From ZADEH@OSSENU.ASTRO.NWU.EDU Mon Dec 2 19:38:27 1996 From: ZADEH@OSSENU.ASTRO.NWU.EDU Date: Mon, 2 Dec 1996 18:34:40 -0600 (CST) To: gcnews@astro.umd.edu Subject: The nature of faraday screen... *************************************************** \documentstyle[11pt,aasms4]{article} %\documentstyle[11pt,aaspp4]{article} %\documentstyle[aas2pp4]{article} \received{00 March 1996} \accepted{00 1996} %\journalid{337}{15 January 1989} %\articleid{11}{14} % Authors may supply running head information, if they wish to do so, although % this may be modified by the editorial offices. The left head contains a % list of authors, usually three allowed---otherwise use et al. The right % head is a modified title of up to roughly 44 characters. Running heads % are not printed. \lefthead{Yusef-Zadeh, Wardle \& Parastaran} \righthead{The Nature of the Faraday Screen} % This is the end of the "preamble". Now we wish to start with the % real material for the paper, which we indicate with \begin{document}. % Following the \begin{document} command is the front matter for the % paper, viz., the title, author and address data, the abstract, and % any keywords or subject headings that are relevant. \begin{document} \title{The Nature of the Faraday Screen Toward the Galactic\\ Center Nonthermal Filament G359.54+0.18} \author{F. Yusef-Zadeh} \affil{Department of Physics and Astronomy, Northwestern University, Evanston, Il. 60208 (zadeh@ossenu.astro.nwu.edu)} \author{M. Wardle} \affil{Research Centre for Theoretical Astrophysics, University of Sydney NSW 2006, Australia (wardle@physics.usyd.edu.au)} \author{P. Parastaran} \affil{Panasonic Factory Automation, Frankslin Park, Illinois (payman@nwu.edu)} \begin{abstract} We present multifrequency VLA observations of the intensity and polarized emission from G359.54+0.18, a system of nonthermal filaments near the Galactic Center. The intrinsic magnetic field lines run primarily along the filaments. The rotation measure (RM) varies between --4200 and --370 rad m$^{-2}$ on scales of several arcseconds, implying that the ionized, magnetized medium responsible for the Faraday rotation is less than 0.1 pc thick. In turn, this implies that the magnetic field in the Faraday screen is large, suggesting that it is located close to the Galactic center. Further evidence is provided by the anisotropy of the RM fluctuations. The structure of the eastern portion of G359.54+0.18 suggests that the magnetic field in the filaments is highly distorted as a result of an interaction with an adjacent Galactic center molecular cloud. \keywords{Galaxy: center--- ISM: magnetic fields---radiation mechanisms: non-thermal--- polarization---filaments} \end{abstract} \vfill\eject \section{Introduction} Radio continuum studies of the Galactic center region over the last decade have revealed a number of synchrotron-emitting filamentary structures that run roughly in the direction perpendicular to the Galactic plane (Yusef-Zadeh, Morris \& Chance 1984; Liszt 1985; Bally \& Yusef-Zadeh 1989; Gray et al. 1995). Single-dish polarization studies of broad features surrounding the linear filaments suggest that the large-scale magnetic fields are organized on a scale of 100 pcs (Sofue \& Handa 1984; Inoue et al. 1984; Seiradakis et al. 1985; Tsuboi et al. 1986; Haynes et al. 1992). These studies also suggest that the geometry of the magnetic field is generally poloidal near the Galactic center region. It has long been suspected that the linear filaments trace magnetic field lines, but strong Faraday rotation toward these sources even at 32 GHz (Reich 1994) has prevented a determination of the intrinsic field direction. A polarization study of a similar filament, G359.1-00.2, the ``Snake'' by Gray et al. (1995) could not reliably determine the intrinsic field direction because of the small frequency range covered. In this {\it Letter} we present observations of the Faraday rotation towards an isolated system of filaments known as G359.54+0.18, and address the intrinsic orientation of the magnetic field associated with the fine-scale structure, the nature of the Faraday medium, and the possible evidence for the interaction of the nonthermal filaments with a nearby molecular cloud. %\placefigure{fig1} %\placefigure{fig2} \section{Observations and Data Reduction} Multi-frequency observations at C ($\lambda$6cm) and X ($\lambda$3.6cm) bands were obtained using the VLA\footnote{The VLA of the NRAO is a facility of the National Science Foundation, operated under a cooperative agreement by Associated Universities, Inc.