------------------------------------------------------------------------ vlba7mm.tex ApJL accepted To: gcnews@astro.umd.edu Date: Tue, 3 Feb 1998 12:45:30 +0100 (MEZ) X-Mailer: ELM [version 2.4 PL22] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit % http://www.aoc.nrao.edu/mpivlb/bower/ \documentstyle[aasms4,12pt,psfig]{article} \lefthead{Bower \& Backer} \righthead{7 mm $\lambda$ VLBA Observations of Sgr A*} \begin{document} \newcommand\degd{\ifmmode^{\circ}\!\!\!.\,\else$^{\circ}\!\!\!.\,$\fi} \newcommand{\etal}{{\it et al.\ }} \title{7 mm $\lambda$ VLBA Observations of Sagittarius A*} \author{Geoffrey C. Bower} \affil{Max Planck Institut f\"{u}r Radioastronomie, Auf dem H\"{u}gel 69, D 53121 Bonn Germany} \author{Donald C. Backer} \affil{Astronomy Department \& Radio Astronomy Laboratory, University of California, Berkeley, CA 94720} \begin{abstract} We present 7 mm $\lambda$ VLBA observations of the compact nonthermal radio source in the Galactic Center, Sgr A*. These observations confirm the hypothesis that the image of Sgr A* is a resolved elliptical Gaussian caused by the scattering of an intervening thermal plasma. The measured major axis of Sgr A* is $0.76 \pm 0.04$ mas, consistent with the predicted scattering size of $0.67 \pm 0.03$. We find an axial ratio of $0.73 \pm 0.10$ and a position angle of $77\degd 0 \pm 7\degd 4$. These results are fully consistent with VLBI observations at longer wavelengths and at 3 mm $\lambda$. We find no evidence for any additional compact structure to a limit of 35 mJy. The underlying radio source must be smaller than 4.1 AU for a galactocentric distance of 8.5 kpc. This result is consistent with the conclusion that the radio emission from Sgr A* results from synchrotron or cyclo-synchrotron radiation of gas in the vicinity of a black hole with a mass near $10^6 M_{\sun}$. \end{abstract} \keywords{Galaxy: center --- galaxies: active --- scattering } \section{Introduction} The radiation from the compact radio source in the Galactic Center, Sgr A*, has been clearly determined to be nonthermal in nature. VLBI observations have found the source to have a brightness temperature in excess of $1.4 \times 10^{10}$ K and a size less than 1 AU (Rogers \etal \markcite{roger94} 1994). The compact source has been interpreted as a black hole undergoing accretion at a very low rate ($\sim 10^{21}$ to $10^{22} {\rm\ g\ s^{-1}}$), either through advection dominated accretion (Narayan, Yi \& Mahadevan \markcite{naray94} 1994) or through spherical accretion which may include a disk at small radii (Melia \markcite{melia94} 1994). In both models the accreting material is mass lost from nearby massive stars through winds. The radio emission may originate in an infalling spheroid, a disk or a low-power Blandford-K\"{o}nigl jet (Falcke, Mannheim \& Biermann \markcite{falck93} 1993). These theories are constrained by the broadband spectrum and the compact size of the radio source. Recent dynamical evidence supports the black hole hypothesis. The proper motions of early type stars within 0.01 pc of Sgr A* are greater than 1000 km s$^{-1}$ (Genzel \etal \markcite{genze97} 1997). The velocity dispersion as a function of radius suggests a contained mass of $2.6 \pm 0.35 \times 10^6 M_{\sun}$. Further, if the kinetic energies of these stars are in equipartition with that of Sgr A*, then we find that the proper motion of Sgr A* (Backer \markcite{backe96} 1996) implies a minimum mass of $1.4 \times 10^4 M_{\sun}$. If this mass is confined within 1 AU as the VLBI results imply, then a mass density of $3 \times 10^{19} {\rm M_{\sun} pc^{-3} }$ is required. Considerations of the short time scales of stability of a cluster of dark objects with this density lead to the strong conclusion that Sgr A* indeed harbors a massive black hole (Maoz \markcite{maoz97} 1997). Due to diffractive scattering by electrons in the turbulent interstellar medium near the Galactic