide, the smallest baseline for which V is measured corresponds to largest angular scale that can be represented reliably in the final image. Hence, an interferometric observation will be insensitive to scales larger than 1/B_{min}; this problem of missing short spacing measurements is referred to as the problem of “missing short spacing”. When imaging extended objects in the sky, like the ones imaged for this dissertation, the shortest spacing for which a reliable measurement exist has for reaching implications – missing short spacings result in missing extended emission in the image.

If γ(u, v) is completely sampled, at least at the Nyquist rate, it can be inverse Fourier transformed to recover the source brightness distribution I(l, m). With a finite number of antennas located at discrete locations on the ground, the visibility function is sampled at a discreet set of points. The observed visibility can, therefore, be thought of as the true visibility, multiplied by the sampling function given by

S(u, v) = δ(u − u(t), v − v(t))  (2.13)

where (u(t), v(t)) represents the points sampled at time t. Using the convolution theorem for Fourier transform (?), it can be shown that the function I, recovered by the inverse Fourier transform of S(u, v)γ(u, v), will be convolved by the inverse Fourier transform of S. The inverse Fourier transform of S, denoted by B, is usually referred to as the dirty beam or the point spread function or the telescope transfer function. I^{d} = I ⋆ B is referred to as the dirty map, where ‘⋆’ represents the convolution operator. I is recovered from I^{d} using non-linear deconvolution techniques (???).

The approximation that l^{2}+m^{2} ≪ 1 breaks down at low frequencies and Equation ?? accurately described the measured visibility function. However, this is not a Fourier transform relation. Techniques used to recover I in such cases are described in Chapter ??.

Figure 2.3: Figure shows a simplified one dimensional block diagram of a two element interferometer. A compensating delay τ_{i} is introduced in the path of one of the signals. The two signals are then multiplied and integrated to measure the mutual coherence between the signals from the two antennas.

2.1.1 Interferometry in practice

In practice, γ is measured by a number of two element interferometers, one of which is shown in Fig. ??. The signal from antenna 1 lags behind the signal from the antenna 2 by a phase equal to 2π \frac{b_{12}·s⃗_{o}}{c} where s⃗_{o} is the reference unit vector mentioned in the previous section. Under the plane wave approximation, the signals from the two antennas can be written as

\begin{matrix}S_{1} = e_{1} + ϵ_{1} \\ S_{2} = e_{2} + ϵ_{2} = e_{1}e^{2π \frac{b_{12}·s⃗o}{c}} + ϵ_{2} \end{matrix}  (2.14)

where ϵ_{1} and ϵ_{2} are independent additive random noises from the two antennas. These signals are multiplied and the product averaged in the complex correlator to form the visibilities as

\begin{aligned}V (u, v, w) & = ⟨S_{1} · S_{2}^{⋆}⟩ \\ & = ⟨e_{1} · e_{2}^{⋆}⟩ + ⟨e_{1} · ϵ_{2}^{⋆}⟩ + ⟨e_{2} · ϵ_{1}^{⋆}⟩ + ⟨ϵ_{1} · ϵ_{2}^{⋆}⟩ \end{aligned}  (2.15)

Since ϵ_{1} and ϵ_{2} are independent zero mean gaussian random variables, the last three terms will reduce to zero.

The response of the interferometer to a point source of flux density I, located at the phase centre (l = 0, m = 0) is therefore

V (u, v, w) = Ie^{2πι^{\frac{b_{12}·s⃗o}{c}}} = Ie^{2πιw} = Ie^{2πιντ_{g}}  (2.16)

where τ_{g} is the geometrical delay mentioned earlier. It is equal to the time delay due to the extra path length (equal to the projected separation between the antennas along s⃗_{o}) which the radiation has to travel to reach one of the antennas. With reference to Fig. ??, ντ_{g} = \frac{D}{λ} sin(θ) = w_{λ} where D = |b⃗_{12}| and w_{λ} is the instantaneous component of the separation between the antennas along the w-axis measured in units of the wavelength of the incident radiation. Equation ?? can therefore be rewritten as

V (u, v, w) = I(l, m) [cos(2π \frac{D}{λ} sin(θ(t))) + ι sin(2π \frac{D}{λ} sin(θ(t)))]  (2.17)

Antennas receive radiation from a finite part of the sky, defined by the antenna primary beam. For an extended source, within the antenna primary beam, V (u, v, w) will be an integral over the source (integral over l and m;Equation ??) and can be thought of as a superposition of plane waves from the individual infinitesimal elements constituting the extended source given by Equation ??.

As the interferometer tracks the source in the sky, the projected separation and hence the geometrical delay changes with time. θ changes slowly going from −θ_{max} to θ_{max} when the antennas track a source from rise to set over several hours. θ_{max} depends on the declination of the source and the minimum elevation limits of the antennas. Over short intervals of time, θ changes almost linearly with time. The interferometer response to a point source (the real and imaginary parts) therefore varies quasi-sinusoidally over short periods of time with a frequency proportional to the separation between the antennas. This quasi-sinusoidal variation of the interferometer output, due to the changing geometrical delay, is referred to as the fringe pattern. The amplitude of this fringe pattern is directly proportional to the power emitted by the source in the sky. The phase of these fringes also changes sinusoidally with time with a period of 24 hours. The phase of this fringe pattern due to the geometrical delay however carries no astronomically useful information about the sky (it only carries information about the direction in the sky being tracked). In practice therefore, the geometrical delay is continuously compensated by introducing a time variable compensating delay τ_{i} in the signal from one of the antennas. This operations is referred to as delay tracking. The radio-frequency (RF) signals from the antenna feeds, centred at a frequency ν_{RF}^{∘}, are converted to an intermediate frequency band centred at ν_{IF}^{∘} to be transported to the correlator (in the case of GMRT, over optical fiber cables). The path length for the signals from the antenna to the correlator introduces a time invariant fixed delay τ_{F ix} suffered by the signals at ν_{IF}. The compensating delay τ_{i} must therefore compensate for τ_{F ix} as well.

For the GMRT, the compensating delay τ_{i} = τ_{g} + τ_{F ix} is applied to the signals at baseband frequencies in the correlator. However, the signals suffer the delays τ_{g} and τ_{F ix} at the RF and IF frequencies respectively. Delay compensation at the baseband therefore leaves a residual phase given by

\begin{aligned}\frac{Δϕ}{2π} & = [τ_{g}ν_{RF}^{∘} + τ_{F ix}ν_{IF}^{∘}] + [(τ_{g} + τ_{F ix} − τ_{Int}) ν_{i}] \\ & ≡ \frac{Δϕ^{∘}}{2π} + \frac{Δϕ_{i}}{2π} \end{aligned}  (2.18)

where ν_{i} is the centre frequency of the i^{th} frequency channel and τ_{Int} is the time delay, applied in the correlator Delay/DPC system (see ?? for details). This delay compensated signal is fed to the FFT section of the correlator to be split into a number of frequency channels. Δϕ^{∘} is applied at the very first stage of the FFT butterfly network in the FFT section. The remaining phase gradient, denoted by Δϕ_{i}, is applied as a phase gradient in the last stage of the FFT network.

Effectively, the phase of the visibilities is rotated by Δϕ, equivalent to the residual delay due to the differences in the RF, IF and base band frequencies. The phase of the visibility for a point source located at the phase centre is thus reduced to zero at all times. This final rotation of the fringe phase is referred to as fringe stopping or fringe rotation.

Note that the total phase applied to the visibilities via delay tracking and fringe rotation is equal to 2πw and this effectively phases the interferometer for a point in the sky (the phase centre). Application of this total phase is achieved in the GMRT correlator in two stages, as explained in Section ??.

The response of the interferometer is integrated over the signal bandwidth as seen by the multiplier in the correlator. If H(ν) represents the voltage response of the antennas as seen by the multiplier, the effect of a finite bandwidth is to modulate the output of the interferometer by the Fourier transform of H. If the receiver has a flat response for a range of frequencies ν_{o} ± Δν, the output V, for a source of unit flux density, will be given by

V (u, v, w) = \frac{sin(πΔντ)}{πΔντ}e^{2πν_{o}τ}  (2.19)

where τ = τ_{g} − τ_{i} − τ_{F ix} is the total residual relative time delay between the signals from the two antennas after delay compensation. The Fourier transform of H is referred to as the fringe washing function. Since H is a band limited function, the fringe washing function is finite for a limited range of τ and defines the coherence time of the fringe pattern, which is 1/Δν for the above example. The total relative residual delay between the two signals before multiplication, therefore, must be ≪ 1/Δν for the signals from the two antennas to remain coherent when they arrive at the multiplier. Large departures of τ from this value would result in decoherence of the signals, resulting in reduction of the amplitude of the interferometer output. Therefore, in practice, knowledge of both the instantaneous geometric delay and the fixed delay is important.

w is the relative antenna separation along the w-axis. As is clear from Equation ??, the geometrical delay involves the measurement of the relative (X, Y, Z) co-ordinates of different antennas. It is therefore important to measure the relative antenna co-ordinates as well as the fixed delays for phasing the array (reducing the fringe phase to zero for the phase centre). The procedure used for measuring the relative antenna co-ordinates (referred to as baseline calibration) and fixed delays (referred to as fixed delay calibration) for the GMRT is described in Sections ?? and ?? respectively.

As mentioned earlier, V (u, v, w) is measured for several values of u, v and w by tracking the source in the sky for several hours, during which the projected baseline of a single interferometer changes with time. In practice, a number of antennas are used and the output of all the N(N − 1)/2 interferometer pairs made by an array of N antennas provide instantaneous measurements at several values of u, v and w. The instantaneous set of points measured in the uvw frame by an array of antennas is referred to as the snapshot uv-coverage. As the array tracks a source in the sky, each interferometer generates a track in the uv-plane, dramatically increasing the uv-coverage of the array. The set of u, v, w points, measured by an array of antennas over several hours of source tracking, is referred to as the full synthesis uv-coverage. The shape and density of the uv-coverage of the array determines the telescope transfer function and the geometry of the array is usually optimized to maximize the uv-coverage (?). The configuration of the 30-antenna GMRT array and resulting uv-coverage are described in Section ??.

2.2 The Array

The GMRT antennas are fully steerable parabolic dishes each of 45m diameter each with an Alt-azimuth mount. A turret at the prime focus of the antenna is supported by a quadripod and holds a sealed metallic cube which houses the broadband low noise amplifier (LNA), RF filters, the polarizer and the RF switch for swapping the polarization channels for each RF band (see Section ??). The feeds for 150, 327, 233/610, and 1420 MHz are mounted on the four faces of the turret which can be rotated to bring the desired feed in focus using the feed positioning system (FPS). The feed bandwidths and the range of frequencies covered by the various feeds are listed in Table ??. The feed bandwidths correspond to a Standing wave ratio of ≤ 2. The 233-MHz feed has the smallest bandwidth while the cross-polar characteristic of the 150-MHz feed is the worst. The measured cross-polar power at 327 and 610 MHz bands is ∼ −42 and ∼ −47 dB respectively while that for the 150-MHz feed is ∼ −22 dB. The value away from the centre of the radiation pattern is ∼ −22 dB for 327 and 610 MHz bands while that for the 150-MHz feed is ∼ −20 dB (see ? for more details). Since the GMRT is predominantly a low frequency instrument, the reflecting surface of the antennas is a light weight wire mesh. The wire mesh is held in place by a network of steel ropes, creating patches of flat surfaces which approximate a parabola. This design is referred to as the Stretched Mesh Attached to Rope Trusses design or the SMART design (?). Three sizes of wire mesh are used, going from smallest sized mesh (10 mm) in the inner region of the parabola to the largest size (20 mm) towards the edge to produce a tapered illumination pattern which reduces the side-lobe levels of the antenna radiation pattern. Mesh of different sizes each covers one third of the total surface area. The reflecting surface for each antenna was measured by theodolite, to determine the surface accuracy compared to an ideal parabola. An RMS deviation of 8, 9 and 14 mm from an ideal parabola was measured for the three regions of the surface (?).

The GMRT is composed of 30 such antennas. The antennas are located in a roughly ‘Y’ shaped geometry (?), as shown in Fig. ??. Fourteen antennas are located randomly in a region of size ≈ 1 km×1 km, referred to as the Central Square (see Fig. ??). These antennas provide the short spacing coverage of the uv-plane, which is essential for mapping large scale structures. The rest of the antennas are located in ∼ 14 km long Western-, Eastern-, and Figure 2.4: The location of the GMRT antennas. The three arms of the ‘Y’ shaped array are each ≈ 14 km long.

Southern-arms. The Eastern- and Southern-arms each have 5 antennas, roughly along a straight line, while the Western-arm has 6 antennas. This arrangement of antennas was designed to maximize the telescope sensitivity to large scale emission as well as to provide high resolution. The shortest spacing of ∼ 60 m in the Central Square is provided by the antennas C05, C06 and C09 while the largest spacing of ∼ 25 km is provided by the arm antennas. The Central Square antennas together provide a uv-coverage up to 1 km. The uv-coverage for a full 12^{h} synthesis observation using the full array is shown in Fig. ??. The uv-coverage due to Central Square antennas alone, for a full 12^{h} synthesis at a few declinations is shown in Fig. ??.

2.3 Signal flow

A detailed description and analysis of the analog signal flow for the GMRT has been described elsewhere (??). This section briefly describes the aspects of the GMRT analog receivers which are relevant from the point of view of astronomical observations.

The GMRT operates at the 150, 233, 327, 610 and L-band extending from 1000 − 1450 MHz. The L-band is split into four sub-bands centred at 1060, 1170, 1280 and 1390 MHz with a bandwidth of 120 MHz while the bandwidth at other bands is ∼ 40 MHz.

Figure 2.5: The location of only the Central Square GMRT antennas.

Fig. ?? shows a simplified schematic diagram, with the major components of the GMRT receiver. The L-band feeds measure two orthogonal linear polarizations while the feeds at all other bands measure circular polarizations. The 233 and 610 MHz feeds are co-axial feeds. The front-end low noise amplifiers have been designed to either receive two polarization signals from a single feed or the same polarization signal from two different feeds. This, for the case of 233/610 MHz feeds, allows simultaneous single polarization observations at these bands. An RF switch after the front-end box allows swapping of the two polarizations signals. Solar attenuators of 14, 30 and 44 dB are also available. Four calibrated noise sources, named Low, Medium, High and Extra-high cal can be used to calibrate the receiver system. However, the planned periodic injection of calibrated noise has not yet been implemented. The Front-end electronics also has the facility for Walsh switching of the two polarization channels using orthogonal Walsh functions to minimize polarization leakage. However this is also not yet operational at the GMRT.

The RF band is first converted to an IF band centred at 70 MHz using what is referred to as the First LO (First Local Oscillator). Here, bandwidths of 5.5, 16 or the full RF bandwidths can be selected. The two IF signals corresponding to the two polarizations are then converted to 130 and 175 MHz with a maximum bandwidth of 32 MHz using the Second LO. These signals are then transported over optical fibers to the Central Electronics 54 CHAPTER 2. THE GIANT METERWAVE RADIO TELESCOPE Figure 2.6: Full synthesis uv-coverage of the full GMRT array at declinations of 20^{∘}, −20^{∘}, 40^{∘} and −40^{∘} respectively.

2.3. SIGNAL FLOW 55 Figure 2.7: Full synthesis uv-coverage of the GMRT Central Square at declinations of 20^{∘}, −20^{∘}, 40^{∘} and −40^{∘} respectively.

56 CHAPTER 2. THE GIANT METERWAVE RADIO TELESCOPE Figure 2.8: Block diagram showing the GMRT receiver system. The diagram is taken from ?.

Table 2.1: Table of GMRT feeds and corresponding bandwidths for standing wave ratios of ≤ 2. The 233 and 610 MHz feeds are co-axial feeds.

Nominal Centre Freq. Feed Bandwidth Freq. Range Reliable Range
(MHz)  (MHz)  (MHz)  (MHz)
150  130  117 − 247  150 − 158?
233  12  228 − 240  232 − 238
327  138  286 − 424  315 − 335
610  127  580 − 707  590 − 630
1420  580  1000 − 1580 1000 − 1450

Building (CEB). Variable attenuators in the range of 0 − 30 dB, which can be varied in steps of 2 dB are available separately for the two IF signals. An automatic level controller (ALC) at the output of the IF can be bypassed if required (e.g. for observations requiring measurement of variations at high time resolution). At the CEB, the 130- and 175-MHz signals, recovered from the output of the optical fibers, are fed to the Base Band system for conversion to base-band signals. These signals are first converted to 70 MHz band and then split into Upper- and Lower-Sidebands using the tunable Fourth LO. This LO can be tuned between 50 − 90 MHz in steps of 100 Hz. At the base band, bandwidths of the 62.5, 125, 250, 500 KHz or 1, 2, 4, 8, 16 MHz can be selected. Another ALC is provided at the output of the baseband. Signal levels are kept at 0 dBm by this ALC before being fed to the correlator (see Section ??). This ALC also can, however, be bypassed.

For the purpose of astronomical observations, settings of the attenuators and the First and Fourth LOs are important. The combination of these two LOs determine the exact RF frequency used for observations.

2.4 Telescope parameters

The output of the individual antennas is a random signal composed of the signals from the source of interest in the sky, the sky background emission and the thermal noise generated by the various electronic components through which the signal flows. The output of the antennas and the receiver is usually expressed in terms of the temperature of a blackbody which will emit equivalent power. The system temperature (T^{sys}) of an antenna at a particular frequency, is equivalent to the total power from the antenna when it points towards a

Table 2.2: Table of GMRT system parameters

Band T^{sys} Sensitivity Field of view Resolution Max. angular
(MHz) (K)  (K/Jy) HPBW/1^{st} Null C.Sq./Full scale^{a}(arcmin)
150 450  0.35  2^{∘}.6/3^{∘}.1  7′/17′′  60
233 180  0.30  1^{∘}.6/2^{∘}.0  4′/11′′  44
327 100  0.35  1^{∘}.2/1^{∘}.4  3′/8′′  32
610  90  0.30  38′/46′  1′.7/4′′  17
1420^{b} 70  0.25  25′/30′  43′′/2′′  8

aComputed for a reliable data up to ∼ 100λ

bEffective antenna diameter is ∼ 33 m due to leakage from the mesh

blank sky. The power received by an antenna due to the celestial source alone is represented by the antenna temperature (T^{a}).