} in its CnB and DnC hybrid arrays in June 1988 and May 1989, respectively. The phase center was chosen at $\alpha(1950)=17^h 40^m 39^s, \delta(1950)=-29^0 12' 20"$ (l=359.55$^0$, b=+0.18$60$) for both bands in both arrays. Additional pointing at $\alpha(1950)=17^h 40^m 57.5^s, \delta(1950)=-29^0 13' 0"$ (l=359.57$^0$, b=+0.12$^0$) was also obtained only in the DnC array at $\lambda$6cm. In order to remove the effect of Faraday rotation, we centered four distinct frequencies at C band between 4.585 and 4.885 GHz each separated by 100 MHz, and two frequencies 8.4149 and 8.4649 GHz at X band. Unlike the C band data, the X band data was combined because a small rotation of only 0.045 radians is expected in this band when the RM is assumed to be 3000 rad/m$^2$. However, there is a rotation of about 3 radians between 4.5 and 5 GHz in the C band, thus, determination of rotation measure is complicated by n$\pi$ ambiguities if the C band data is not analysed separately. The data at 4.785 GHz was discarded because of strong interfering signals. Bandwidth depolarization was too small to have appreciable effect on the RM presented here. We used 3C286 and 1748-253 as the flux and phase calibrators, respectively, for each individual data set. The flux density of the flux calibrator was estimated using the Baars et al. (1977) formula. After editing and calibrating the data in each array and then combining the data corresponding to both arrays in C band, four separate Stokes I, Q, U images (three at C and one at X band) were made in AIPS, all of which were convolved with a Gaussian CLEAN beam size of $4''\times4''$. The noise level of the polarization (total) intensity images are $\approx$ 37 (54) and 20 (28) $\mu$Jy at C and X bands, respectively. The corresponding brightness temperatures of the noise level of the total intensity at 4.8 and 8.4 GHz are 181 and 31 mK, respectively. The rms noise of the polarization (total) intensity of the data centered on the second pointing is 60 (150) $\mu$Jy at C band. The polarization intensity, P=(Q$^2$+U$^2)^{0.5}$, fractional polarization, m=P/I, and polarization angle, $\Psi$=0.5 arctan (U/Q), images were then constructed. The four polarization angle images and their corresponding error images were incorporated into a cube and then images of the distribution of the RM and magnetic field orientation were made using the RM algorithm in AIPS. The polarization angles having errors that exceeded 5 degrees were blanked in the RM calculations. We also used the STFUN algorithm in AIPS to determine the structure function for the central region of the RM image, where the filaments are polarized and the RM is determined wth sufficient accuracy. \section{Results} The distribution of the total intensity at $\lambda$6cm is shown in the top panel of Figure 1, and the corresponding linearly polarized intensity image is shown in the bottom panel. Two major linear filaments run parallel to each other. The surface brightness of the total and polarized intensities peak in the central region with values of about 2.8 and 1.55 mJy beam$^{-1}$, respectively. The fractional polarization is as much as 60\% at $\lambda$6cm in the central region of the filaments. Unlike the total intensity image, the polarized intensity is clumpy but still shows that the individual parallel filaments are linearly polarized. A radiograph of the total intensity of the emission from the eastern extension of the linear filaments, based on the second antenna pointing, is presented in Figure 2. This reveals extended features with typical surface brightnesses of 1 to 2 mJy/beam. The features are unpolarized except for two discrete sources near $\alpha(1950)=17^h 41^m, \delta(1950)=-29^0 13'$ having fractional polarization of $\approx$50\% (Staghun et al. 1996). At the eastern extension of G359.54+0.18, the linear filaments are most distorted near $\alpha(1950)=17^h 41^m 10^s, \delta(1950)=-29^0 14'$ as they merge with