Center, the angular size of Sgr A* is broadened (e.g., Yusef-Zadeh \etal \markcite{yusef94} 1994 and references therein). The source is elliptical at a position angle of approximately $80\arcdeg$ with an axial ratio near 0.5. The major axis has a $\lambda^{2.01 \pm 0.02}$ dependence that extends from 20 to 0.3 cm. The scattering hypothesis is supported by the discovery of a similar angular broadening and asymmetry in the images of OH masers within 15 arcmin of Sgr A* (van Langevelde \& Diamond \markcite{vanla91} 1991). Since the effect of scattering decreases more rapidly with wavelength than angular resolution, at a short enough wavelength the compact source should appear unobscured. Currently VLBI observations at millimeter wavelengths stand in conflict. At 3 mm $\lambda$ Rogers \etal \markcite{roger94} (1994) found an upper limit to the apparent size of 0.2 mas, in agreement with an extrapolation of the scattering law. Observing at 7 mm $\lambda$ in August 1992, Backer \etal \markcite{backe93} (1993) found with 5 stations of the National Radio Astronomy Observatory\footnote{ The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.} Very Long Baseline Array (VLBA) an apparent size of 0.7 mas, also in agreement with the scattering law. However, Krichbaum \etal \markcite{krich93} (1993), observing with an array of 4 VLBA stations at 7 mm $\lambda$ in May 1992, found a size $1.7 \times 0.7$ mas at a position angle of $-20 \arcdeg$. They also consider a two component model in which the brighter component has a size of $ 0.7 \pm 0.1$ mas and the fainter component is at a position angle of $-25\arcdeg$. In this paper we present 7 mm $\lambda$ observations of Sgr A* using the full VLBA. The additional baselines in these observations significantly improve the density and extent of $uv$ coverage over the previous experiments. We present a map as well as a study of the visibility data. \section{Observations and Data Reduction} The VLBA observed Sgr A* on 1994 September 29 at 43 GHz with a bandwidth of 64 MHz. The data were correlated in Socorro, New Mexico. The compact blazar NRAO~530 was used as an amplitude calibrator and fringe detection source. High SNR detections of NRAO~530 were made on all baselines. Initial reduction of the data was performed with the Astronomical Image Processing System (AIPS). {\it A priori} amplitude calibration was performed first. We determined that the zenith atmospheric optical depth ranged from 0.05 at Mauna Kea to 0.18 at Hancock. Singleband delays were determined with fringe fitting to a short segment of NRAO~530 data and then applied to the Sgr A* visibilities. Multiband delays and rates were found by fringe fitting directly to the Sgr A* visibilities. The SNR of detections and the consistency of fringe rate and multiband delay solutions indicate that detections were made to all stations except Mauna Kea, Saint Croix and Hancock. No detection of Sgr A* was made at a $uv$ distance greater than 250 $M\lambda$. Data were averaged to 64 seconds after fringe detection. We improved the amplitude calibration of Sgr A* through mapping of NRAO~530. A single Gaussian with a size of 0.102 by 0.056 mas fits the NRAO~530 visibilities very well. Station gains deviated from unity by 20\% or less. These station gains were applied to the visibility data of Sgr A* and used for imaging and visibility analysis. This calibration significantly reduced the scatter in the Sgr A* visibility amplitudes. We self-calibrated the visibility phase of Sgr A* with iterative mapping. We show in Figure~\ref{fig:sgra} an image of Sgr A* made with a robustness parameter of 2 (Briggs \markcite{brigg95} 1995). The corresponding beam FWHM is $2.230 \times 0.720$ mas at a position angle of $12\degd 9$. We show the same image with the CLEAN components convolved with a circular beam with FWHM of 0.400 mas in Figure~\ref{fig:sgrasup}. \section{Results} \subsection{Size and Flux of Sgr