The normalized visibility amplitude from antennas 1 and 2 is given by

|V_{12}| = \sqrt{\frac{T_{1}^{a}T_{2}^{a}}{(T_{1}^{sys} + T_{1}^{a})(T_{2}^{sys} + T_{2}^{a})}}  (2.20)

where T^{sys} = T^{r} + T^{bg} + T^{spill}, T^{r} is the receiver temperature, T^{bg} is the temperature of the sky background emission, and T^{spill} is antenna spill-over temperature. An unpolarized point source of flux density S (in units of W m^{−2}Hz^{−1}) will result in T^{a} = A_{e}S/2k = ηS where A_{e} is the effective collecting area of the antenna, k is the Boltzman’s constant and η is the antenna sensitivity. For identical antennas and for the range of S where T^{a} ≪ T^{sys}, |V_{12}| ≈ T^{a}/T^{sys} ∝ S. T^{r}, T^{sys} and η are therefore important telescope parameters, which together determine the sensitivity of the telescope.

These and other astronomically relevant parameters of the GMRT are listed in Table ??^{1}. Fifth column is listed the angular resolution for both Central Square and full array.

2.5 The GMRT correlator

The prototype 4 and 8 antenna correlator, all of the initial design and most of the implementation of the final 30 antenna single sideband correlator currently in use and which was used for the observations for this dissertation were designed and built by the team consisting of C.R.Subramanya, A.Dutta, V.M.Tatke, A.Dikshit, R.K.Malik, U.Puranik, M.Burse and others. Further development for the second sideband correlator and maintenance is now done by Y.Gupta, M.Burse, S.Sirothia, C.P.Kanade, K.H.Dahimiwal, I.Halagalli and others, with contributions from A.Roshi. This section describes aspects of the GMRT correlator relevant from the point of view of astronomical observations. A more detailed description of the current correlator hardware design is given by ?. The correlator control and data acquisition software for potentially multiple sub-array mode of operation was designed and implemented by R.K.Singh and C.R.Subrahmanya. A detailed description of the current correlator control and data acquisition software is given by ?. The sub-array mode of operation is described by ?.

1Initial measurements of T^{sys} and sensitivity at 327 MHz were done by me and others. Later, these measurements were done by A.P.Rao, N.G.Kantharia and others and also by various users from the Raman Research Institute, Bangalore for L-band. The method used is described in Section ??

2.5.1 Overview

The GMRT back-end for interferometric observations is an FX-type digital correlator. The block diagram in Fig. ?? shows the various stages of the correlator. The first stage of this correlator consists of a set of four samplers per antenna - one for each of the two IFs per side-band of the antenna. Each antenna produces two IFs which can carry either the two orthogonal polarization signals or the same polarization from two different RF bands (as in the case of 233/610 MHz dual frequency feed). The analog to digital converter (ADC) of the samplers converts the input analog signal to 8-bit unsigned numbers. These 8-bit samples are converted to 6-bit unsigned numbers before being fed to the next stage of the correlator, referred to as the Delay and Data Preparation Cards, or the Delay/DPC system. These samples are further converted to 4-bit signed numbers in the Delay/DPC system (see the section on Samplers below), before being fed to the next stage of the correlator. This conversion from 8-bit to 4-bit samples is required since the VLBA FFT chips used in the correlator work with 4-bit signed numbers. Part of the compensating delay equivalent to integral units of correlator clock is applied in the Delay/DPC stage. Any residual delay (corresponding to a fraction of the correlator clock) is applied as a phase ramp across the band, after the signals have been Fourier transformed (see Section ??). The Delay/DPC stage is followed by the Fast Fourier Transform or the FFT stage which performs a 512point FFT corresponding to 256 point complex spectra (the other 256 points being the complex conjugate spectra). The output complex numbers are represented in 4,4,4-bit format consisting of two 4-bit numbers for the mantissa of the real and imaginary parts and a common 4-bit exponent.

Figure 2.9: Schematic diagram of a single correlator pipeline. Signals from each antenna pass through independent pipelines consisting of the Sampler, Delay/DPC, and the FFT sections. Signals from two independent pipelines are multiplied in the MAC section. The output of the MAC section is fed to the DAS card on the Host computer. The Host computer also controls the Delay/DPC, FFT and MAC hardware.

The correlation between signals from two antennas with the same polarization is referred to as the co-polar visibilities. This correlation is done by multiplying the antenna signals and averaging the result in the correlator. The output of the FFT stage is therefore fed to the Multiplier and Accumulation (MAC) stage of the correlator. Each MAC chip accepts 4 input data streams – 2 IFs from the two antennas. However each MAC can only handle a total of 256 channels per antenna. Therefore, either the number of channels per IF must be reduced from 256 to 128 or, only one IF with all the 256 channels must be fed to the MAC. This reduction of 256 channels for each IF to 128 channels to produce the co-polar visibilities is done by averaging two adjacent frequency channels. However, the GMRT correlator can also be used with a resolution of 256 frequency channels by sacrificing one of the polarization signals from the antennas.

The MAC output format consists of two 15-bit mantissa for real and imaginary parts and a common 6-bit exponent (this format is referred to as 15,15,6-bit format). The accumulators in the MAC stage provide the Short Term Accumulation (STA). Each STA cycle corresponds to 512 correlator clock cycles, required for reading the 512 points into the FFT section plus 4 clock cycles required to set-up the FFT cards before it can perform an FFT. Thus, each FFT cycle requires 516 correlator clock cycles. The correlator runs on an effective clock of 32 MHz and the STA accumulates the data for 4096 FFT cycles. Thus, the STA corresponds to an integration of (512 + 4) ∗ 4096/(32MHz) = 66 ms of time. (Strictly speaking, the samplers run on a 32 MHz clock. This is the shortest time resolution that the GMRT correlator can provide. The Delay/DPC system reads the input data at the rate of 32 MHz but output data rate is 32.125 MHz. The rest of the correlator operates at 32.125 MHz to effectively take care of the dead time corresponding to the 4 clock cycles required for FFT setup).

The data rates corresponding to a STA time interval is large (8 MBytes/sec) and difficult to sustain for any data recording system. The STA data therefore needs to be integrated further to reduce the data rate by accumulating in the Long Term Accumulation (LTA) stage of the correlator. This stage has not yet been implemented in the hardware and therefore, the STA stage has been set to integrate for 8192 FFT cycles corresponding to a minimum integration time of 132 ms. This brings down the data rates to 4 MBytes/sec and the data is further integrated in the software for an integration time than can be set by the user to produce the final LTA data. The output of the STA stage is the final product of the correlator and is produced in the form of three data streams from the three MAC racks per sideband.

All the three MAC output streams are fed to the Data Acquisition System (DAS), via a 16-bit bus. The DAS consists of a dual CPU PC running under the GNU/Linux Operating System (OS) with a data acquisition card on its PCI bus. The STA data from all MACs is acquired on this card at the rate of 4 MBytes/sec consisting of all the 256 channels (256 frequency channels with only one polarization, or 128 channels with both polarizations). The software device driver (which runs in the kernel space of the OS) and the supporting program (running in the user space of the OS) convert the input complex numbers from the correlator representation to the IEEE floating point representation. The software LTA is done at this stage for a time interval set by the user and the data rate further reduced. Through a series of network software, this data is transfered to another machine over the fast Ethernet to be recorded on the disk in what is referred to as the LTA-format (?). The last stage in the chain of software also provide facilities for further integration in time and frequency and for defining sub-arrays, etc. (the usage of the sub-array mode of the software is described by ?).

Samplers

The analog-to-digital converter (ADC) used in the GMRT samplers is an 8-bit flash ADC (?). The input to these samplers is the band limited gaussian random noise from the antennas, converted to base-band (BB) (corresponding to a frequency range of 0 to 16 MHz). The output power of the baseband system is proportional to the antenna temperature which is a function of the sky temperature. The sky temperature, can vary by as much as a factor of 4 − 5 between the Galactic plane and away from it. However, the samplers are designed to sample a fixed range of input signal. The BB output signals are therefore maintained at 0 dbm by the Automatic Level Controller (ALC) before being fed to the samplers. This corresponds to a peak-to-peak variation of ±1 V spanning the input random signal up to the six sigma level. In order to preserve the statistical properties of the input, the 2^{8} comparator voltage levels (in the ADC) must be optimally set such that the samplers neither saturate when the input voltage deviates by six sigma from the mean, nor sample the weaker signals too coarsely (corresponding to much smaller deviations from the mean). As of now, the 2^{8} voltage levels corresponding to 8-bit sampling are uniformly distributed across this range of voltage, corresponding to a voltage resolution of 7.8 mV (provisions however exist for a more sophisticated scheme to distribute the levels across the range of input signal). However, before being fed to the next stage of the correlator (namely the Delay/DPC stage), the 8-bits samples are converted to 6-bit samples by dropping the 2 least significant bits (LSB) of the samples. Effectively, this corresponds to 2^{6} levels covering the full range of ±1 V, with a resolution of 31.25 mV, but which still sample the full range of the input signal up to six sigma, although at a coarser resolution. These 6-bit samples are unsigned. Inside the Delay/DPC system these samples are further converted to 4-bit signed values via a look-up table. The look-up table is made such that the 2^{4} levels are again uniformly distributed for the entire range of the input signal (in this case, the 6-bit samples). Hence, effectively, the input signal with 6-bit resolution is further sampled at a coarser resolution of 4-bits without statistically altering the signal.

For the purpose of astronomical observations, this entire operation of converting the 8-bit unsigned samples to 4-bit signed samples can be ignored and the GMRT samplers can be treated as an effective 4-bit samplers.

Long Term Accumulation (LTA) and time keeping

This section describes the mechanisms used in the correlator data acquisition software for deriving accurate time information. This is essentially a description of the work done by ?.

The input data to the DAS is averaged for a length of time set by the user to produce the long term accumulated (LTA) data. This interval is typically set to 10 − 20 sec. The LTA operation is currently done in the software and may be moved to hardware in future (if required).

As mentioned earlier, a synthesis radio telescope like the GMRT utilizes the earth rotation to synthesize an effective large aperture. To keep the array instantaneously phased, the time varying geometrical delay must be continually compensated. The phasing of the array is therefore a time critical operation requiring accurate time keeping. Accurate time information is also required for proper pointing of the antennas and tracking of an astronomical source. Stamping of astronomical data with accurate time is therefore very important.

Absolute time for the GMRT is kept using the real time clock (RTC) of the GMRT correlator control computer. This clock is synchronized with the GPS time using a GPS receiver. The GPS and correlator system clocks are used to remove any time jumps and/or slow drifts of this real time computer clock as described below. This time stamping of the visibility data in the GMRT correlator/data acquisition achieves an accuracy of ∼ 100 μsec.

The correlator provides a synchronization pulse to the DAS to indicate the start of each STA cycle via an STA interrupt. This information is also supplied to the DAS via one of the bits of the data bus, referred to as the data synchronization bit. The DAS software uses this information to (1) do a consistency check (2) determine the start of the STA data in a stream of continuous data flowing on the data bus from the MAC. The DAS card also receives an interrupt signal at the start of each minute from the GPS receiver. The interrupt handler (the software which does time critical operations when a hardware interrupt is received) for both these interrupts (STA and GPS interrupts) reads the PC time from the PC RTC at each interrupt and maintains a list of corresponding PC time stamps. The list of PC time stamps recorded at each GPS interrupt is then examined for a constant difference of 1 minute. A continuous series is selected such that the time difference between successive samples is accurate to 100 μsec. This series of PC time stamps is referred to as a series of “good” GPS-interrupted time stamps. This series is used to set up a linear equation between the GPS time and the PC time. Since GPS time can be easily converted to the local time standard (Indian Standard Time or IST), this equation essentially converts the PC time to accurate IST time. This equation provides a first order calibration of the PC time, and takes care of any short glitch in the PC time (which can happen due to variety of reasons including overloading of the PC bus). Similarly, the PC time is recorded at each STA interrupt. This list of STA-interrupted PC time stamps is also examined and a continuous series selected such that the time difference between successive PC time stamps is equal to one STA cycle, to an accuracy of 100 μsec. This series of “good” PC time stamps is used to set up a linear relation between the PC time and STA time. The PC time to IST time equation is then used to convert the STA time to IST time, and is also used to tag each STA data block with a sequence number.

The three sources of timing information to the DAS (1) the STA interrupts (2) the GPS interrupts, and (3) the data synchronization bit, all provide time information with respect to the PC RTC. In the above scheme, on a short time scale, unless all these three sources produce drifts and/or glitches, time stamping of the data will remain accurate to 100 μsec. Since all these are independently running clocks, the probability of all three producing error at the same time is very low and it has been shown that the above time stamping scheme is quite robust to short time scale glitches and time drifts.

To account for slow drifts in the PC time, an attempt is made to set up a new linear equation between the STA sequence number and PC time after every 16 STA cycles. The new relation is not accepted unless it matches with the previous one within 100 μsec. Similarly, a new relation is set up between GPS and PC time at each GPS interrupt.

On a longer time scale, an error can occur due to some catastrophic error in either of these sources (e.g. the interrupts not arriving at the PC due to hardware failures). If the DAS software cannot set up the new equations for more than a threshold time interval, it is assumed that an irrecoverable error has occurred rendering the current equations invalid. In such a case, the DAS sets up fresh equations and the data between such an event and the time interval required to set up valid equations is unreliable and is flagged. In practice, however, such events are very infrequent.

However, a slow drift in the PC RTC, with respect to which all three sources of timing information are measured, can produce a drift in the final IST time stamps in the data. Data blocks are expected to arrive at the DAS at a pre-determined constant rate. Data blocks themselves therefore can be effectively used as yet another clock, which is independent of the PC time. Any drift of the PC clock will show up as a consistent shift in the equations between the GPS and PC time and between STA and PC time with respect to the arrival of the data blocks. Hence, any consistent error in the arrival of the data blocks measured with respect to the IST time, derived from the two linear equations, will indicate a drift in the PC time. This fact is used to monitor a slow drift in the PC time over the time scale of setting up new equations.

The PC time is also synchronized to the minute pulse from the GPS. Errors in the PC RTC less than half a minute can therefore be corrected and PC clock synchronized to the GPS clock. However if the PC RTC is in error by more than half a minute, this synchronization will result into minimum of 1 min in the PC RTC. It is therefore important to set the PC RTC to within 1/2 min of the GPS time.

2.5.2 Delay compensation

As mentioned earlier, the compensating delay (equal to τ_{g} + τ_{F ix}; see Section ??, page ??) which needs to be applied to one of the antennas of an interferometer is applied in the GMRT correlator in two stages. A delay equivalent to an integral multiple of the correlator clock (τ_{Int}) is applied in the Delay/DPC section of the correlator. The input data stream is copied into a dual port RAM at the location given by the write-counter. Data is read simultaneously from this RAM from the location given by the read-counter. The offset between the read- and the write-counters for this RAM is maintained such that the readcounter lags behind the write-counter. Since the output samples are read with a time delay (equal to the difference between the counters multiplied by the correlator clock cycle), the output data stream corresponds to the input data stream with a time delay. The time delay, however, can only be in multiples of the correlator clock cycle. The residual delay, corresponding to a fraction of the correlator clock cycle is applied in the fractional sample time correction or FSTC operation. The last stage of the FFT butterfly network provides a facility to apply a channel dependent phase. The frequency channel dependent time varying, phase corresponding to this residual delay, represented by τ_{F ST C}, is applied as a linear phase gradient across the band as

τ_{F ST C}(t) = \frac{1}{2π} \frac{dϕ}{dν}|_{t}  (2.21)

Note that τ_{F ST C} includes the residual delay due to delay resolution in the Delay/DPC system of the correlator plus the channel dependent residual delay of Equation ??.

The output of the FFT stage of the correlator is a set of 256 independent complex numbers. These complex numbers are represented by three 4-bit numbers; one each for the mantissa of real and imaginary parts and one for a common exponent. The complex gains, applicable at the last stage of the FFT butterfly network, are represented by 5 bits each for the real and imaginary parts but has no exponent bit. Thus the channel dependent phase gradient for the FSTC is also limited to a 5-bit representation.

The FFT stage of the correlator performs a real-time Fourier transform of the input signal effectively splitting the input bandwidth of Δν into 128 frequency channels, each of width Δν/128 (the FFT stage of the correlator can be treated as a set of 128 filter banks). The time series from each of the 128 frequency channels from an antenna, are then multiplied with the corresponding channels from all other antennas, before being integrated in the MAC section of the correlator. The effective input bandwidth, as seen by the multiplier is therefore Δν/128. For the GMRT, the maximum value of Δν is 16 MHz corresponding to a maximum channel width of 125 KHz, giving a fringe washing function of width ∼ 8 μsec. Therefore, for the GMRT correlator, the residual delay must remain less than a fraction of this width (typically less then few micro seconds).

2.5.3 Imaging modes

In the final double sideband correlator, in the continuum, non-polar mode, the correlator can be used to record the two co-polar visibilities (the nominal RR and LL correlations) per antenna with a full bandwidth of 32 MHz (both sidebands). In the current single sideband correlator only one sideband of 16 MHz can be processed. In the full polar mode, which will be available with the dual sideband correlator, the cross polar visibilities (namely RL and LR) cal also be recorded. Since the correlator can handle only 256 channels per antenna at the MAC stage, the cross polar mode can be used with only one of the sidebands with a maximum bandwidth of 16 MHz.

The GMRT correlator naturally produces spectral visibilities with a maximum of 256 channels across the entire observing band, if only one polarization is used, or with 128 channels, if both polarizations are used. For normal continuum observations, the 128 channels across a 16 MHz band provide a channel resolution of 125 kHz. For observations where bandwidth smearing is not important (and in the absence of RFI), these channels can be collapsed on-line to produce continuum visibilities. At lower frequencies where primary beams are large, bandwidth smearing can be important for sources away from the phase centre. Also, at frequencies below 610 MHz, intermittent RFI is always a possibility. To reduce bandwidth smearing and to detect and flag narrow band RFI-contaminated data, all the 128 channels are usually recorded. Provision for frequency averaging before recording does however exist and can be used where RFI and bandwidth smearing problems are not perceived to be serious.

For spectral line observations, channel resolution can be increased by controlling the sampling rate of the input signal. The sampling rate can be changed between 32 MHz and 0.125 MHz in steps of two. This corresponds to an effective bandwidth between 16 MHz and 0.25 MHz with a frequency resolution between 125 kHz and ∼ 1.95 kHz respectively.