the extended structure that resembles an HII region. Figure 3 shows the color image of the RM distribution toward the filaments with typical RM values ranging roughly between --3000 and --1500 rad/m$^2$ and with extreme values between -4200 and -370 rad/m$^2$. There are four large clumps with right ascension ranging between 17$^h 40^m 40^s$ and 17$^h 40^m 46^s$. The top panels of Figure 4 show the RM along lines of constant declination through the center of each clump, with the data points for a given pixel in the RM distribution image plotted as triangles. Each clump of polarized emission exhibits a more or less uniform RM with variations of few hundred rad m$^{-2}$. The most negative RM is noted in the western portion of the filaments and the average RM varies greatly among the four clumps with the median RM's --2110, --1550, --2040, --2780 rad m$^{-2}$. The lower panels show the wavelength dependence of the Faraday rotation at a sample point in each clump, with the solid line showing the least-squares fit to a quadratic wavelength dependence. The quadratic dependence of the polarization angle on $\lambda$ implies that the Faraday screen is external to the system of filaments. This is supported by the large rotation of the plane of polarization, 300$^0$ to 400$^0$, and the high fractional polarization: internal Faraday rotation cannot rotate the plane of polarization by more than 90$^0$ without very high depolarization (Burn 1966). There is a reduction by a factor of ten in the polarized emission at $\lambda$6cm in the region between polarized clumps. This effect could either be due to the rotation of the plane of polarization across the synthesized beam or due to internal Faraday depolarization. We consider it more likely that the depolarization is caused by a large rotation measure gradient in the Faraday screen since the biggest change in the RM occurs on either side of the clumps where fractional polarization is reduced substantially at $\lambda$6cm. In particular the highest RM gradient, 250 rad m$^{-2}$ arcsec$^{-1}$, coincides with a feature at $\alpha(1950)=17^h 40^m 33.4^s, \delta(1950)=-29^0 12' 12"$ that is not polarized at $\lambda$6cm. Figure 5 shows the distribution of the intrinsic direction of the magnetic field in the central region of G359.5+0.18 superimposed on contours of total intensity at $\lambda$6cm. The magnetic field is predominantly oriented parallel to the filaments. However, the intrinsic direction of the field changes perpendicular to the direction of the filaments at some positions along the linear filaments, in particular, along the western segment of G359.54+0.18 in Figure 1 near $\alpha=17^h 40^m 33^s, \delta=-29^0 12' 15"$. At these locations, we note that the RM gradient (see Fig. 3) is larger than in the region where the field runs along the filaments. In addition, the polarization angle still follows $\lambda^{2}$. It is possible that the non-parallel fields are artifacts because they are distributed mostly at the edge of the clumps. The variations in the derived RM image appear to be anisotropic, with a characteristic angular scale of ten arcseconds present in the direction running along the filaments. The variation in RM over an angular scale $\delta\theta$ can be quantified using the two-dimensional RM structure function $\kappa(\delta\theta)=<[RM(\theta+\delta\theta)- RM(\theta)]^2>$ (e.g. Simonetti \& Cordes 1988). Our data allow this to be evaluated for angular scales between 0 and 40$''$ parallel to the filaments, and 0 to 10$''$ across the filaments; at larger seperations the number of pixels available to form the structure function becomes small and the curves become noisy. The resulting structure function is shown in Figure 6 for angular separations parallel and perpendicular to the filaments. At the smallest scales, errors in the RM measurements dominate and are responsible for the break in the structure functions at 1--2 arcseconds. It is clear, however, that the structure function is anisotropic, with a fairly strong correlation between separations of ten arcseconds along the filaments. The filament is tilted by about 50\arcdeg with respect to the Galactic plane, and the major axis of the structure function is tilted by a further 