2.6 Baseline and fixed delay calibration

A synthesis radio telescope measures the two-dimensional spatial frequency spectrum of the source structure. Instantaneous projected separations between the elements of the interferometer in the uvw-frame determine the spatial frequency being sampled by the antenna pairs. The projected separation between the antennas, given by w, gives rise to the geometrical delay which needs to be compensated by delay tracking before the signals are multiplied. The value of w is given by

w = [X_{ij} cos(H ) − Y_{ij} sin(H )] cos(δ) + Z_{ij} sin(δ)  (2.22)

where (X_{ij}, Y_{ij}, Z_{ij})=(X_{i}−X_{j}, Y_{i}−Y_{j}, Z_{i}−Z_{j}). The geometrical delay is therefore a function of the relative antenna positions. Precise measurement of the relative locations of the antennas is hence important for phasing the array, which is necessary for imaging with such a telescope.

The radio frequency (RF) signals from the two orthogonal feeds of the antenna are converted to two separate intermediate frequencies (IF) and brought to the Central Electronics building (CEB) for correlation via the optical fiber cables. The fixed delay suffered by the signals from each antenna varies from antenna to antenna since the physical length of the optical fibers to various antennas differ. This fixed delay is largely constant, showing small and slow variations due to changing ground temperature. Since the optical fiber cables are dispersive, any relative fixed delay between antenna pairs results in a time invariant phase ramp across the band in the visibility data. This phase ramp must also be removed or calibrated before averaging the channels to produce the continuum visibilities or before being used for imaging.

The following two sections describe the methodology used and results of baseline and fixed delay calibration.

2.6.1 Baseline calibration

Historically, the GMRT antenna positions were first determined using theodolite measurements. These were refined using P-band observations following the procedure laid down by ?. Later, dual frequency GPS measurements (?) were done to independently determine the antenna co-ordinates.

The GPS measurements provided the antenna co-ordinates relative to the reference GPS antenna, to a quoted accuracy of ∼ 2 cm. However, monitoring the phase as a function of hour angle at 327 MHz indicated errors in excess of few meters for some antennas. These GPS co-ordinates were then further refined using P-band observations of celestial sources. Antenna based phases were determined using the GMRT off-line program rantsol (?) from a continuous (∼ 7 hours) tracking of 3C48 at 327 MHz. The antenna based phases were modeled as a function of hour angle to measure the relative antenna co-ordinates (see below and ?). The set of co-ordinates from these measurements were accurate to ∼ 1 m for the arm antennas and ∼ 0.1 m for the central square antennas. The phase variations at 327 MHz due to other factors (∼ 30 arcsec error in antenna pointing which was later corrected, ionospheric contributions, etc.) did not allow determination of X and Y to better accuracies. The Z co-ordinate could not be calibrated at 327 MHz since not enough 327-MHz calibrators could be found which could cover a large declination range but were close enough in hour angle. The proximity of calibrators in hour angle for Z calibrations was necessary to eliminate any unwanted scatter in the phase as a function of declination due to residual errors in the X and Y co-ordinates (see page ??).

These co-ordinates were then further refined using L-band observations (?). Since the residual phase is proportional to the projected baseline length measured in units of the wavelength of the incident radiation, L-band is the best frequency to determine the residual co-ordinate errors in the antenna positions. For this purpose, VLA L-band calibrators 0217+738 and 1125+261 were tracked for several hours at 1280 MHz to compute the antenna based phases. Corrections of 0.5 − 1 m, consistent with the residual co-ordinate errors from the 327-MHz measurements, were found for a few antennas. The final co-ordinates for the Central Square antennas are now known to an accuracy of ≈ 0.05 m. The residual phases for arm antennas correspond to position errors of 0.02 − 0.36 m. These errors do not repeat from day-to-day and are also different for different sources indicating that the residual phases are probably not due to antenna position errors.

The procedure used

Assuming no errors in the antenna pointing (ΔH = Δδ = 0), the antenna based phase for an antenna with a position error of (ΔX, ΔY, ΔZ) with respect to a reference antenna located at the origin ((X, Y, Z) = (0, 0, 0)), as a function of the hour angle and declination is given by

ϕ = 2π \frac{ν_{RF}^{o}}{c} [ΔX cos(δ) cos(H ) − ΔY cos(δ) sin(H ) + ΔZ sin(δ)] + 2πτ_{F ix}ν_{IF}  (2.23)

Table 2.3: List of antenna measured antenna co-ordinates and fixed delays. All positions and fixed delays are measured with respect to antenna C02. Currently, same fixed delays are set for both the IF signals from an antenna. With the new version of Delay/DP C system (currently under development), the fixed delays for the two IFs will need to be calibrated separately.

Ant. No. Name  X(m)  Y (m)  Z(m) Fixed delay(m)
00  C00  6.95  687.88  -20.04  -497.89
01  C01  13.24  326.43  -40.35  179.15
02  C02  0.00  0.00  0.00  588.10
03  C03  -51.10  -372.72  133.59  480.47
04  C04  -51.08  -565.94  123.43  80.98
05  C05  79.09  67.82  -246.59  84.89
06  C06  71.23  -31.44  -220.58  -177.43
07  C08  130.77  280.67  -400.33  -463.19
08  C09  48.56  41.92  -151.65  259.30
09  C10  191.32  -164.88  -587.49  -442.73
10  C11  102.42  -603.28  -321.56  -284.13
11  C12  209.28  174.85  -635.54  -1044.71
12  C13  368.58  -639.53 -1117.92  -1347.68
13  C14  207.30  -473.71  -628.63  -423.23
14  E02  -348.04 2814.55  953.67  -3877.18
15  E03  -707.58 4576.00 1932.46  -7742.26
16  E04 -1037.11 7780.69 2903.29  -13748.08
17  E05 -1177.37 10200.00 3343.20  -20440.99
18  E06 -1571.32 12073.46 4543.13  -25151.18
19  S01  942.99  633.92 -2805.93  -5486.16
20  S02 1452.85  -367.30 -4279.16  -9232.06
21  S03 2184.54  333.03 -6404.96  -13826.41
22  S04 3072.86  947.68 -8979.50  -18670.27
23  S06 4592.71  -369.04 -13382.48  -27847.16
24  W01 -201.50 -1591.94  591.32  -1336.69
25  W02 -482.67 -3099.41 1419.39  -4642.84
26  W03 -992.01 -5199.90 2899.11  -9608.61
27  W04 -1734.55 -7039.03 5067.53  -15280.83
28  W05 -2706.09 -8103.13 7817.14  -21583.03
29  W06 -3102.11 -11245.60 8916.26  -29257.26

where ν_{RF}^{o} is the frequency of the centre of the RF band, H is the Hour Angle, δ is the declination of the phase center, τ_{F ix} is the fixed delay suffered by the signal at the IF frequency ν_{IF} and c is the speed of light. The orientation of the X, Y, and Z axis is shown in Fig. ??.

As can be seen from Equation ??, an error in Z will contribute a constant phase for a fixed value of δ. It is therefore necessary to observe a number of sources at different declinations to distinguish between the phase contributed by the terms involving ΔZ and τ_{F ix} (both of which are independent of H).

The terms involving ΔX and ΔY in Equation ?? have a sinusoidal dependence on H. Hence, by tracking a point source for several hours (to get coverage in H while keeping δ constant), the left hand side of the above equation can be modeled as

ϕ = C + A sin(\frac{2π}{24.0}H + 2πψ)  (2.24)

where C is a constant and H is in unit of hours. Equating this to the RHS of Equation ?? the expressions for ΔX and ΔY (in meters) can be written as

ΔX = \frac{A sin(ψ)c}{cos(δ)2πν_{RF}^{o}}  (2.25)

ΔY = \frac{A cos(ψ)c}{cos(δ)2πν_{RF}^{o}}  (2.26)

A and ψ can be measured by fitting Equation ?? to the antenna based phases, with A, C and ψ as the parameters of the fit. Equations ?? and ?? then gives the antenna position errors along the X- and Y-axis. ϕ, which is the antenna based phase computed with respect to the reference antenna located at the origin, was computed as a function of Hour Angle using the program rantsol. Equation ?? was then fitted to the phases from individual antennas to derive the values of C, A and ψ and Equations ?? and ?? used to derive the corrections for the X and Y co-ordinates of the antennas.

The ΔZ correction requires observation of point sources at various declinations. A set of VLA L-Band calibrators with L-band flux densities > 1 Jy and covering a declination range of ≈ ±40^{∘} were used to measure ΔZ. Since the observations of each of these calibrators were separated in time, any residual error in the X and Y co-ordinates would reflect in the data as an undesirable spread of the phases as a function of declination. To minimize the effects due to residual errors in X and Y co-ordinates, these calibrators were chosen to Table 2.4: List of L-band VLA calibrators used for ΔZ calibration

Source  RA  Dec Flux density
(J2000)  (J2000)  (Jy)
0828 − 375 08^{h}28^{m}04^{s}.8 −37^{∘}31′06′′.3  2.9
0735 − 175 07^{h}35^{m}45^{s}.8 −17^{∘}35′48′′.4  2.6
0820 − 129 08^{h}20^{m}57^{s}.5 −12^{∘}58′59′′.2  1.5
0725 − 009 07^{h}25^{m}50^{s}.7 −00^{∘}54′56′′.5  2.4
0739 + 016 07^{h}39^{m}18^{s}.0 01^{∘}37′04′′.6  1.8
0825 + 031 08^{h}25^{m}50^{s}.3 03^{∘}09′24′′.5  1.1
0745 + 101 07^{h}45^{m}33^{s}.1 10^{∘}11′12′′.7  3.3
0738 + 177 07^{h}38^{m}07^{s}.4 17^{∘}42′19′′.0  2.2
0842 + 185 08^{h}42^{m}05^{s}.1 18^{∘}35′41′′.0  1.4
0741 + 312 07^{h}41^{m}10^{s}.7 31^{∘}12′00′′.2  2.0
0713 + 438 07^{h}13^{m}38^{s}.2 43^{∘}49′17′′.0  2.2

be within ∼ 1^{h} of each other in Right Ascension. The Z co-ordinate can then be found by fitting ΔZ sin(δ) to the antenna based phase as a function of declination. The final antenna co-ordinates, measured using this procedure, are tabulated in Table ??. The list of calibrators used for this purpose is given in Table ??. A typical phase variation as a function of declination, before and after correcting for the Z co-ordinate, is shown in Fig. ??. The variation of phase as a function of HA derived from ∼ 5h long observation of 3C286 (28 Jy at 327 MHz), for a representative set of Central Square and arm antennas is shown in Figs. ?? and ?? respectively. The source of the short term drifts of ≈ 5 − 10^{∘} is likely to be the ionosphere. Phase variations over similar time scales and magnitude have been seen at the VLA and have been, to some extent, corrected using GPS based measurements of the variation in the ionospheric total electron content (?).

The estimated accuracy of the antenna co-ordinates, derived from the variations in the phase as a function of hour angle and declination is ∼ 5 cm. This will produce a maximum phase variation of ∼ 0^{∘}.2 per degree in declination and ∼ 5^{∘} per hour in hour-angle at 1420 MHz due to errors in the antenna co-ordinates. Thus, observations of a calibrator located 20^{∘} away in the sky from the target source every half-an-hour, would result in a phase error of a few degrees when the antenna based complex gains derived from the calibrator scans are transferred to the data on the target source. These figures will be scaled down by a factor of ∼ 4 at 327 MHz. At this level, phases of many antennas drift in an unsystematic manner and constitute the source of dominant phase errors. The residual phase errors due to errors in the antenna co-ordinates after fringe stopping are therefore negligible.

Figure 2.10: A typical antenna based phase variation due to an error in the Z co-ordinate of the antenna, before and after the application of co-ordinate correction. The ‘+’ symbol marks the measurement of an antenna based phase before the correction and the ‘×’ symbol represents the measurement taken after the correction.

2.6.2 Fixed delay calibration

The geometrical delay τ_{g} is suffered by radiation at the RF frequency ν_{RF} while the dominant fixed delay is suffered at the IF frequency ν_{IF}. The compensating delay is applied at the baseband (BB) frequency ν_{BB} at the correlator. The total time delay applied at the correlator, (τ_{corr}) is therefore related to τ_{g} and τ_{F ix} as

τ_{g}(ν_{RF}^{o} + ν_{i}) + τ_{F ix}(ν_{IF}^{o} + ν_{i}) = τ_{corr}(ν_{BB}^{o} + ν_{i})  (2.27)

where ν_{i} is the centre frequency of the i^{th} frequency channel and equal to iν where Δν is the channel width. ν_{RF}^{o} , ν_{IF}^{o} and ν_{BB}^{o} are the centre frequencies of the RF, IF and the Figure 2.11: A typical antenna based phase variation at 327 MHz for a representative set of Central Square antennas. The y-axis represents the phase in degrees. The variation in phase over time scales of hours is probably due to ionospheric changes. The phase jump seen in C03 at around HA= 1^{h} is either due to a phase jump in the local oscillator or due to errors in the FSTC.

base-band respectively. Noting that ν_{BB}^{o} = 0 the above equation can be written as

τ_{corr} = (τ_{Int} + τ_{F ST C}) = (τ_{g} + τ_{F ix}) + \frac{τ_{g}ν_{RF}^{o} + τ_{F ix}ν_{IF}^{o}}{ν_{i}}  (2.28)

τ_{Int} corresponds to the time delay applied at the Delay/DPC stage while τ_{F ST C} corresponds to the residual delay applied in the FSTC operation (see Section ??).

In terms of the various frequency conversions in the signal flow, the RF band, for the purposes of delay compensation, can be written in terms of the first and the second local oscillator frequencies (which convert the RF signal to IF signal and the IF signal to baseband signal respectively) as ν_{RF}^{o} = ν_{LO1} + ν_{LO2} where, ν_{LO1} and ν_{LO2} are the the first and the second local oscillator frequencies respectively.

The residual phase across the band after delay compensation can therefore be written as Figure 2.12: A typical antenna based phase variation at 327 MHz for a representative set of arm antennas. The y-axis represents the phase in degrees. The long term systematic variation corresponds to a position error of few centimeters but the corrections do not repeat for different days.

\frac{ϕ}{2π} = (τ_{g} + τ_{F ix} − τ_{Int} − τ_{F ST C})ν_{i} + τ_{g}(ν_{LO1} + ν_{LO2}) + τ_{F ix}ν_{LO2}  (2.29)

Assuming that τ_{Int} + τ_{F ST C} accurately compensates for τ_{g}, τ_{F ix} can be written as

\frac{1}{2π} \frac{∂ϕ}{∂ν} = τ_{F ix}  (2.30)

The largest contribution to the fixed delay is due to the propagation delay in the optical fibers from the antenna base to the Central Electronics Building (CEB). These delays were measured by computing the antenna based complex gains for each of the 128 channels using the off-line program rantsol, for a strong point source observed at 327 MHz using the full band 16 MHz. This essentially provided the antenna based amplitude and phase across the band. The slope of the phase across the band was measured and τ_{F ix} derived using the Equation ?? (the slope of phase as a function of frequency). The fixed instrumental delays thus measured are also listed in Table ??. The phase across the band before and after the Figure 2.13: Antenna based phases across the band are plotted as a function of channel number before the fixed delay correction. The y-axis for each panel corresponds to the phase in degrees and the channel width corresponds to ∼ 128 kHz.

Figure 2.14: Antenna based phases across the band are plotted as a function of channel number after the fixed delay correction. The y-axis for each panel corresponds to the phase in degrees and the channel width corresponds to ∼ 128 kHz. fixed delay correction is shown in Figs. ?? and ?? respectively for a representative set of antennas.

For interferometric observations, frequency averaging (to produce continuum or multichannel continuum visibilities) is done after correlation and only the relative fixed delays are important. Since the same set of reasonably identical filters are selected at all antennas, the relative change in the fixed delays due to change of filters is not large. Also, since the ground temperature variation is similar from antenna to antenna and slowly varying over the scale of the array, its contribution to change in delays is not large. Although the delay component due to the filter selection and that due to diurnal variations must ultimately be tabulated and used for the delay compensation software, it is not a limiting factor and can be easily calibrated. The phase calibrators used for the continuum mapping observations used in this dissertation were strong (> 5 Jy) and were observed every half-an-hour. The antenna band shapes were computed from the data on these calibrator scans and the interpolated gains for each channel applied to the visibilities of the target source. This provided the calibration for changes in the delay due to filters (small and fixed as function of time) and diurnal variations (small and slowly varying in time).

Data analysis software

This chapter describes briefly the off-line data analysis software, developed to satisfy the data analysis needs for debugging the GMRT as well as for developing new algorithms for calibration and imaging at low frequencies. A modular, hierarchical software environment was therefore developed over the course of this dissertation. This software system is organized in the form of general purpose libraries at the lowest layer and a suit of general purpose application programs at the top-most layer. This design required much extra work, but it was perceived to be well worth the effort with the hope that ultimately, at the highest software layer, a large number of programmers would be professional astronomers writing complicated (but interesting) numerical analysis code.

The entire software now constitutes in excess of 50,000 lines of C++ code and in excess of 10,000 lines of C and FORTRAN code. Some others in the GMRT group have used these general purpose tools to write more software. In a software development cycle, the number of bug reports per unit of time (week or month) is generally considered to be an indicator of the stability of the software. Assuming this to be a good measure, the libraries are now well debugged and stable (however, a low rate of bug reports could also be due to lack of sufficient number of careful users).

3.1 Introduction

The correlator output is used for on-line monitoring of the health of the array (cross and self correlated band-shapes, closure phases, amplitude and phase of various baselines, antenna based amplitude and phase, system temperature (T^{s}), antenna temperature (T^{a}) variations as a function of time, etc.) as well as for on-line phasing of the array for the phased array mode. Recorded data is extensively used for the measurements of various telescope parameters (baseline calibration, fixed delay calibration, antenna pointing calibration, beam shape measurements at various frequency bands, measurement of T^{s}, T^{a}, antenna sensitivity (η) and their variation as a function of time/elevation, etc.). All this requires extensive data analysis and data display capabilities to be easily available for on-line and off-line usage. The GMRT correlator produces 435 cross correlations plus 30 self correlations corresponding to 465 complex numbers per integration time per IF per frequency channel. If all the 128 frequency channels are recorded, this corresponds to 465 baselines × 128 channels × 2 IFs × 2 floating point numbers of size 4 bytes each= 952320 bytes of data per integration cycle. With a typical observing time of 8 hours with an integration time of ∼ 20 seconds, this corresponds to a database of size ∼ 1.5 GBytes. Hence the software should also efficiently handle such large multi-dimensional database and allow easy browsing through the database.

The visibility data is an explicit function of the baseline length (projected separation between the antennas). Implicitly however, it is a function of many other parameters like local sidereal time (LST), observing frequency, the antenna co-ordinates, the co-ordinates of the phase center, compensating delay applied to the various antennas, etc. Most of the processing (on-line as well as off-line) requires efficient access to the visibility data potentially as a function of many of these parameters. During the debugging stage of the telescope, it is also important to have a short turn-around time between observations and results. This in turn demands a fairly sophisticated data analysis package to analyze the data recorded in the native recording format as well as evolve continually with the potentially rapidly changing environment (including the format itself!). Preferably, such a data analysis package should also be usable on-line. The application programs must also provide a user interface for the software to be usable by a larger community.

Section ?? describes the design of the software system which was designed to meet most of the above mentioned requirements. Section ??^{1} briefly describes the design of the low level libraries used for accessing the visibility database. Section ?? describes the design of the user interface, while Section ?? describes some of the application programs used in the observations and data analysis for this dissertation.

3.2 The software design

The GMRT off-line data analysis package was designed to (1) provide efficient means for browsing the multi-dimensional dataset represented by V (b_{ij}(t), ν, τ, ∂τ/∂t, ...) (2) be robust to changes in the database format (3) provide a higher level astronomically useful view of the data, (4) provide a programming environment which can be used by knowledgeable astronomers to write novel instrumental debugging, data calibration and analysis tools, (5) provide easy means of data selection and (6) provide a simple user interface to the data analysis program.

1A description of the latest application programs and libraries is available via http://langur.ncra.tifr.res.in/_{}˜ sanjay/Offline

The design for the entire software was therefore dominated by the following basic design goals:

• the application programming interface (API) be such that the application developer need not manage software/book keeping details not relevant for the goal in mind.

In terms of the design of the libraries, this translates to a modular software with the API of each module carefully designed to mesh well with the other modules

• to keep the user interface simple and easy (but robust) while still providing mechanisms for more general, possibly more complicated usage by more enterprising users.

In terms of software development, this translates into implementing generalized software solutions with a programmable interface.

• it should be easy to supply the results from one application program to another.

With this, it is often possible to effectively perform a complicated data processing/filtering operation using a number of stand-alone programs without writing a monolith program (which is difficult both to write as well as maintain).

• it should be easy to display and view the data and the results of data processing.

Since it is virtually impossible to write a data display software which satisfies all present and future needs, it is best to design the data analysis software such that external stand-alone display software can be used. This way, the task of development of display software (requiring very different software skills and professional motivation) is separated.

This also allows the freedom to use a display software that one is most familiar with and satisfies the needs. A large number of stand-alone plotting/data display software packages are now freely available. With such a design, one is not restricted to use locally designed specific display software allowing enormous scope for creativity and an unrestricted, independent development path.

The Object Oriented design methodology was used to design a hierarchical software where each layer hides the details of the layers below it via the interface presented by each layer. Data access, manipulation, extraction and selection mechanisms have, wherever possible, been implemented in a general form in the libraries (see Section ??) while keeping their usage as simple as possible at higher levels via their API.

The package is organized in the form of three layers of libraries over which a suite of application/data analysis programs are built. The lowest layer has been written in the C programming language while the rest of the software have been written in C++. With a lightweight wrapper (also written but almost never used), this lowest layer provides a FORTRAN interface for basic access to the LTA database. The user interface was designed as an embedded shell and is implemented as a set of four separate libraries including an arbitrary mathematical expression parser. An application using this interface provides an interactive shell which is largely independent of any external files.

Most application programs have been written as filters (which operate on an LTA database and produce an LTA database) . The user interface provides easy mechanisms for piping such filters to effectively perform complicated tasks.

3.2.1 On-line usage of the software

The correlator output is first written in a shared memory resource provided by POSIX compliant operating systems. The program record, which is part of the Data Acquisition Software, converts the data in the shared memory format to the LTA-format. This program was modified to write the output LTA formatted visibility data to the standard output instead of writing to a disk file. As mentioned above, most off-line programs have been written to accept the input data from a pipe. This feature of the off-line software system can then be used, in combination with the modified record, for on-line data analysis by piping the data to the programs from the shared memory. Thus, all programs used for off-line data browsing, data validation, automatic detection of bad data, etc. (see Sections ??, ??, ??, ??) can also be used as on-line programs. The locally developed data display/plotting software also accepts plotting instructions and arbitrary data via UNIX sockets. The output of the off-line programs, along with embedded plotting instructions, can be easily supplied to the display software over UNIX sockets. Thus, with a combination of the data piping facility, modified record and the display software, the off-line software can be effectively used for on-line data display.

3.3 Data manipulation libraries

The GMRT visibility database is recorded in the LTA format. The database is always multi-channel and is composed of zero or more scans. Each scan represents the data for one pointing direction and is composed of zero or more data records. The database begins with an ASCII header referred to as the global header which carries information about the observations common to all the scans. Each scan begins with an ASCII header of its own, referred to as the scan header. The scan header constitutes information relevant for the scan alone (e.g. source RA, DEC, object name, information about the frequency contents of the data, time reference information, etc.).

The LTA data manipulation libraries are organized in three layers. The lowest layers is written in C and is responsible for parsing and reading/writing the LTA database headers. It is also responsible for maintaining the consistency of the output LTA database. The interface for reading from and writing to the global and scan headers in the memory is provided by this layer. Higher level C and FORTRAN bindings are provided via light weight wrappers, which hide the details of managing the linked lists etc. However, using these interfaces, only one LTA database can be opened in a single application. Using the C++ interface, a single application program can handle any number of databases. This interface also provides many more astronomically useful features while manipulating the visibility database, and is the recommended interface to use. These libraries maintain two copies of the global header in the memory as a doubly linked list for the entire lifetime of the application (unless explicitly destroyed). Hence all changes, if any, in the output are represented in the output-header in the memory, which becomes the header of the output LTA database. One of them represents the input database while the other applies to the output database. However, only the latest scan header is maintained in the memory.

At even higher level, the C++ classes (also referred to as C++ objects) called LTAFMT, LTAVIEW and LTARec encapsulate the LTA format. Any number of these objects can be instantiated in a single C++ application allowing the handling of multiple LTA databases. These objects, briefly described below, were used in application programs for data calibration and testing some automatic data filtering algorithms. There are other C++ objects which were used for maintaining and manipulating antenna gains and other tables (in the memory and on disk), which are not described here. Those are described in a set of NCRA Technical reports.

3.3.1 The LTAFMT Object

The LTAFMT object is the base class for handling LTA database. This object encapsulates the functionality which is expected to be a common factor between all classes which manipulate LTA databases and perform higher level operations (e.g. see the LTAVIEW object below). It provides the I/O interface to the LTA headers, and presents the visibility data as a two dimensional array of complex numbers. The data-records, along with the visibility data, also carry other auxiliary data (e.g., parameters for fringe stopping, fringe rotation, FSTC, etc.). The interface to this auxiliary data is also provided by this object.

All higher level objects derived from this class (also referred to as derived classes) would have all the functionality of LTAFMT object plus the additional functionality of the inherited class. Almost all the methods of the LTAFMT (functionally, the services offered by this object), have been declared as virtual which allows the derived objects to modify the behavior of these methods. A redefinition of these methods in a derived object would override their functionality. This leaves the scope for development of higher level objects with minimal effort.

3.3.2 The LTAVIEW object

This is an object derived from LTAFMT and is designed to provide a view of the data with selection on the source name and integration in time and/or frequency applied to the data.

With a source selection, this object behaves exactly as LTAFMT except that it will give a view of the database with scans only of the selected source. The source selection can be specified via a POSIX egrep compliant regular expression (with the exception that ’+’ regular expression operator has been disabled since its interpretation as a regular expression operator causes conflict with the astronomical source naming convention where ’+’ appears as a valid character in the name). Data selection based on scan number is also possible.

Vector, scalar and robust averaging algorithms are built into this object and can be used to average the data in time or frequency. The averaging interval is supplied as the number of seconds of effective integration required. LTAVIEW will then average the data for the closest possible interval of time. This averaging of the data is, however, restricted to the scan and does not cross the scan boundary. Most of the application programs use this object for data manipulation.

3.3.3 The LTARec object

Data recorded in the LTA database is composed of the data timestamp and the auxiliary data, followed by the real and imaginary parts of the visibility and self correlation data for each baseline for all recorded frequency channels. The LTAVIEW and LTAFMT objects provide access to the raw contiguous buffer of floating point numbers in the memory representing the complex visibility data record.

The LTARec object provides an astronomically useful view of this raw buffer. It is initialized using an LTA database object (LTAFMT or LTAVIEW). It can then be used to access the data timestamp, auxiliary data indexed by the antenna number, and the visibility data as a two dimensional array of complex numbers. The array indexing operator (the ’operator[]’ in C++ syntax) is overloaded in this object to allow indexing inside the array of visibility with the baseline and channel number as the index. It also provides services for mapping between the baseline number and the two antenna numbers which constitute the baseline.

3.4 The user interface for off-line programs

The user interface libraries provide an embedded interactive shell in the application programs – the user interface is part of the compiled binary code of the application programs. In an interactive session, the user is presented with a list of keywords corresponding to the parameters which control the behavior of the application. The user can set/reset, save, load and transfer values from one keyword to another, etc. in the interactive shell. Each keyword can potentially take multiple values which can be supplied as a set of comma-separate values. Numerical values can be expressed as arbitrary mathematical expressions which are parsed at run-time.

The keywords presented to the user are detected automatically at runtime. Since the code for the user interface is part of the binary executable file, this ensures that the interface presented to the user is always consistent with the functionality of the program. This eliminates the possibility of the application program and the user interface going out of synchronization, which is, in the long term, a very desirable property. The user interface can (and frequently does!) go out of synchronization with the functionality of the programs, when the user interface depends on external files to determine the keywords; these must be independently maintained and evolved as the application code evolves.

The input data file name is usually specified via the 'in' keyword while the output file name by the 'out' keyword. By default, the input is read from the standard input and output written to the standard output. If the input file name begins with the ’<’ character, the rest of the file name is treated as a command of the underlying operating system. The output of this command becomes the input of the application. Similarly if the output file name begins with the ’|’ character, the rest of the file name is treated as a command which reads the output of the parent application. These features are used to supply the output of one program to another.

The applications can also be started in the non-interactive mode by supplying “help = noprompt” as one of the command-line options. Other keywords of the application can also be set via “key=<val0>,<val1>,<val2>,...” styled command-line options. This is often useful in setting up a UNIX pipe consisting of a number of programs or when using these off-line programs as part of a shell script. On-line help is also available via the “explain” command in the interactive sessions and via the “help=explain” as one of the the command-line options in non-interactive sessions.

The user interface can be customized to a large extent and can also be used to effectively generate specialized versions of existing applications (see Appendix ??). These can be generated by writing the .def and .config files for the applications (see the explanation for the environment variables GCONF and GDEFAULTS in Section ??).

3.5 Data analysis and display programs

This section describes a few of the application program which were extensively used while observing with the GMRT as well as for instrumental calibration and the measurement of various telescope parameters.

3.5.1 The program xtract and its variants

The visibility function, denoted by V, depends on a number of parameters such as the local sidereal time (LST), observing frequency, the antenna co-ordinates, the co-ordinates of the phase center, the compensating delays applied to the various antenna, antenna fixed delays, antenna positions, etc. (i.e. V (b_{ij}(t), ν, τ, ∂τ/∂t, ...)). During debugging, it was frequently required to view this data in various representations (e.g., Cartesian versus polar representation of complex numbers). Also, V depends on a multitude of parameters, and different debugging purposes require viewing V with respect to different quantities. It was therefore not useful to implement a program to extract the data as a function of a fixed set of parameters. Since, as a design philosophy, stand-alone data display software was used, the need for the extracted data to be in a variety of formats (binary as well as in plain ASCII) directly readable by the display/plotting programs was also frequently felt. It was therefore necessary to develop a compact macro language parser to extract and display the data in a flexible and programmable manner.

xtract (?) was designed to extract the visibility data and its parameters in a programmable fashion via a compact macro language. It was also designed to be as general as possible and easily interface with the many stand-alone data display programs in use. In fact, it was designed with the wider goal of making it easier for a large spectrum of astronomers/engineers using the GMRT to be able to access the visibility data and do further processing if required. This program was extensively used for this dissertation and is now being regularly used for a variety of applications ranging from on-line and off-line data browsing and display, beam shape, pointing offset, antenna sensitivity measurements, band shape monitoring, etc.

The xtract macro language (described in Appendix ??) provides a mechanism to define the contents and the output data format. The macros are constructed using the three operators of the language, namely ant, base and chan and the various elements (Table ??). The three operators loop over all the selected antennas, baselines and frequency channels respectively. The language syntax allows arbitrary grouping of the operators with a semicolon separated list of elements as the body of these operators. This effectively provides a compact way of defining macros to extract visibilities and/or other parameters as a function of antenna, baseline and/or frequency channel number. These macros are, in fact, nested loops over the lists of antennas, baselines and/or frequency channels. The entire macro is implicitly the body of the loop over time and is executed for every input data record. The list of available elements are listed in Table ??.

For example, the xtract macro to produce a table with the first column containing the time stamp (Indian Standard Time (IST)) followed by two columns for the amplitude and phase of the visibility from each selected baseline, will be “ist;base{chan{a;p}};\\n”. The list of baselines and channels for which data is to be extracted can be specified via the user interface keywords baselines and channels. Similarly the u, v, w co-ordinates of antennas can be extracted in a table as a function of HA by the macro “ha;ant{ua;va;wa};\\n”. The list of antennas can be specified via the antennas keyword.

The xtract macro language complier is also available as a stand-alone library. The API of this library can be used by other application programs to parse, execute and get the result of the macros. An attempt was also made to write one such application for the graphical display of the LTA database (line and gray scale plots). This application unfortunately did not stabilize and is not in use.

Antennas are identified by the correlator sampler to which they are connected. In the final double sideband GMRT correlator, there will be 4 samplers per antenna, i.e. 2 samplers for the two polarization channels per sideband. The four signals from each antenna (2 polarizations from each sideband) can therefore be treated as four logical antennas. All samplers in the correlator are also uniquely numbered. The logical antennas can therefore be specified by the sampler number to which they are connected, or by an antenna name consisting of three hyphen separated fields – the antenna, the side-band and the polarization names. A name for a logical antenna is said to be “fully qualified” when all the three fields in the name are specified. All these fields can be regular expressions. Similarly, baselines can be specified by a baseline number or by a baseline name composed of colon (’:’) separated logical antenna names. Here again, the entire antenna names (before and after the ’:’) can be regular expressions. The use of regular expressions for the components of logical antenna names as well as for specifying the two antennas of a baseline provides a very general, compact and powerful selection mechanism. The antenna and baseline naming conventions are described in detail in Appendix ??. This convention is uniformly followed in all off-line programs where data selection based on antenna and/or baselines is required.

xtract normally writes the output in ASCII format with a header specifying the names of different columns and other information about the extracted data. Formats required by a number of freely available line and gray scale plotting programs can be generated by writing the required xtract macro. The extracted data can be directly read by these programs for display. The data can also be extracted with the header in ASCII followed by the data in binary format by specifying the output file name beginning with the character ’*’ (it is conceivable to write a xtract macro to produce a FITS file to be displayed using any of the FITS image display programs, e.g. for the dynamic spectra from selected baselines).

The user interface provides mechanisms to externally set keywords to some fixed default value(s) and to suppress these keywords from the user interface. This is used to effectively generate specialized variants of xtract. One such variant named oddix was extensively used for on-line display of the amplitudes and phases from various baselines. The data was read from the shared memory using a modified version of the record program, and an xtract macro defined to produce the output as a binary table with each row corresponding to a single integration time. The output was then piped to a program which further supplied the data to a display program over the network via a UNIX socket. The display program, also written as part of the off-line package, displays an arbitrary number of stacked scrolling line plots. The display surface itself is scroll-able, allowing the viewing of a very large number of line plots at a time.

3.5.2 The rantsol and badbase programs

The observed normalized visibility can be written as

ρ_{ij}^{Obs} = g_{i}g_{j}^{⋆}ρ_{ij}^{∘} + ϵ_{ij}  (3.1)

where g_{i} is the antenna based complex gain, ρ_{ij}^{∘} is the ideal point source visibility and ϵ_{ij} is the baseline based noise. For an unresolved source of unit flux density, ρ_{ij}^{∘} = 1. For an N antenna array, the g_{i}s represent 2N − 1 unknowns - the amplitudes and phases of all the g_{i}s (the phase of one of the antennas can be treated as the reference and hence set to zero). ρ_{ij}^{Obs} represents N(N − 1)/2 observed complex quantities. For N > 4 this is an over-determined problem and hence solvable. The program rantsol implements an algorithm to solve for the antenna-based complex gains for an unresolved source. The algorithm itself is described in Appendix ??.

The visibility data includes data from non-working or malfunctioning antennas as well as data affected by closure errors due to any malfunctioning of the correlator. Since the antenna based complex gains are obtained using a global fit involving all the data, the presence of bad data can result into problems ranging from noisy solutions even for the good antennas to no convergence at all. This can happen even in the presence of a few bad antennas and/or presence of as few as 10 − 20% bad baselines. It is therefore important to remove bad data before attempting to solve for the antenna gains.

This identification and flagging of bad data is done automatically in two passes for every solution interval. Antenna based complex gains are first solved for using all the data. Solutions from the first pass are then examined and antennas with amplitude gain less than the user defined threshold are flagged for the second pass. Antennas which are found to be bad in this manner are assigned a complex gain of 1. The solution for an antenna can also be interpreted as a weighted average of the complex visibilities from all baselines with the given antenna (see Section ??). This averaging in each successive iteration can be done robustly by on-the-fly flagging of data points, which deviate by more than a threshold defined in units of the variance of the series of complex numbers being averaged. Data from a baseline with large closure errors will have large deviations from the mean defined by the data from ’good’ baselines. Such data will be identified and flagged in robust averaging. Both these techniques are used in the algorithm implemented in the program rantsol to make it robust, even in the presence of time variant closure errors (the latter have been noticed on several occasions).