17\arcdeg. \section{Discussion} The polarization of the nonthermal emission from G359.5+0.18 shows that the intrinsic magnetic field is predominantly oriented parallel to the filaments, and the high degree of polarization and the alignment of the magnetic field along the central portion suggest that the field is highly uniform. The eastern end of the filaments appear to be associated with an HII region and a newly-discovereed molecular cloud (Staghun et al. 1996). A more detailed examination of this region, where the synchrotron-emitting filaments appear to be interacting with thermal gas clouds, may elucidate the particle acceleration mechanism responsible for the nonthermal filaments near the Galactic center. The spatial extent of the filaments allows us to characterize the variation of Faraday rotation over small angular scales. In principle, the RM structure function can be related to the properties of inhomogeneities in the Faraday screen. For example, if fluctuations in $n_e B_\parallel$ have an isotropic three-dimensional Kolmogorov spectrum, the structure function scales as $\delta\theta^{5/3}$ (Simonetti \& Cordes 1988; Clegg et al. 1992). The observed structure function, however, is more consistent with the $\delta\theta^{2/3}$ scaling indicative of the two-dimensional Kolmogorov turbulence that is expected to exist in the magnetised interstellar medium (Higdon 1984, 1986; Goldreich \& Sridhar 1995) and has been observed towards extragalactic radio sources (Minter \& Spangler 1996). In that case, the electron density and magnetic field should fluctuate least rapidly along the mean field direction, and the RM should vary most rapidly for seperations perpendicular to the projection of the mean field on the plane of the sky. However, the major axis of the structure function is tilted by roughly 70 degrees with the galactic plane, inconsistent with the large scale poloidal field that has been inferred to exist in the inner 100 pc of the Galaxy (Yusef-Zadeh \& Morris 1987a; Serabyn \& Morris 1994). The RM towards G359.5+0.18, roughly 3000 cm$^{-3} \mu$G pc, is more than one hundred times that for sources outside the Galactic center region. Similar rotation measures have been measured for a number of other sources located within a degree of the Galactic center (Inoue et al. 1984; Yusef-Zadeh \& Morris 1987b; Gray et al. 1995), suggesting that the Faraday rotation occurs close to the Galactic center where the magnetic field strength is of order a milliGauss. A large RM could be produced by the $10^8$K gas in the inner hundred parsecs of the Galaxy (Koyama et al. 1989; Yamauchi et al. 1990). If the gas is homogeneous, it has a density of 0.03 cm$^{-3}$ and a milliGauss magnetic field would produce the observed RM. However, the variations in RM along the filaments are difficult to explain unless the medium is clumped on scales of 0.1 pc with at most a few clumps along a given line of sight, implying a volume filling factor of about one percent. In that case, the X-ray emissivity implies a clump density of 0.3 cm$^{-3}$ and the high RM imply a field strength of 10 mG, an order of magnitude larger than has generally been estimated for the region. In summary, the magnetic field is predominantly aligned along the Galactic center filaments. The unusually large rotation measure, its variation on arcsecond scales, and the anisotropy in the RM structure function, all suggest that the Faraday screen is located close to the Galactic center. \acknowledgments F. Yusef-Zadeh's work was supported in part by NASA grant NAGW-2518. %\vfill\eject \begin{references} \reference {b77}Baars, J.W.M., Genzel, R., Pauliny-Toth, I.I.K. \& Witzel, A. 1977, A\&A, 61, 99 \reference {by89}Bally, J., Yusef-Zadeh, F. 1989, ApJ, 336, 173 \reference {b66}Burn, B.J. 1966, MNRAS, 133, 67 \reference {c92}Clegg, A.W., Cordes, J.M., Simonetti, J.H. \& Kulkarni, S.R. 1992, ApJ, 386, 143 \reference{gs95}Goldreich, P. \& Sridhar, S. 1995, ApJ, 438, 763 \reference {g95}Gray, A.D., Nicholls, J., Ekers, R.D. \& Cram, L.E. 1995, ApJ, 448, 164 \reference {h92}Haynes, R.F., Stewardt, R.T., Gray, A.D., Reich, W., Reich, P. 1992, A\&A, 264, 500 \reference{h84}Higdon, J.C. 1984, ApJ, 285, 109 \reference{h86}Higdon, J.C. 1986, ApJ, 309, 342 \reference {i84}Inoue, M., Takahashi, T., Tabara, H., Kato, T. \& Tsuboi, M. 1984 PASJ, 36, 633. \reference {m96} \reference {k89}Koyama, K., Awaki, H., Kunieda, H., Takano, S., Tawara, Y., Yamauchi, S., Hatsukade, I. \& Nagese, F. 1989, Nature, 339, 603 \reference {l85}Liszt, H. 1985, ApJ, 293, L65 \reference {m96}Minter, A.H., \& Spangler, S.R. 1996, ApJ 458, 194 \reference {r94}Reich, W. 1994, in The Nuclei of Normal Galaxies: Lessons from the Galactic Center, ed. R. Genzel \& A.I. Harris (Dordrecht:Kluwer), 54 \reference {s85}Seiradakis, J.H., Lasenby, A.N., Yusef-Zadeh, F., Wielebinski, R. \& Klein, U. 1985, Nature, 17, 697 \reference {sm94}Serabyn, E. \& Morris, M. 1994, ApJ, 424, 91 \reference {sc88}Simonetti, J.H. \& Cordes, J.M. 1988, in AIP 174, Radio Wave Scattering in the Interstellar Medium, ed. B.J. Rickett \& D.C. Backer (NY:AIP), 134 \reference {sh84}Sofue, Y. \& Handa, T. 1984, Nature, 310, 568 \reference {s96}Staguhn, J., Stutski, J., Yusef-Zadeh, F., Uchida, K.I. 1996, in The 4th ESO/CTIO Workshop on the Galactic Center, ed. R. Gredel, in press \reference {t86}Tsuboi, M., Inoue, M., Handa, T., Tabara, H., \& Kato, T. 1986, AJ, 92, 818 \reference{tms91}Thompson, A.R., Moran, J.M. \& Swenson, G.W. Jr. 1991, in Interferometry and Synthesis in Radio Astronomy, 434 \reference {y90}Yamauchi, S., Kawada, M., Koyama, K., Kunieda, H. \& Tawara, Y. 1990, ApJ, 365, 532 \reference {ymc84}Yusef-Zadeh, F., Morris, M. \& Chance, D. 1984, Nature, 310, 557 \reference {ym87a}Yusef-Zadeh, F. \& Morris, M. 1987a, AJ, 94, 1128 \reference {ym87b}Yusef-Zadeh, F. \& Morris, M. 1987b, ApJ, 322, 721 \end{references} %\clearpage \begin{figure} \figcaption{Radiographs of the total (top) and polarized (bottom) intensity of the nonthermal filaments G359.54+0.18 with a resolution of 4$''\times4''$ at $\lambda$6cm. The polarized emission is greatest near the center where the two filaments appear to cross each other.} \figcaption{Radiograph of the total intensity of the easternmost region of the linear filaments at $\lambda$6cm with a resolution of 10$''\times10''$. The garayscale range is shown as a bar at the bottom of the figure. The straight filaments noted in Figure 1 appear to become clumpy and distorted as they are extended to the east where there is a concentration of molecular material.} \figcaption{Color image of the distribution of the RM along the extent of G359.54+0.18. The four extended clumps seen near the center of the image correspond to the region of the filaments with maximum polarized intensity as shown on the bottom panel of Figure 1. The corresponding errors of the RM image ranges between 8 and 39 rad/m$^2$. The light and dark green colors to the east and to the west represent RM with typical values of --1500 and -3200 rad/m$^{-2}$), respectively.} \figcaption{{\bf Top:}Plots of the RM along slices of constant declination through each of the four polarized regions of the filaments. { \bf Bottom:} Plots of the polarization angle vs. the square of the wavelength for positions corresponding to a point on the plots directly above. A straight line fit whose slope corresponds to the RM is drawn through the points.} \figcaption{Intrinsic orientation of the magnetic field lines superimposed on contours of total intensity of the central region of the filaments in G359.54+0.18 at 4.585 GHz. Contour levels of the corresponding total intensity are set at (1, 3, 7, 9.5)$\times$0.31 mJy/beam area.} %\clearpage %\vfill\eject \figcaption{The RM structure function for angular separations parallel and perpendicular to the filaments. This is a typical plot which was created from the structure function image constructed from a 30$''\times80''$ box centered on the filaments. The extent of the plot beyond 10$''$ and 40$''$ in the direction perpendicular and parallel to the filaments, respectively, are dominated by noise. We note a clear asymmetry in the structure function with values which differ by a factor of two at angular separation of 10$''$ in two primiary axis nearly parallel and perpendicular to the direction of the filaments. The major (minor) axis of the anisotropy lies to within 17$^0$ (26$^0$) of the direction of the filament (the galactic latitude).} \end{figure} \end{document} ----- End Included Message -----