In practice, rantsol has been found to be very robust in the presence of non-working or malfunctioning antennas and malfunctioning MACs in the correlator (which produce large closure errors). It can be used almost as a black box for most of the calibrator databases without the need to identify and flag bad data. rantsol was regularly used to compute the antenna based complex gains and another program, badbase was used to identify bad data from calibrators scans. badbase examines the amplitude and phase of the calibrated visibilities (defined as ρ_{ij}/g_{i}g_{j}^{⋆}) and reports the fraction of time a given baseline was found to be bad (badness defined as |ρ_{ij}| and arg(ρ_{ij}) greater than a user defined threshold). Antennas and baselines which are continuously bad for large fractions of the total observing time were easily identified and flagged before mapping. This was found to be extremely important as the calibration tasks of the AIPS package (used for calibration and mapping) are very sensitive to bad data and sometimes resulted in no convergence at all due to the presence of about 10% bad baselines!

The GMRT typically produces a few hundred baselines per snapshot. Monitoring the data quality for phase, amplitude and closure errors corresponds to monitoring data streams from each of these baselines. This is obviously not practical. However there are only N antenna based complex gains corresponding to N antennas. Solution for antenna-based complex gains using rantsol effectively enforces closure constraints. On-line monitoring of these antenna based complex gains, derived using rantsol therefore gives a good summary of the data quality. rantsol output was also therefore routinely used to on-line inspect the quality of data. The gains were supplied to the online display software mentioned above which displayed the solutions as a set of scrolling line plots (the antenna based amplitudes and phases for the calibrator scans). This was of immense use in identifying time variable problems while observing and ensured that the recorded data was of reasonably good quality.

rantsol is now regularly used as a black box for a variety of purposes ranging from baseline and fixed delay calibration (Figs. ?? and ?? are examples of typical rantsol output), pointing offset, beam shape, sensitivity, system temperature measurements to the GMRT phase array operations for pulsar observations (?).

The output of rantsol can be formatted to be directly read by the QDP^{2} plotting package using the awk scripts getamp, getphs and getres. These scripts extract the amplitude and phase of the calibrated visibilities (ρ_{ij}/g_{i}g_{j}^{⋆}) respectively.

2Written by Allyn Tennant, originally at Cambridge, but developed at NASA Marshall Space Flight

3.5.3 The closure program

The antenna based complex gain g_{i} can be written as g_{i} = a_{i}e^{−ιϕ_{i}} where a_{i} and ϕ_{i} are the antenna based amplitude and phase. For the ideal case with no baseline based errors (ϵ_{ij} = 0 for all i and j), the phase of the triple product for an unresolved source, ρ_{ijk} = arg(ρ_{ij} · ρ_{jk} · ρ_{ki}) = 0 and the amplitude of ρ_{ijkl} = |ρ_{ij} · ρ_{kl}/ρ_{kj} ·ρ_{il}| = 1 . The phase of ρ_{ijk} is referred to as the closure phase and the amplitude of ρ_{ijkl} is referred to as the closure amplitude. These closure quantities are a good measure of the baseline based errors in the system. Ideally, the signals from various antennas, flowing through independent paths, are mixed only in the MAC stage of the correlator. Although there are several sources which can produce small closure errors, catastrophic closure errors, which severely limit the final dynamic range in the maps, can be traced to malfunctioning MACs in the correlator. The closure phases are therefore a very important quantity to monitor during the observations. It is also important to examine these closure quantities while processing so as to identify bad data; this is done using the closure program.

The output of this program, which computes all the closure quantities from the data, was also used for on-line display of the closure phases. This output was simultaneously also supplied to another program which raised an alarm in case the closure phases for the calibrator scans deviated from the expected value by more than some threshold amount. This helped in identifying problems with data before spending long hours of observing and recording of otherwise unusable data.

3.5.4 Conversion to FITS format

The final inversion and mapping of the visibility data was done using the AIPS^{3} package. The visibility data was imported into AIPS by first converting the data from the LTA format to FITS format using the off-line program gl2fit^{4} (however, see Section ?? for some details about use of other data filters before gl2fit). The FITS file was then imported to AIPS using the AIPS task FITLD.

Center

3Developed by the National Radio Astronomy Observatory (NRAO), USA., primarily for calibration and analysis of the data from the Very Large Array (VLA) but now used for other telescopes as well.

4Developed by V.K.Kulkarni of NCRA(TIFR), Pune

3.5.5 Miscellaneous programs

In addition to the programs mentioned above, various other programs, which were routinely used during the course of this work, were also developed. Although these programs are not used for numerical computation, they are nevertheless useful and often indispensable.

• The program ltainfo lists the astronomically useful summary of each scan in the LTA database (total number of scans in the database, string identifier for the astronomical object, RA and Dec of the pointing center (in date epoch), the hour angle corresponding to the first data record, centre frequency of the RF band and the width of each frequency channel).

• The program ltacat concatenates multiple LTA databases into a single database. Since the LTA-global header applies to the entire database, all constituent databases are checked for consistency with the first LTA database. Those LTA databases which do not conform to the global header of the first database are rejected. Quite often, due to various interruptions during long observations, the LTA database was split into several files. These individual files were concatenated into one using ltacat (this was necessary for data browsing and detection of bad data as discussed in Chapter ??).

• The program ltacleanup checks a LTA database for conformity with the LTA format and attempts to fix some of the inconsistencies. It can also be used as a filter to select scans and/or perform integration in time and/or frequency. Due to problems related to synchronization between the online array control and correlator control softwares, bad scans may be recorded in the LTA database (e.g. scans with zero data records, scans with wrong values for the frequency/bandwidth settings, scans with wrong pointing centre, scans with un-usable data due to a variety of reasons, etc.). Such scans need to be removed to produce a database with only usable scans. ltacleanup was used to remove such scans as well as to correct some inconsistencies with respect to the LTA format.

• The program fixit was used to edit the values of keywords in the global header and/or the scan headers.

• The program tmac checks for time stamp related errors in the LTA database. Due to synchronization problems between the various network programs comprising the Data Acquisition System (DAS), situation sometimes arise where the time stamp of successive data records does not monotonically increase. tmac rejects all data records till it finds a valid time stamp. It was often used as a filter before gl2fit to eliminate any offending data records.

• The program offstop was written for off-line fringe stopping when on-line fringe stopping in the correlator was not implemented. It later evolved into a program to apply residual compensating delay due to frequency offsets or antenna position offsets. The frequency and/or antenna position offsets for which fringe-stopping should be carried out are the input parameters. This program was extensively used to test the derived antenna co-ordinate corrections and fixed delay corrections during baseline and delay calibration efforts.

• The program calibbp does primary phase and bandpass calibration. This was written to allow freedom to test various calibration schemes for the GMRT data. The antenna based complex gains are determined using the phase calibrator scans and antenna based band-passes are determined using the bandpass calibrator. Average gains can be found by integrating the calibrator visibility data. As an alternative, antenna based gains can be averaged to determine the average gains. The latter has the advantage that the automatic bad data detection algorithm is effective while determining the antenna gains.

• The program lin subtracts linear slopes across the band for each baseline. This was required for tracing the source of spectral features across the band at P-band (and possibly at other bands as well). The data was time and bandpass calibrated using calibbp and linear slopes removed from each baseline. This is the equivalent of the UVLIN (?) operation done for spectral line data analysis. The spectral features seen across the band after passing it though the program lin, probably limits the detection of weak spectral lines, at least at P-band, and this is still an unsolved problem.

92 CHAPTER 3. DATA ANALYSIS SOFTWARE

The GMRT Data

Recent Galactic plane observations at 843 MHz, using the Molonglo Synthesis Telescope (MOST) (?) and at 2.4 GHz, using the Parkes 64-m single dish (?), have revealed a number of new candidate SNRs. However many of these objects were in complicated regions of the Galaxy and these observations also suffered from contamination due to thermal emission at these high frequencies. Although the MOST observations were at a relatively low frequency, the side-lobes due to nearby strong sources severely limited the fidelity of images. With only single frequency data available for most of these fields (these observations did not have any overlapping fields), the identification of the candidate SNRs in these fields remained inconclusive.

A sample of candidate SNRs, accessible to the GMRT, were selected from these observations. Continuum observations of this sample were done with the GMRT at 325 MHz during the period of 1998 to 2000. The telescope hardware, on-line and off-line software were all in a state of being debugged during this period and observations were invariably intermingled with debugging activity and related observations. Consequently, the data acquired was often unusable, sometimes requiring several observing sessions involving the same field to get good data. This chapter describes the procedure used for on-line data monitoring and identification of a potential source of data corruption, off-line data flagging and finally imaging using the AIPS package.

Section ?? gives the general description of the observations done at 325 MHz. Imaging at these low frequencies requires the use of algorithms and techniques not usually used for mapping at higher frequencies. These low frequency specific problems for inversion of visibilities and image deconvolution, and the techniques used to overcome these problems are discussed in Section ??. Section ?? discusses the problem of bandwidth smearing of sources away from the phase centre, which necessitates the multi-channel mode of observations. The procedures used for on-line system and data monitoring are described in Section ??. The detailed procedure used for off-line data editing and calibration is described in Sections ??. Section ?? describes the procedure used to finally map the data and while Section ?? presents the full primary beam images after correcting for the primary beam attenuation.

4.1 GMRT Observations

325 MHz observations for continuum imaging of a sample of nine candidate SNRs were done during the period of 1998-2000. The parameters of these observations are summarized in Table ??. Most of the objects of interest in these fields were extended, with emission at angular scales ∼ 2 − 20 arcmin requiring reliable observations at the smallest available baselines. Observations at 325 MHz are often affected by intermittent radio frequency interference (RFI) and, since RFI from nearby sources of emission remains partially correlated for the smallest baselines, data from the smallest baselines are also most severely affected by RFI. Fortunately, RFI is often narrow band and can be identified if the observing band is split into a number of narrow band frequency channels. The observations were therefore done with the full 16 MHz band split into 128 frequency channels of each having a width of ∼ 125 kHz.

The current single side-band GMRT correlator measures only the co-polar visibilities, i.e. only signals of the same polarization are correlated using the Indian mode of the VLBA Multiplier and Accumulator chips (MACs). All the 128 frequency channels of the co-polar visibilities corresponding to the right and left circular polarized signals were recorded for all available baselines. The data was kept in the multi-channel format throughout the imaging process to minimize the band-width smearing of sources away from the phase centre (see Section ??). After editing the RFI-affected or otherwise bad data, a typical bandwidth of about 5−6 MHz was finally used for imaging giving a typical RMS noise of ∼ 10 mJy/beam.

The background sky temperature can vary by a factor of 2−3 within the Galactic plane, resulting in a change in the total power output by similar factors. The correlator samplers are, however, optimized to work with an input signal of 0 dBm. To keep the sampler inputs at this level, automatic level controllers (ALCs) are introduced at the output of the baseband (BB) which effectively changes the gain to keep the output at 0 dBm. To keep the ALC operating point within its linear operating range, an attenuation of 16 db was typically used for the IF and BB signals.

As mentioned earlier, the GMRT was in a state of being debugged during the period Table 4.1: Parameters of observations with GMRT

Frequency of Observations (MHz)  325
RF Bandwidth (MHz)  16
Bandwidth used (MHz)  5 − 6
Integration time (sec)  16.9
Average time spent on the source (hr)  5
No. of Antennas used  20 − 27
Max. baseline (kλ)  15 − 25
Min. baseline (λ)  60 − 100
Max. spatial scale(arcmin)  ∼ 30
Average Antenna Sensitivity (K/Jy)  0.32
Primary beam (degree)  1.4
Synthesized resolution (arcsec)  10 − 20
RMS noise (mJy/beam)  ∼ 10

of the observations. Consequently, the number of antennas and the longest baseline available changed from observation to observation. As a result, the resolution changes from observation to observation. However, most of the Central Square antennas, plus some of the arm antennas were available for all observations giving angular resolution in the range ≈ 60−10 arcsec. Some of the fields, which needed higher resolution were observed when the long baselines antennas were available. Since most of the target objects were extended, it was essential that the short antenna spacings were well sampled. Hence the three antennas, C05, C06 and C09 which provide the shortest spacings, were used for all observations giving a shortest baseline of ∼ 100λ (after flagging bad data) for which reliable data was measured. This corresponds to a largest angular scale of ∼ 30 arcmin. Most of the sources of interest were well within this limit in angular size and we believe that most of the emission up to angular scales of ∼ 30 arcmin is well represented in the GMRT 325-MHz images.

4.2 Low frequency specific problems

The visibility measured by a properly calibrated interferometer is given by

V (u, v, w) = ∫∫ I(l, m)P (l, m)e^{−2πι(ul+vm+w(\sqrt{1−l^{2}−m^{2}}−1))} \frac{dldm}{\sqrt{1 − l^{2} − m^{2}}}  (4.1)

where (u, v, w) are the antenna co-ordinates in the uvw co-ordinate system, l, m, and n are the direction cosines in this system, I(l, m) is the source brightness distribution (the image) and P (l, m) is the far field antenna reception pattern (the primary beam). For further analysis we will assume P = 1, and drop it from all equations (for typing convenience!), remembering all along that the effect of P (l, m) is to limit the part of sky from which the antenna can receive radiation to ∼ λ/D radians, where D is the diameter of the antennas.

For a small field of view (l^{2} + m^{2} << 1), the above equation can be approximated well by a 2D Fourier transform relation. The other case in which this is an exact 2D relation is when the antennas are perfect aligned along the East-West direction. Here, we discuss the problem of mapping with non-East-West arrays. The derivation presented here of results for devising algorithms used for imaging large fields of view presented here follow the treatment of ? and ?.

4.2.1 Mapping with non co-planar arrays

Equation ?? also reduces to a 2D relation for a non-East-West array, if the integration time is sufficiently small (snapshot observations). However modern arrays are designed to maximize the uv-coverage with the antennas arranged in a ’Y’ shaped configuration (non East-West arrays) (?). Fields, such as the ones observed for this dissertation, with emission at all angular scales, require maximal uv-coverage. Telescopes such as the GMRT use the rotation of earth to improve the uv-coverage and observations of complex fields typically last for several hours. Hence, Equation ?? needs to be used to map the full primary beam of the antennas, particularly at low frequencies.

Let n = \sqrt{1 − l^{2} − m^{2}} be treated as an independent variable. A 3D Fourier transform of V (u, v, w) can be written using (u, v, w) and (l, m, n) as a set of conjugate variables as

F (l, m, n) = ∫∫∫ V (u, v, w)e^{2πι(ul+vm+wn)}dudvdw  (4.2)

Substituting for V (u, v, w) from Equation ?? we get

F (l, m, n) = ∫∫ \{ \frac{I(l′, m′)}{\sqrt{1 − l^{′^{2}} − m^{′^{2}}}}
∫∫∫ e^{−2πι(u(l′−l)+v(m′−m)+w(\sqrt{1−l^{′^{2}}−m^{′^{2}}}−n−1))}dudvdw
} dl′dm′  (4.3)

The −1 in the coefficient of w in Equation ?? comes from fringe rotation. In the above equation, it corresponds to a shift by one unit along the n−axis. Since this is only a change of the origin of the co-ordinates system, it can be absorbed in the n without loss of generality. Using the general result

\begin{matrix}δ(l′ − l) = & ∫ e^{−2πιu(l′−l)}du \\ = & \{ \begin{matrix}1 : & l = l′ \\ 0 : & otherwise \end{matrix} \end{matrix}  (4.4)

we get

\begin{aligned}F (l, m, n) & = ∫∫ \frac{I(l′, m′)}{\sqrt{1 − l^{′^{2}} − m^{′^{2}}}} δ(l′ − l)δ(m′ − m)δ(\sqrt{1 − l^{′^{2}} − m^{′^{2}}} − n)dl′dm′ \\ & = \frac{I(l, m)δ(\sqrt{1 − l^{2} − m^{2}} − n)}{\sqrt{1 − l^{2} − m^{2}}} \end{aligned} (4.5)

This equation then provides the connection between the 2D sky brightness distribution given by I(l, m) and the result of a 3D Fourier inversion of V (u, v, w) given by F (l, m, n) referred to as the Image volume. Here after, I use I(l, m, n) to refer to this Image volume.

The effect of including the fringe rotation term (−2πw) would be a shift of the Image volume by one unit in the conjugate axis (n−axis) (shift theorem of Fourier transforms; ?). Hence, the effect of fringe stopping is to make the lm−plane coincide with the tangent plane at the phase center on the Celestial sphere (the point where the tangent plane touches the Celestial sphere) with the rest of the sphere completely contained inside the Image volume (Fig. ??).

Noting that the third variable n of the Image volume is not an independent variable and is constrained to be n = \sqrt{1 − l^{2} − m^{2}}, Equation ?? gives the physical interpretation of I(l, m, n). Imagine the Celestial sphere defined by l^{2} + m^{2} + n^{2} = 1 enclosed by the Image volume I(l, m, n), with the top most plane being tangent to the Celestial sphere as shown in Fig. ??. Equation ?? then tells that only those parts of the Image volume Figure 4.1: Graphical representation of the geometry of the Image volume and the Celestial sphere. The point at which the Celestial sphere touches the first plane of the Image volume is the point around which the 2D image inversion approximation is valid. For wider fields, emission at points along the intersection of Celestial sphere and the various planes (labeled here as the Celestial Sphere) needs to be projected to the tangent plane to recover the undistorted 2D image. This is shown for 3 points on the Celestial sphere, projected on the tangent plane.

correspond to the physical emission which lie on the surface of the Celestial sphere. However, the Image volume will be convolved by the telescope transfer function. The telescope transfer function is the Fourier transform of the sampling function S in the uvw frame (see Chapter ??, page ??). The telescope transfer function, referred to as the dirty beam and defined as B(l, m, n) = FT [S(u, v, w)], also defines a volume in the image domain. The dirty image volume defined by the relation I^{d}(l, m, n) = I(l, m, n) ⋆ B(l, m, n) is a convolution of I(l, m, n) with B(l, m, n). Since the dirty beam is not constrained to be finite only on the Celestial sphere, I^{d} will be finite away from the surface of the Celestial sphere corresponding to non-physical emission due to the side lobes of B(l, m, n). A 3D deconvolution using the dirty image and the dirty beam volumes will produce a Clean image volume. An extra operation of projecting all points in the CLEAN image-volume along the Celestial sphere onto the 2D tangent plane to recover the 2D sky brightness distribution is Figure 4.2: Graphical illustration to compute the distance between the tangent plane and a point in the sky at an angle of θ.

therefore required. Graphical representation of the geometry for this is shown in Fig. ??.

3D imaging

The most straight forward method suggested by Equation ?? for recovering the sky brightness distribution, is to perform a 3D Fourier transform of V (u, v, w). This requires that the w axis be also sampled at the Nyquist rate (??)). For most observations, it turns out that this is rarely satisfied and doing a FFT along the third axis would result into severe aliasing. Therefore, in practice, the Fourier transform on the third axis is usually performed using the direct Fourier transform (DFT) on the un-gridded data.

To perform the 3D FT (FFT along the u− and v− axis and DFT along the w−axis) one still needs to know the number of planes needed along the n−axis. This can be found using the geometry shown in Fig. ??. The size of the synthesized beam along the n−axis is comparable to that along the other two directions and is given by ≈ λ/B_{max} where, B_{max} is the longest projected baseline length. The separation between the planes along n should be ≤ λ/2B_{max}. The distance between the tangent plane and a point separated by θ from the phase center, for small values of θ, is given by 1 − cos(θ) ≈ θ^{2}/2. For a field of view of angular size θ, critical sampling would be ensured if the number of planes along the n−axis, N_{n}, is

N_{n} =B_{max}θ^{2}/λ
=λB_{max}/D^{2} (for θ = Full Primary beam)

(4.6)

where D is the diameter of the antenna (B_{max} ≈ 25 km for the GMRT at 325 MHz). Therefore, for mapping a 1^{∘} field of view without distortions, one would require 8 planes along the n-axis. However, for mapping with Central Square alone (B_{max} ≈ 1 km), one plane is sufficient. At these frequencies, it becomes important to map most of the primary beam since the number and often the intensity of the sources in the field increase and the side-lobes due to these sources limit the dynamic range in the maps. Hence, even if the source of interest is small, it requires a full 3D inversion (and deconvolution).

Another reason why more than one plane would be required for very high dynamic range imaging is as follows. Strictly speaking, the only point which lies in the tangent plane is the point at which the tangent plane touches the Celestial sphere. All other points in the image, even close to the phase center, lie slightly below the tangent plane. Deconvolution of the tangent plane then results into distortions for the same reason as the distortions due to the deconvolution of a point source which lies between two pixels in the 2D case (?). As in the 2D case, this problem can be minimized by over sampling the image which, in this case, implies having more than one plane along the n-axis, even if Equation ?? implies that one plane is sufficient.

Polyhedron imaging

As mentioned above, emission from the phase center and from points close to it, lie approximately in the tangent plane. Polyhedron imaging relies on exploiting this by approximating the Celestial sphere by a number of tangent planes, referred to as facets, as shown in Fig. ??. The visibilities are recomputed to shift the phase center to the tangent points of each facet and a small region around each of the tangent points is then mapped using the 2D approximation.

The number of planes required to map an object of size θ can be found simply by requiring that the maximum separation between the tangent plane and the Celestial sphere be less than λ/B_{max}, the size of the synthesized beam. As shown earlier, this separation for a point θ degrees away from the tangent point is ≈ θ^{2}/2. Hence, for critical sampling, the number of planes required is equal to the solid angle subtended by the sky being mapped Figure 4.3: Approximation of the Celestial sphere by multiple tangent planes (polyhedron imaging).

(θ_{f}^{2}) divided by θ^{2}/2(= λ/2B_{max})

N_{poly} = 2θ_{f}^{2}B_{max}/λ
= 2B_{max}λ/D^{2} (for θ_{f} = Full primary beam)

(4.7)

Notice that the number of planes required is twice as many as required for 3D inversion. However, since a small portion around the tangent point of each plane is used, the size of each of these planes can be small, off-setting the increase in computations due to the increase in the number of planes required. Another approach which is often taken for very high dynamic range imaging, is to do a full 3D imaging on each of the planes. This would effectively increase the size of the field that can be imaged on each tangent plane, thereby reducing the number of planes required.

The polyhedron imaging scheme is implemented in the current version of the AIPS data reduction package and the 3D inversion (and deconvolution) is implemented in the (no longer supported) SDE package developed by T.J. Cornwell et al. Both these schemes, in their full glory, are available in the (recently released) AIPS++ package.

The GMRT 325-MHz data was imaged using the IMAGR task in AIPS. This program implements the polyhedron algorithm and requires the user to supply the number of facets to be used and a list of the locations of the centre of each facet with respect to the image centre and the size of each facet. This list of facets and their parameters were computed using the task SETFC in AIPS, typically resulting in a grid of 5 × 5 facets, each of size 256 × 256 pixels.

4.2.2 Bandwidth Smearing

The effect of a finite bandwidth of observation as seen by the multiplier in the correlator, is to reduce the amplitude of the visibility by a factor given by \frac{sin(πlΔν/ν_{o}θ)}{(πlΔν/ν_{o}θ)} where θ is the angular size of the synthesized beam, ν_{o} is the center of the observing band, l is location of the point source relative to the field center and Δν is the bandwidth of the signal being correlated.

The distortion in the map due to the finite bandwidth of observation can be understood as follows. For continuum observations, the visibility data integrated over the bandwidth Δν is treated as if the the observations were made at a single frequency ν_{o} – the central frequency of the band. As a result the u and v co-ordinates and the value of visibilities are correct only for ν_{o}. The true co-ordinates at other frequencies in the band are related to the recorded co-ordinates as

(u, v) = (ν_{o} \frac{u_{ν}}{ν} , ν_{o} \frac{v_{ν}}{ν} )  (4.8)

Since the total weights W, used while mapping, does not depend on the frequency, the relation between the brightness distribution and visibility at a frequency ν becomes

V (u, v) = V (u_{ν} \frac{ν_{o}}{ν} , v_{ν} \frac{ν_{o}}{ν} ) FT (\frac{ν}{ν_{o}} )^{2} I (l\frac{ν}{ν_{0}} , m\frac{ν}{ν_{0}} )  (4.9)

Hence the contribution of V (u, v) to the brightness distribution get scaled by (ν/ν_{o})^{2} and the co-ordinates get scaled by (ν/ν_{o}). The effect of the scaling of the co-ordinates, assuming a delta function for the Dirty Beam, is to smear a point source at position (l, m) into a line of length (Δν/ν_{o})\sqrt{l^{2} + m^{2}} in the radial direction. This will get convolved with the Dirty Beam and the total effect can be found by integrating the brightness distribution over the bandwidth as given in Equation ??

I^{d}(l, m) = [ \frac{∫_{0}^{∞}|H_{RF} (ν)|^{2} (\frac{ν}{ν_{o}} )^{2} I (\frac{lν}{ν_{0}} , \frac{mν}{ν_{0}} ) dν}{∫_{0}^{∞}|H_{RF} (ν)|^{2}dν} ] ∗ DB_{o}(l, m)  (4.10)

where H_{RF} (ν) is the band-shape function of the RF band and DB_{o} is the Dirty Beam at frequency ν_{o}. If the synthesized beam is represented by a Gaussian of standard deviation σ_{b} = θ_{b}/\sqrt{8ln2} and the bandpass by a rectangular function of width Δν, the fractional reduction in the strength of a source located at a radial distance of r = \sqrt{l^{2} + m^{2}} is given by

R_{b} = 1.064\frac{θ_{b}ν_{o}}{rΔν} erf (0.833\frac{rΔν}{θ_{b}ν_{o}} )  (4.11)

Equation ?? is equivalent to averaging a large number of maps made from quasi-monochromatic visibilities at ν. Since each such map scales by a different factor, a source away from the center would move along the radial line from one map to another, producing the radial smearing mentioned above, convolved with the Dirty Beam.

The effect of bandwidth smearing can be reduced if the band is split into frequency channels with smaller channel widths. This effectively reduces the bandwidth Δν as seen by the mapping procedure and while gridding the visibilities, u and v can be computed separately for each channel and assigned to the appropriate uv-cell. The FX correlator used in GMRT provides up to 128 frequency channels over the entire bandwidth of observation and the visibilities can be retained as multi-channel in the mapping process to reduce bandwidth smearing. Although purely from the point of view of bandwidth smearing, averaging ∼ 10 channels at 325 MHz would be acceptable, keeping the visibility database with all the 128 channels is usually recommended to allow identification and flagging of narrow bands RFI.

4.3 Observational procedure

For T^{a} ≪ T^{sys}, the amplitude of the visibility function V is proportional to the flux density of the source and the normalized visibility amplitude is converted to flux density units using the measurement of V for a source of known but non variable flux density (referred to as the flux density calibrator). Also, the complex antenna based gain can potentially vary as a function of time. These slow time variations can be corrected using periodic observation of a source of known structure, usually an unresolved source, referred to as the phase calibrator. The flux density of the phase calibrators, the flux density of which is potentially variable over time scales of days, is also calibrated using the flux density calibrator. Each observation therefore requires at least one observation of a flux density calibrator and periodic observation of phase calibrators to properly calibrate the data.

The VLA flux density calibrators, 3C48 and 3C286 was used for all observations. One of three calibrators close to the Galactic plane namely, 1830-36, 1709-299 and 1822-096, were used as the phase calibrator. A flux calibrator was observed for ∼ 10 min at the beginning and at the end of each observing session and the phase calibrator was observed for ∼ 10 min at an intervals of ∼ 30 min.

The planned periodic injection of noise from a calibrated noise source to measure the system temperature has not yet been implemented for the GMRT. As a result, the system temperatures for the flux density calibrator fields (T_{Cal}^{sys}) and the field being mapped (T_{s}^{sys}) must be measured and a correction equal to T_{s}^{sys}/T_{Cal}^{sys} be applied as part of the flux density calibration. T_{Cal}^{sys} was measured to be ∼ 110 K while T_{s}^{sys} was estimated from the all-sky maps at 408 MHz (???). For a few fields, T_{s}^{sys} was also measured at few points around the source of interest and the measured system temperature was consistent with that estimated from the 408 MHz data to within ∼ 10%. None of the phase calibrators used for these observations are known to be variable over few hours. These calibrators were therefore also used as secondary amplitude calibrators to effectively correct for any slow variation in the receiver temperature.

The observing schedule if the GMRT on-line array control system can be supplied via a computer readable file. This file, apart from a few other system-related commands, contain instructions about the source to be tracked and the integration time on each source. However since the feedback of the antenna pointing status is not used, this file needs to be tweaked by inserting delays between various commands. For example, the amount of time taken for antennas to move from one tracking direction to another varies from antenna to antenna, and appropriate time delays must be inserted between the various commands in this file to make sure that the data recording begins only after all antennas have reached a given tracking position. The commands for alternately tracking the phase calibrator and the target source were put in an infinite loop, which allowed the above mentioned periodic observations of the phase calibrator. However, since only an infinite loop is possible, the observations had to be manually terminated at the end of observing session. Information about the status of the antennas as well as a mechanism to derive time-of-the-day information in the command syntax used in this file is highly desirable and will allow a better and more automated observing session.

4.3.1 On-line monitoring

The data could be corrupted due to a number of reasons including (1) RFI, (2) catastrophic hardware failures (irrecoverable in a short time), (3) intermittent hardware failures from which a quick recovery is possible (e.g. breakdown of communication between correlator control hardware and software), (4) antenna-based breakdown (for e.g., failure of the servo system resulting in stoppage of source tracking), (5) failure of the communication link between the antenna based computer (ABC) and the on-line control computer at the CEB,

(6) power supply failure to some of the antennas, (7) loss of phase-lock for the four local oscillators (LOs) or a phase jump in the LOs, (8) onset of ionospheric scintillations, (9) problems in the online array control, (10) problems in the correlator control software/hardware, etc. Data affected by any or many of these sources manifests itself in various forms in the recorded data. Such data needs to be flagged from the database before it is used for mapping. The flagging information for the database was generated by on-line monitoring of the critical array control parameters as well by off-line examination of the data itself. The procedure used for this is described below.

System monitoring

It was noticed that problems related to items (3), (4), (5) and (10) listed above, occurred frequently enough to require careful monitoring of various related telescope parameters as well as on-line monitoring of the visibility data. The GMRT on-line array control system maintains a large amount of information about the status of the various sub-systems. This information is updated once every few seconds and is available in the shared memory resource of the control computer. Any arbitrary information from this resource can be extracted using the table^{1} program. This program was used to extract the following information as a function of time:

• the packet sequence number

• the azimuth and elevation angles of the antennas

• the error between the target and current antenna azimuth and elevation angles

• the antenna servo system related flags

The table program produces the output in the form of a table which was supplied to a shell script which generated an alarm if any of the following conditions occurred:

• the error on azimuth or elevation angles of any of the antennas exceeded a threshold value. This usually was an indication of the antenna not receiving the the periodic tracking instructions from the GMRT on-line array control system computer • the packet sequence number did not change for a threshold length of time. This

1Developed by R.K.Singh of NCRA(TIFR), Pune

usually indicated loss of communication between the antennas and the GMRT on-line array control system computer

• the flag for servo brakes was raised for any of the antennas. This usually indicated either a malfunctioning antenna servo system and/or the detection of extra antenna load (due to wind loading or due to some spurious signal indicating extra load)

In case of any of the above problems, manual intervention was required. However, this rather primitive “automation” did help enormously in long observing sessions. This procedure, while already quite useful, should ultimately be made part of the link between the GMRT on-line array control system and the correlator control software to (1) record on-line flagging information, and (2) control the recording of the data.

Data monitoring

On-line monitoring of the visibility data was done in two ways. First, the matmon^{2} program was used to monitor the normalized correlation coefficient for the phase calibrators. This program displays single integration cycle snapshots of the amplitude (or the phase) of the visibility data for all baselines in the form of a matrix. This display was used to determine the general health of the system before starting the observations and was useful in quickly locating catastrophic problems. Once the observations were started, the data from the correlator was monitored using the programs xtract, rantsol and closure (see Chapter ??). The amplitude and phase from all baselines were continuously displayed as a set of stacked scrolling line plots using the program oddix (which uses xtract and the plotting package of the GMRT off-line software). This display provided a 1 − 2 hour long snapshot of the data covering two or more observations of the phase calibrator. Since most problems in the system can be detected using the data from the phase calibrators, the onset of a problem in the data between two calibrator scans was easily detected using these plots.

The output of rantsol (namely, the antenna based complex gains) for the calibrator scans was also similarly plotted. These plots provided information about the health of the system containing all the data on the calibrator scans. Problems ranging from a significant loss in antenna sensitivity (e.g. due to change in the antenna pointing offset across HA = 0h seen for some of the antennas) to the onset of closure errors due to a malfunctioning correlator or the onset of ionospheric scintillations were quickly detected from these plots.

2Developed by A.P.Rao of NCRA(TIFR), Pune

The output of closure (the closure phase for all possible triangles) was supplied to another program which raised an alarm if the closure phases exceeded a threshold value for a threshold length of time. This procedure quickly identified time varying correlator related problems quite effectively.

The output of the table and closure programs as a function of time were also saved in a file. This data was later examined and used to generate a flagging table readable by AIPS. These procedures, effectively generated first order on-line data flagging information, which is the crucial first step in improving the final data quality. Lack of time did not permit implementing these procedures as part of the on-line array control and correlator control software, but must be done in the near future to improve the reliability and quality of the final data.

4.4 Data Analysis

Two types of data analysis were required for mapping: (1) off-line data analysis (before and after importing the data into AIPS) for further, more careful identification of bad data, and (2) data analysis involving 3D inversion, deconvolution and phase calibration for the purpose of imaging. This section describes the procedure used for the data analysis required for data editing and calibration. Section ?? describes the procedure used for mapping.

4.4.1 Data Editing

In addition to the data flagging information derived from on-line system and data monitoring, the data was also examined off-line using the programs xtract, rantsol and badbase (see Chapter ??). In long observing sessions, there were invariably antennas which did not produce usable signals for some fraction of time. Often, this was either due to th malfunctioning of a subsystem or the antenna being taken for some kind of maintenance work over time scale much longer than the threshold time intervals set in the on-line monitoring programs (see Section ??). Such situations were easily identified from the plots of amplitude from all baselines (or for all baselines with a single antenna) as a function of time for the calibrator scans. The calibbp program was also used for bandpass calibration of the data, using the phase calibrator scans. The antenna-based average bandpass solutions and the baseline based band-passes were examined to identify frequency channels affected by intermittent narrow band RFI or by any other source of data corruption.

The program badbase uses the output of rantsol to generate a summary of the antenna based solutions (see section ??, Chapter ??). This was found to be very useful in identifying intermittent baseline based problems in the data. The AIPS tasks used for calibration are rather sensitive to the presence of bad baselines in the data. Flagging data corrupted by baseline based errors was therefore essential. The algorithm for the computation of antenna based complex gains implemented in rantsol is robust in the presence of such data and was hence crucial for the identification and flagging of such data.

The above mentioned procedure was followed for data from both the polarization channels separately. All the flagging information generated from on-line monitoring and off-line data analysis, was converted to flagging tables to be used later for flagging data in AIPS.

Data recorded in the native LTA format was imported to AIPS via the FITS format. The program gl2fit was used to convert the LTA database into FITS format. It was noticed that data for some of the baselines was in the illegal number representation identified as NaN (not-a-number) or Inf (infinite) numbers. Most of the data analysis programs (including the robust algorithm of rantsol) behave erratically in the presence of such numbers. However, computer representation of such numbers is well documented in the IEEE number representation format and can be easily and reliably identified in the software. This form of bad data was therefore removed using an on-the-fly filter used in all off-line data analysis programs, including gl2fit. Another form of bad data manifests itself in the form of the normalized visibility amplitude being greater than unity. This is again easily identified in the software, and the gl2fit program flags such data while converting it to the FITS format.

Due to synchronization problems between the various network programs of the GMRT data acquisition software and the online array control software, the time stamp of the data records is sometimes corrupted and the value of time stamp of the successive data records does not increase monotonically. Data with such time stamp corruption is unusable in AIPS. Also, a few data records at the beginning of each scan were found to be regularly bad. All such data records were filtered out using the program tmac. tmac was used as a data filter in a data pipe-line, before the program gl2fit. If the observation was split into a number of LTA files, the program ltacat was also used before tmac in the data pipe-line to concatenate the various LTA files into one file. LTA files for some observations also required changing the values of some of the keywords in the Global an Scan headers of the LTA data base. This was done using the program fixit.

A typical data pipe-line set up to convert the and LTA file to FITS format was therefore, [ltacat]⇒ [fixit]⇒ tmac⇒ gl2fit, where ’⇒’ indicates the flow of data and the parenthesis are used to indicate that the program were used only if necessary. Use of UNIX pipes eliminated the necessity of saving the intermediate LTA files, which would otherwise have required several giga bytes of disk space.

Further data editing was done after importing the data into AIPS. The bad data/ antennas/ baselines identified earlier were translated to AIPS readable flagging files and applied inside AIPS. Various steps used for further data editing and calibration inside AIPS are described below.

4.4.2 Data Editing and Calibration in AIPS

The first step in the sequence of data analysis is the amplitude and phase calibration of the visibilities. This section describes, in a stepwise fashion, the sequence of various AIPS tasks that were used for data calibration. A typical AIPS task depends on a large number of parameters, which control the behavior of the tasks. The settings of the relevant parameters of these tasks are also discussed below.

1. The FITS file generated using the procedure described above, was imported into AIPS using the task FITLD. This results into a multi-source visibility database written in AIPS, by default in the compressed format.

2. Normally, multi-source file contains a number of tables, including the CL table, version

1 (CL1)

At present, the CL1 table is not generated when the GMRT data is converted into FITS format. This table is also used by AIPS calibration programs as a template to determine the time resolution for the subsequent CL and antenna gain tables (the SN tables). Hence, the task INDXR was always run to generate the table CL1. This also generates the NX table, which is used by AIPS to navigate in the database. This, by default, produces a CL table with a time resolution of 5 min. Since the phase calibrators used for all the observations were strong enough to provide sufficient signal to noise ratio, the antenna based gain solutions could be computed for every integration cycle of ∼ 17 sec. The CL and SN tables were later used to not only calibrate the data but also identify bad data. The minimum time resolution for gain solutions was therefore set to ∼ 20 sec by setting APARM=0.33,0 before running INDXR.

3. The flux density for the flux calibrators must be accurately set before proceeding for calibration. The flux density scale of the standard VLA flux calibrators 3C48 and 3C286 is encoded in the task SETJY. This task was run on the multi-source visibility database to set the flux densities for these flux density calibrators using the following

settings: OPCODE='calc'; SOURCE='3C286','3C48',''.

4. The task UVFLG reads the data flagging information from a disk file supplied via the INFILE keyword. This task was used to apply all the flagging information generated from the on-line monitoring and off-line data analysis described earlier.

5. The visibility amplitude of an unresolved source remains constant as a function of baseline length. Plot of visibility amplitudes as a function of \sqrt{u^{2} + v^{2}} for the flux density calibrator scans was examined using the task UVPLT. The SOURCE keyword was appropriately set for the purpose. Obviously discrepant data were identified, after allowing for some spread due to differences in antenna sensitivities. Such data, which either had very low or very high amplitude can have severe repercussions for calibration.

UVFLG was used to flag these discrepant points with INFILE=''. The keywords ANTENNA, BASELINE, and TIMERANGE were used to specify the offending antennas/baselines and any time range for which the data was required to be flagged.

The primary task for calibration in AIPS is CALIB. This task is, however, rather sensitive to the presence of bad/dead antennas. (e.g., in one case (G356.3-1.5) the presence of about 10 bad baselines out of a total of about ∼360 good baselines (for antennas C06 and C05) gave severely under estimated antenna gains). The initial effort outside AIPS to identify and flag bad data/baselines paid good dividends at this stage of processing.

6. In some cases, the graphical flagging task TVFLG was also used to interactively flag bad data.

7. CALIB was then used to compute the antenna based complex gains for the flux density calibrator scans with SNVER=0, GAINUSE=0, SOLINT=0.33. This generates the first antenna gains table (SN1) containing complex gain solutions with a time resolution of ∼ 20 sec.

8. To further identify bad data, the data was examined using UVPLT and VPLOT with DOCALIB=1 and SNVER=1. With these settings, the SN1 table is applied to the data on-the-fly. This essentially takes care of any short term variations in the antenna gains as well as variations in the sensitivity of the antennas.

This procedure helps in identifying mildly discrepant data, which cannot be corrected by any antenna based correction. As before, UVFLG was used to flag such data. SN1 was then deleted using the task EXTDEST with INEXT='SN' and INVERS=0. This deletes the latest SN table generated in any previous run of CALIB. Steps ?? to ?? were repeated till a satisfactory SN1 table was generated for the flux density calibrator.

9. The task CLCAL was then used with INTERPOL = 'MWF'; INTPARM = 0.5,0.5; CALSOURCE

= '3C286','3C48',''; SOURCE = '' to generate the second version of CL table (CL2) containing the median window filtered solutions derived from SN1. The resulting table CL2 contains flux calibration for all sources in the database and constitutes the basic flux calibration table.

10. Steps ?? to ?? were repeated for each phase calibrator to identify and flag bad data. This resulted into the third CL table (CL3) containing the median window filter solutions for the antenna gains, derived from the phase calibrator scans; this was used later to correct for slow variations in the antenna based complex gains. A fourth CL table (CL4) was also generated containing the the gain solutions for the phase calibrator with a time resolution of ∼ 20 sec (INERPOL='2PT'). This was later used for band pass calibration.

11. GETJY was then used with CALSOURCE='3C286','3C48' and SOURCE='' to derive the

flux density of the phase calibrator. If all was well in the above procedure, the derived flux density should be close to the value listed in the VLA calibrator manual and the error bars of less than 10% (after multiplication by the ratio of the system temperatures for the flux and phase calibrator fields, since the GMRT visibility database as yet does not contain the T^{sys} table). This corrects for the difference in the system temperatures between the flux and phase calibrators.

12. In all the above, a single, clean frequency channel, free from RFI, was used. All the calibrators used were strong enough to warrant the use of a single frequency channel. However, to use other channels for the purpose of imaging, a bandpass calibration also needs to be applied to calibrate any channel dependent gain variations. In the calibration procedure adopted here, it is assumed that the time calibration (determined in the above procedure) and bandpass calibration can be separated and determined independently. The time calibration table (CL4) was therefore applied to all the channels before deriving the band pass calibration table, the BP table. AIPS offers interpolation of the BP table in time to apply band pass calibration to data of the target source. Hence, the time calibrated data within the calibrator scans needs to be averaged, to generate a scan averaged band pass solution. The resulting band pass solutions (one per calibrator scan) can then be interpolated in time to take care of any slow variations in the band shape.

However, data affected by intermittent RFI needs to be flagged before the data is averaged in time. RFI on calibrator scans was identified using the task FLGIT on these calibrator scans. This task examines the data after subtracting a linear fit to the band shapes from individual baselines. A user specified set of channels is used to determine the linear fit. All data with residuals outside the user specified limits are then flagged. All channels were flagged for a given integration time containing bad data. This was achieved with the following settings for FLGIT: BCHAN=C0; ECHAN=C1; DOCALIB=1; GAINUSE=4 where, C0 and C1 are the first and the last frequency channels to be used. Several sets of (C0, C1) for range of clean frequency channels can be specified, which alone will be used for the linear fits, via the NBOXES and BOX keywords. The flagging criterion can be specified via the APARM keyword.

FLGIT was also used later on the calibrated data on the target sources. However, since the signal to noise ratio on individual baselines for extended sources can vary a lot, such automated procedures are of limited use. Identification of bad data on the target source was therefore usually done manually using tasks like UVPLT, UVFLG, TVFLG and

SPFLG.

13. The graphical data editing task SPFLG was sometimes used at this stage to identify and flag bad data. This task displays the data in the time-frequency plane from one baseline at a time and provides the same interface as that of TVFLG to graphically flag data.

14. Next, the BP table was derived by time averaging the data within the phase calibrator scans (after application of the time calibration). This was done using the task BPASS

with DOCALIB=1; GAINUSE=4; BPASSPRM(5)=1; BCHAN=C0; ECHAN=C1 where C0 and

C1 refer to the first and the last frequency channel to be used.

15. The BP table and band pass corrected band shapes were examined using the task POSSM. Large oscillations across the band were sometimes found in a few antennas. These antennas were usually flagged from the entire data base.

16. Finally, the task SPLIT was used to apply the time and band pass calibration (the CL and BP tables respectively) to the data on the phase calibrators as well as the data on the target source and single source multi channel calibrated databases generated. This

     was done using the following settings: DOCALIB=1; GAINUSE=3; DOBAND=3; BPVER=1.

Flux density calibration

Flux density calibration was done using observations of one of the two VLA flux density calibrators, 3C286 or 3C48. Time variability of these sources has been found to be small from the VLA monitoring of the flux densities of these sources. The absolute flux densities of these sources was derived by careful observations by ? using the VLA in D-array configuration and they found that the Baars scale (?) was slightly in error. They adjusted the flux density of 3C295 to that of Baars value and derived corrections for the flux densities of 3C286 and 3C48. These corrected flux densities are encoded in the AIPS task SETJY which was used to set the flux densities for these sources used for flux density calibration. The adopted flux densities of 3C286 and 3C48 were 28 and 42.7 Jy respectively (at 325 MHz). Observations of 3C48 with the VLA has shown that the flux density derived using SETJY gives the 325-MHz flux density with an accuracy of ∼ 2%.

The flux density calibrators were typically observed at the beginning and at the end of each observation. The phase calibrators used for these observations are also listed as good secondary VLA calibrators. The flux density calibrator scans were used to derive the flux densities of these secondary calibrators as a consistency check. The phase calibrators were also used as secondary calibrators to correct for any slow variations in the antenna gains. All fields observed for this dissertation also had many other sources in the field. For some of these sources, the 325-MHz flux densities were available from other independent observations as well (VLA calibrators, targeted VLA observations or the Texas survey (?) which gives the spectral index and point source flux densities at 365 MHz). These flux densities were also used for a consistency check on the flux calibration and to eliminate the possibility of any systematic flux calibration error.

The background temperature in the Galactic plane can change quite substantially for separate pointings. For accurate flux density calibration, one must measure the system temperature for the flux density calibrator field as well as for the target field. To also account for small time dependent variations in the system temperature, it should be monitored regularly during the length of the observations. The planned periodic injection of calibrated noise at the front-end of each antenna to measure the system temperature has not yet been implemented at the GMRT. In its absence, the system temperature was measured at a few positions around the target source in the Galactic plane and the measured system temperature used to correct for the differences in the background temperature between the field of interest and the flux density calibrator. The background temperature from the 408-MHz all sky survey (?) was also estimated as a consistency check. With this scheme, we estimate that the 325-MHz flux densities from GMRT are accurate to ∼ 15%.

Phase calibration

Slow variations of the antenna based complex gains occur on time scales of a few tens of minutes. The relative phase variations between the antennas due to this needs to be corrected so as to phase the array over several hours. These slow variations are measured using periodic observations of a phase calibrator. Since the system temperature at 325 MHz in the Galactic plane is a factor of 3-5 higher than away from the plane, the phase calibrators must also be strong (typically > 10 Jy) to provide enough signal to noise ratio for the computation of antenna based complex gains. Temporal as well spatial variations in the ionospheric total electron content at 325 MHz is expected to be the major source of phase corruption. This can produce phase variations over the scale of the array (and sometimes even across the primary beam of each antenna). It is therefore not advisable to use a phase calibrator too far from the target field since the antenna based complex gains obtained from the phase calibrator may not reflect the phase variations in the direction of the target field.

Using the antenna based phase variation derived from continuous observations of the phase calibrators for several hours (Figs. ?? and ??), it was estimated that phase variations over a time scale of about half an hour could be approximated well by linear interpolation. This is thus the time scale at which one needs to observe the phase calibrator (∼ 30 minutes). The three VLA 327 MHz calibrators 1709-299, 1830-36, and 1822-096 with 327-MHz flux densities of 6, 28, and 13 Jy respectively, were used as phase calibrators. The angular separation in the sky between the phase calibrators and the target field was typically 10−15^{∘}. The maximum error in phase due to errors in the antenna co-ordinates, when the phases from the phase calibrator are transferred to the target source was estimated to be a few degrees (see Section ??). Tests done by phasing the data from one calibrator using periodic observations of another calibrator show that the array is phased over time scales of ∼half an hour using this procedure.

Bandpass calibration

The antenna based complex gains vary across the passband, primarily due to the antenna based band shape and residual fixed delay errors. These variations in the complex gains must be corrected before the visibilities from individual frequency channels are averaged.

As mentioned above, the phase calibrators were strong enough to provide enough signal to noise ratio for the computation of channel dependent antenna based complex gains. The antenna band shape corrections were therefore derived using the phase calibrators. An average gain was computed for each of the phase calibrator scans per channel and the linearly interpolated values applied to the target source data to correct for the channel dependent complex gains.

4.5 Inversion and deconvolution of GMRT data

The 325-MHz primary beam of GMRT antennas has a full width at half maximum (FWHM) of ∼ 1^{∘}.4. The central square provides a maximum baseline of ≈ 1 km equivalent to an angular resolution of ∼ 3 arcmin. At this resolution, the full GMRT primary beam can be mapped without severe degradation due to non-coplanar effects. As a first step, with the dual purpose of gauging the data quality and locating strong confusing sources, single facet images were made at a resolution of ≈ 1 arcmin using the task IMAGR.

Having identified the sources in the field of view from this lower resolution image, higher resolution imaging was attempted. Typically, a maximum baseline of 20kλ was used corresponding to an angular resolution of ∼ 15 arcsec. Most of the fields had strong extended sources all over the field of view forcing the mapping of the full primary beam. At these resolutions, the number of planes required along the n-axis is 8. Hence, a 3D inversion was required. The IMAGR task of AIPS performs a 3D inversion using the polyhedron imaging algorithm. In this, the entire field of view is divided into a two dimensional grid of facets. A small part of the sky (corresponding to the size of the facet) centred around each facet is then imaged by first shifting the phase centre of the visibility to the centre of the facet and then performing the normal 2D inversion and CLEANing. Since, the 2D approximation is assumed to be valid within the facet, it is important to make sure that the facet is not so big as to re-introduce distortions at the edges of the facets.

The number of facets required for 3D inversion using IMAGR and the appropriate RA and DEC shifts for the centre of each facet, were computed using the relatively new task in AIPS called FCSET. Essentially, given the size of each facet, the size of the field of view and the RA and DEC of the phase center, this task writes out a IMAGR readable list of field specifications (the field number, its RA and DEC shifts and its size in number of pixels along the RA and DEC axis). Typically, this resulted in a 5 × 5 grid of facets, each of size 256 × 256.

After the inversion of each of the facets, the IMAGR task uses the usual 2D Clark CLEAN (?) on each facet. The class of CLEAN and MEM based deconvolution algorithm treats each pixel in the image as a degree of freedom. Even when mapping in the Galactic plane (or close to it), it is clear from the images that most of the pixels do not have any physical emission associated with them. Reconstruction of the physical emission in the field of view should therefore be somehow constrained to use only those pixels where there is significant physical emission from the sky. Not doing so is equivalent to giving more freedom to a nonlinear fitting process (the deconvolution process), than is justified by the data. CLEAN based algorithm (and its variants) are themselves unconstrained. This constraint must therefore be provided externally by setting boxes around the dominant sources in the field of view at each cycle of CLEAN. It has been shown by ? that the best results are obtained by putting as tight a box as justified by the data (essentially by inspection). During the deconvolution process, the IMAGR task provides a facility to dynamically define boxes for each field for every cycle of CLEAN. However, since the emission was usually of complex morphology making it difficult to define tight boxes, simple square boxes enclosing the source of emission were used. This was manually done for each facet.

The resulting set of facet images were put together to reconstruct the sky using the task FLATN. The FLATNed image was then primary beam corrected using the task PBCOR. The GMRT visibilities correspond to the date-epoch at the time of observations. The final image was therefore rotated to the J2000 epoch using the task REGRD.

4.6 The Images

This section presents the final images produced via the procedure described above. All images were corrected for primary beam attenuation using a polynomial approximation of the GMRT primary beam. As mentioned earlier, the resolution in these images changes from image to image due to a combination of declination dependent uv-coverage, changes in the number of available antennas and the flagging of bad data. Images of fields with large angular size sources are presented at a few arcmin resolution. Higher resolution images of some of the fields were also made where necessary (due to the presence of small angular size sources of interest in the field, e.g. the field containing G003.6-0.1).

Fig. ?? shows the GMRT image of the field containing the SNR G001.4-0.0 at the centre of the image. Other well known sources (SNRs and H II) regions in the Galactic Centre region are clearly visible in this image. The RMS noise is relatively high, possible due to the Galactic Center which lies at the south-western edge of the primary beam. Few of the GMRT antennas had servo related errors due to which there were small oscillations in the antenna pointing while tracking. This, in the presence of strong sources at the edge of the fields, results in short time scale differential gain variations which are not easy to correct later and also results in a higher RMS noise.

Fig. ?? shows the full primary beam corrected images of the field containing the SNRs G004.7-0.2, G003.8+0.3 and the unclassified source G003.6-0.1. The low resolution image in the left panel was made using a single facet, while the higher resolution image was made using a grid of 4×4 facets. The lower surface brightness SNR G003.8+0.3 is better discerned in the low resolution image.

The dominant extended source in Fig. ?? is a known Ultra Compact H II region (?). A small angular size SNR G004.2-0.0 was reported by ? in this field at the centre of this image. However there is no indication of this source at the level of 10 mJy/beam in this image. It is, however detected as a compact flat spectrum source in the low resolution image. This sources is unlikely to be an SNR.

Fig. ?? shows the GMRT 325-MHz image of the shell type SNR G004.8+6.2. The strong, marginally resolved source due west of this SNR is the well known Kepler’s SNR (Fig. ??). G004.8+6.2 is again clearly detected in the NVSS image of this region (Fig. ??). This SNR is also detected in the image made from a 327-MHz VLA observation of a region close to this source (Fig. ??).

Fig. ?? shows the field containing the barrel shaped SNR G356.2-1.5. The 843-MHz image of this SNR by ? was severely affected by artifacts due to the grating response of nearby sources. This SNR is however clearly detected in the GMRT 325-MHz image. A marginally extended source of emission is also visible in this image in the north-eastern direction.

Fig. ?? shows the GMRT image of the shell type SNR G356.2+4.5. This SNR is also clearly visible in the NVSS image of this region (Fig. ??). The quality of NVSS images close the Galactic plane is usually poor. However, a few degrees away from the plane, low surface brightness SNRs are often easily visible in NVSS fields (???). A careful examination of the NVSS fields, few degrees away from the plane is therefore likely to result in the identification of more, hitherto unknown SNRs. Deep imaging of such objects can then be followed up with the GMRT/VLA. Detailed multi frequency imaging of a number of high Galactic latitude SNRs can be used to possibly deduce the distribution of ionized gas and examine the statistical significance of the Σ-D-z relation (?).

Fig. ?? shows the GMRT image of the incomplete shell of the SNR G358.0+3.8. This is a low surface brightness SNR, but also detected in the NVSS image (Fig. ??).

Figure 4.4: Full primary beam image of the field containing the sources G001.4−0.0 at the centre of the image. The resolution in the image is ≈ 3 × 2 arcmin^{2}. The RMS noise in the images is ∼ 30 mJy/beam. The Galactic Centre sources (?) Sgr D HII region and Sgr D SNR pair, the SNR G000.9+0.1, Sgr B1 and Sgr B2 are the dominant sources in the south-east direction.

Figure 4.5: Full primary beam image of the field containing the sources G003.6−0.1, G003.7-0.2, and G003.8+0.3. The resolution in the image in the left panel is this image ≈ 98 × 29 arcsec^{2} while that in the image in the right panel is ≈ 20 × 11 arcsec^{2}. The RMS noise in the images is ∼ 5 mJy/beam. The extended emission is more clearly visible in the low resolution image, which was generated using a single facet. The higher resolution image was made with multiple facets.

Figure 4.6: High resolution, multi facet image of the field containing G004.2−0.0. The resolution in the images is ≈ 15 × 10 arcsec^{2} and the RMS noise ≈ 5 mJy/beam. The dominant extended source in the field is an Ultra Compact H II region. There is a hint of a emission at the location of G004.2−0.0, but much below the expected level, probably indicative of thermal source (see Figure ?? for a low resolution image where G004.2−0.0 is detected as compact source).

Figure 4.7: Full primary beam corrected image of the field containing G004.8+6.2. The weaker source, due east of the centre of the image is the SNR G004.8+6.2. The strong source due west of the image centre is the 38 Jy Kepler’s SNR. The resolution in the image ≈ 2.3 × 1.4 arcmin^{2} and the RMS noise is ≈ 23 mJy/beam. Apart from other unknown sources of noise, the higher RMS noise in this image is also due to the wobble in the antenna pointing for some of the antennas used for this observation.

Figure 4.8: Multi facet image of the field containing G356.2-1.5. The resolution in the image on the left is ≈ 1.7 × 0.8 arcmin^{2} and the RMS noise is ≈ 5 mJy/beam. Notice the extended emission north-east of the barrel shaped SNR in the centre of the field. The panel on the right shows a high resolution image of this extended source.

124 CHAPTER 4. THE GMRT DATA Figure 4.9: Full primary beam corrected image of the field containing G356.2+4.5. The resolution in the image is ≈ 3 × 1.5 arcmin^{2} and the RMS noise is ≈ 10 mJy/beam.

4.6. THE IMAGES 125 Figure 4.10: Full primary beam corrected image of the field containing G358.0+3.8. The resolution in the image is ≈ 2.6 × 1.5 arcmin^{2} and the RMS noise is ≈ 15 mJy/beam.

126 CHAPTER 4. THE GMRT DATA

Observations of Supernova

Remnants

This chapter discusses the GMRT 325-MHz observations of candidate and known SNRs. The motivation behind this exercise was two-fold. Firstly, to use the higher sensitivity and resolution provided by GMRT at low frequencies which would unambiguously identify the SNRs. Secondly, GMRT has only recently come to a stage where enough antennas are available in the interferometric mode to attempt imaging of weak extended sources, which truly tests the imaging performance of the instrument. In these early stages of the telescope where a large fraction of time and effort goes into debugging the instrument, it was important to have a scientific goal in mind to provide the focus, direction and motivation to debug the telescope and bring it to a level where it can be used for scientific purposes. These observations provided the required focus where the scientific returns for the debugging effort put-in were perceived to be substantial.

5.1 Introduction

Radio emission from Supernova remnants (SNRs) is due to the synchrotron radiation mechanism which has a non-thermal power law dependence on frequency with a negative spectral index α (S ∝ ν^{α}). This makes the emission progressively stronger at lower frequencies (see Section ??). On the other hand, thermal emission from typical HII regions, the other class of objects with extended radio emission in the Galaxy, has a flat spectrum above ≈ 1 GHz. Below this frequency, the optical depth is much greater than 1 and the spectrum turns over with a spectral index of 2. The low frequency continuum spectra of Galactic objects are therefore frequently used to distinguish between thermal and non-thermal sources of emission (???). The other key observational evidence used to identify SNRs is their morphology. Detection of an extended non-thermal source with no thermal emission has been the criterion used to identify Galactic sources as SNRs.

Kassim (?), in a study of non-thermal emission from known Supernova remnants in the Galaxy, demonstrated that the radio emission from most SNRs gets absorbed at frequencies below about 100 MHz. He observed a number of SNRs, widely distributed in the inner Galaxy and showed that about two thirds of all SNRs show this spectral turn-over due to free-free absorption by the intervening ISM; this indicates the presence of an extended low density warm ionized medium (ELDWIM) in the Galaxy. Since then, many more SNRs has been imaged at frequencies between 1 GHz and 327 MHz (and in some cases even below 327 MHz). A collection of the radio spectra of SNRs have been compiled by ?^{1}. His catalogue of SNR spectra also gives the spectral indices above and below the turn-over frequency and the frequency at which the spectrum turns over. Spectra of about 35% of the SNRs from this catalogue show a low frequency turn-over. The measurement of this turn-over frequency for SNRs distributed throughout the Galaxy can be used to indirectly measure the distribution of this phase of the ISM, which is otherwise inaccessible to direct observations.

Imaging of HII regions at frequencies below ∼ 1 GHz, together with the electron temperature derived from RRL observations have been used to deduce improved estimates of the physical properties of HII regions (????). Low frequency continuum mapping in the Galactic plane is therefore important from the point of view of identification of SNRs, separating thermal emission from non-thermal emission and for studying the intervening ISM.

Radio emission from SNRs is typically extended, often with a low surface brightness. Telescopes which are sensitive to extended emission as well as to total flux, are required to image such objects. Single dish observations are sensitive to emission at all scales in the field. While interferometric telescopes typically provide much higher resolution, they are insensitive to scales larger than those corresponding to the smallest projected baseline. Single dish telescopes, at high frequencies, provide the sensitivity and moderate resolution required for such work. Till recently many observations were therefore done using single dish instruments. However, single dish observations pose a separate problem. While single-dish observations do not discriminate against extended emission, they are more prone to large scale confusing emission, which is abundantly present in the Galactic plane. Low frequency single dish observations do not provide the required resolution to resolve the extended nature of the SNR emission. For these reasons, most Galactic SNRs have been observed using single dishes at high frequencies (> 1 GHz) which provide reasonable resolution (better than 1′). Higher resolution interferometric observations of some Galactic SNRs have also been done. However, such observations are often restricted to observing relatively small sized SNRs. Imaging at low frequencies using interferometers is also relatively difficult due to problems arising from higher level of RFI, higher phase noise at low frequencies (due to various reasons ranging from cross talk to ionospheric phase corruption), non-co-planarity of array requiring much more complex software and higher computing power. Hence, even interferometric observations have been typically done at frequencies > 1 GHz.

1 Available from http://www.ratan.sao.ru/_{}˜ cats on the web

However, observations at high frequencies have another source of emission, namely the thermal emission from HII regions which, in some cases, is fairly strong. The non-thermal emission from SNRs becomes progressively diminished at higher frequencies, while the thermal emission remain fairly constant as a function of frequency at frequencies higher than about 1 GHz. High frequency observations therefore miss extended low surface brightness emission from SNRs. Such observations alone can also wrongly classify sources which have thermal and non-thermal components in the radiation (for example, due to line-of-sight super-position of thermal and non-thermal emission). Thus, while high frequency telescopes provide the required resolution and sensitivity, they alone are not adequate for the identification of Galactic objects as SNRs.

Recently, synthesis telescopes like the GMRT (?) and MOST (?) have been used to image parts of the Galactic plane. The MOST survey, at a resolution of ≈ 90 × 43.5 arcsec^{2} and is sensitive to angular scales up to 30′, identified seventeen candidate SNRs. Most of these object are large (> 5 − 10′). Many of the fields however suffer from the grating response due to nearby strong sources and from confusing thermal emission from nearby strong HII regions.

? used the Parkes 64-m single dish telescope to image a set of large, high latitude SNRs at 2.4 GHz. These observations identified about a dozen new large SNRs (> 15′) south of −25^{∘} declination. Again, besides the lower angular resolution of the single dish, these observations suffered from the problem of separating extended diffused non-thermal emission from thermal emission in and around the Galactic plane using these high frequency.

The GMRT at 327 MHz provides a resolution of up to ∼ 20 arcsec and is sensitive to spatial scales up to 30 arcmin. The relatively smaller field-of-view (half-power beam width of ≈ 1^{∘}.4) of the GMRT also provides an advantage in terms of attenuating confusing emission from near by strong sources. At this frequency, the thermal emission from typical Table 5.1: Observed and derived physical parameters of the candidate SNRs in the fields. Type code ’S’ implies shell-type, ’B’ implies barrel-type while ’N’ means that the object is most likely not an SNR.

Name  RA_{J2000} Dec_{J2000} S_{327MHz}  Size  Type  α
(h m s) (^{∘} ′ ′′)  (Jy)  (arcmin)  (S ∝ ν^{α})
G001.4−0.1 17 49 39 -27 45 4.2 ± 0.5  8.0  S  −0.8 ± 0.3?
G003.7−0.2 17 55 29 -25 50 4.5 ± 0.3  -  B  −0.7 ± 0.1
G003.8+0.3 17 53 02 -25 24 8.7 ± 0.3  18  S  −0.9?
G004.2−0.0 17 55 22 -25 15 0.1 ± 0.2  -  N  -
G004.8+6.2 17 33 24 -24 34 5.5 ± 1.2  17  S  −0.6 ± 0.1
G356.2+4.5 17 18 58 -29 40 8.1 ± 1.7  25  S  −0.7 ± 0.2
G356.3−1.5 17 42 40 -32 52 5.7 ± 0.2  15  S/B > −0.7 ± 0.1
G358.0+3.8 17 26 03 -28 36 2.5 ± 1.3 37 × 39  S  -

HII regions is severely diminished, while the emission from SNRs remain relatively strong. The higher resolution and sensitivity at these low frequencies, make the GMRT an ideal instrument for studies of Galactic SNRs. Compared to the resolutions of about 1′ and 1.5′ and RMS noise of ≈ 20 mJy/beam and 35 mJy/beam in the survey by ? and ? respectively, the GMRT at 327 MHz provides a factor of 2 lower RMS noise and, depending upon the largest baselines used, up to 2–5 times better resolution.

5.2 Candidate SNRs

This section presents the results from the 327-MHz GMRT observations of fields containing candidates SNRs. The list of fields observed and the parameters of SNRs found in these fields are list in Table ??.

5.2.1 G001.4−0.1

The GMRT 327-MHz image of G001.4−0.0 is shown in Fig. ??. A partial arc of ∼ 8 arcmin diameter is clearly visible in this image. A compact source, almost at the geometric centre of the arc is also clearly visible. The morphology is very similar to that of the nearby composite SNR G000.9+0.1 which has a flat spectrum, X-ray emitting compact central Figure 5.1: 327-MHz image of G001.4−0.0 using GMRT. A partial shell with compact source located almost at the centre is clearly detected.

source (?). This SNR lies just north-east of the Sgr D HII region and at the very edge of the VLA 327-MHz wide-field image of the Galactic centre region (?). A weak fuzz of emission is seen in this wide-field image corresponding to this SNR. However, the image quality for this region is too poor (due to primary beam attenuation) to be able measure the flux density or decipher the morphology.

The 327-MHz flux density measured from our observation was found to be 4.2 ± 0.5 Jy. The 843-MHz image (?) suffers from artifacts due to the grating response of Sgr A and the flux density of ∼ 2 Jy is hence only a “tentative” figure. From their 1616 MHz VLA observations of this region, ? reported “an arc of incomplete shell” of diameter ∼ 7 arcmin at this location. The incomplete arc seen in the GMRT image agrees well with the incomplete arc seen in the 1616-MHz image. The MOST image of this object shows a relatively featureless source of emission and the “complete shell” reported by ? is difficult to decipher.

This source was also the target of observations for the detection of OH (1720 MHz) maser emission by ?. In the VLA A-array observation, they detect a maser spot, coincident with the western edge of the arc. Their VLA D-array observations detect an extended arc of emission, almost coincident with the arc seen in the radio continuum images.

The spectral index between 327 and 843 MHz is −0.8 ± 0.3 for the shell. However, given that the 843-MHz flux density is quite uncertain, this value of the spectral index remains tentative and is used only to show the non-thermal nature of emission. Based on the morphology, non-thermal nature of emission and association of OH (1720 MHz) emission, we propose that this is a shell-type SNR in the Galactic plane.

5.2.2 G003.8+0.3

? describes G003.8+0.3 as a “fairly weak, incomplete ring structure most perfectly centered on a slightly extended source”. The morphology of this object in the GMRT 327-MHz image, shown in Fig. ??, matches well with the 843-MHz MOST image. This SNR is also in the field of view for the pointings for G003.7−0.2 and G004.2−0.0. The partial shell is clearly visible in both the images. The IRAS 60μm image, shown in Fig. ??, does not show any significant emission at this position. However, this SNR lies within a ring of IR emission seen clearly in this image. The northern rim of the radio ring is significantly brighter and more extended, almost filling the IR ring, making it difficult to define the center of the radio ring structure. The “central source” in the radio image is fairly close to the center defined by the inner edge of the ring structure, but not close to the center defined by the outer edges. The bridge of emission connecting the central source and the ring is not so clearly seen at 327 MHz.

The integrated flux density of this region at 327 MHz is 8.7 ± 0.3 Jy. The diameter of the ring structure (including the northern extension) is ≈ 18′ while its center is at RA_{J2000} = 17^{h}53^{m}02^{s}, Dec_{J2000} = −25^{∘}24′. The position of the emission peak for the ’central source’ is RA_{J2000} = 17^{h}52^{m}54^{s}, Dec_{J2000} = −25^{∘}28′. The flux density of the VLA 21-cm calibrator J1751−253, which is just west of this region is measured to be 1.3±0.2 Jy. Flux density of this source from Texas survey (?) is 1.41 ± .09 Jy.

The flux density reported by ? at 843 MHz is ≈ 3.5 Jy giving a spectral index of −0.9. Based on the morphological evidence and evidence for non-thermal nature of emission, we propose that this source is a weak, Galactic SNR.

The ’central source’ is detected as a point source at 1400 MHz in the NRAO-VLA All Sky Survey (NVSS) with a flux density of 15.1 mJy. Although it is a weak source in the 327-MHz image with flux density barely at the 2σ level, it is nonetheless stronger than Figure 5.2: GMRT image at 325 MHz of G003.8+0.3. The shell morphology of G003.8+0.3 is clearly visible.

Figure 5.3: 327-MHz contours overlayed on the 60μm IRAS gray scale image of G003.8+0.3. A shell of IR emission is visible and the radio emission from the SNR is completely within the IR shell and almost fills the IR shell in the north. There is, however, no significant IR emission at the location of the SNR itself. The small extension in the eastern edge of the radio shell is coincident with the strong IR compact source.

Figure 5.4: Image of G003.8+0.3 at 11 cm from the 100-m Effelsberg single dish survey. An arc of emission similar to that seen at lower frequencies is clearly visible.

15 mJy, proving that it is a non-thermal source. With a large error in the measurement of the 327-MHz flux density, it is difficult to determine an accurate spectral index.

Image of this SNR from the radio continuum survey of the Galactic plane at 11 cm using the 100-m Effelsberg telescope (?) is shown in Fig. ??. Here too, a partial shell of emission is visible, which matches well with the morphology of this SNR seen at 843 and 327 MHz. Significant amount of linear polarization is also detected in the 11 cm polarized images.

5.2.3 G004.2−0.0

This source is the smallest diameter candidate SNR (size ∼ 3.5 arcmin) reported by ?. He reported the location of this object as RA_{J2000} = 17^{h}55^{m}17^{s}, Dec_{J2000} = −25^{∘}14′51′′. The total 843-MHz flux density was reported to be 200 mJy. However this object sits in a negative bowl and the measured value after tentative correction for this bowl is in the range Figure 5.5: GMRT 327-MHz image of the region containing G004.2+0.0. The strong extended source in this field is a classified Ultra Compact H II region G004.417+0.126. The left panel shows the high resolution image (∼ 15 × 11 arcsec^{2}) of this region where the core-halo morphology of G004.417+0.126 is clearly visible. It’s south-western tail is visible in Grey’s 843-MHz image of this region. The RMS noise in the map is about 5 mJy/beam. The right panel shows the low resolution image where an unresolved source is detected at the location of the candidate SNR just south of G004.417+0.126. The RMS noise in this image is ∼ 8 mJy/beam.

of 100 − 300 mJy (Gaensler, private communication). A high resolution image of this field was made to look for the shell-type structure at 327 MHz. There is a hint of a compact source in this image at RA_{J2000} = 17^{h}55^{m}22^{s}, Dec_{J2000} = −25^{∘}15′01′′, but barely at the 2σ level. No shell-type structure was detected at the level of ∼ 5 mJy/beam with a resolution of ∼ 15 arcsec. The low resolution image, shown in Fig. ?? has a ∼ 100 mJy object at the location of this source. There is probably a compact source in the NVSS image at this location, but again at the 1 − 1.5σ level. The 60μm IRAS image of this region (Fig. ??) also shows significant extended emission at the location of this source (indicated by a cross