A*} We fit Gaussian models directly to the calibrated visibility data with a non-linear least-squares method. We only used visibility data on baselines shorter than 200 $M\lambda$. We show in Figure~\ref{fig:sgrauvd} the visibility amplitudes as a function of $uv$ distance along with circular Gaussian models. A noise bias of 0.140 Jy was added in quadrature to the model. The best circular Gaussian fit has a FWHM of $0.727 \pm 0.033$ mas. An elliptical Gaussian fit gives a FWHM of $0.762 \pm 0.038$ mas in a position angle of $77\degd 0 \pm 7\degd 4$. We find an axial ratio of $0.73 \pm 0.10$. We find consistent results fitting Gaussians to the two images. The absence of a detection on the Hancock-Saint Croix baseline provides an opportunity to place an upper limit on the axial ratio. This baseline has moderate North-South resolution with $v=200 M\lambda$ at the beginning of the track. The average amplitude on this baseline coherently integrated over the fringe detection time scale is $\sim 140$ mJy. We find the axial ratio $a \lesssim 1.0$. The total flux determined from the fit to the visibility data is $1.28 \pm 0.10$ Jy. The quoted error does not include systematic calibration errors, which may be as high as 20\%. \subsection{Is There Asymmetric Structure?} In order to search further for non-elliptically symmetric structure in Sgr A*, we analyzed the closure phases in detail. We extracted the visibility data from AIPS and formed the closure phase in 2 second intervals. We vector averaged this complex phasor for 10 minute segments. Errors were determined from the distribution of the closure phases (Thompson, Moran \& Swenson \markcite{thomp91} 1991, section 9.3). For a weak signal, the distribution is linear in the cosine of the phase and the phase error goes as \begin{equation} \sigma_\phi= {\pi \over \sqrt{3} } \left( 1 - \sqrt{ 9 \over 2 \pi^3} {V \over \sigma} \right), \end{equation} where $V$ is the bispectrum amplitude and $\sigma$ is the noise amplitude. For a strong signal, the distribution is Gaussian and we find \begin{equation} \sigma_\phi={\sigma \over V}. \end{equation} We computed the $\chi^2$ statistic for the Krichbaum \etal \markcite{krich93} (1993) two component model (their model B) and for a symmetric model. We find $\chi^2_{Krichbaum}=2104$ and $\chi^2_{symmetric}=449$ for $N=385$ degrees of freedom, which clearly eliminates the Krichbaum \etal model at the epoch of these observations. We show some of the closure phases along with the Krichbaum \etal model in Figure~\ref{fig:sgracp1}. The closure phase plots reveal that the phase does not deviate significantly from zero where the Krichbaum \etal model predicts substantial variation. These deviations are apparent on both the close inner triangles and on the more spread out triangles which include BR, FD and OV, stations not used in the Krichbaum \etal experiment. Is there any evidence for asymmetry aside from that in the Krichbaum \etal model? The reduced $\chi^2$ value for the symmetric hypothesis is 1.17 which leaves little phase space for a secondary component. The images and the visibility data do not reveal any evidence for asymmetric structure at the level of the beam sidelobes, 35 mJy. The diffuse components in Figures~\ref{fig:sgra} and \ref{fig:sgrasup} coincide with beam sidelobes and are, therefore, unlikely to be real. \section{Conclusions} Imaging with the full VLBA at 7 mm $\lambda$ shows that the size and shape of Sgr A* is fully consistent with the predictions of the scattering law derived at lower frequencies. We find a major axis FWHM of $0.76 \pm 0.04$ mas. The scattering model predicts $0.67 \pm 0.03$ mas. We also find an axial ratio and a position angle consistent with that previously identified at longer wavelengths and with the Backer \etal \markcite{backe93} (1993) results at 7 mm. We find no evidence for structure that is not elliptically symmetric to a limit of 35 mJy. We cannot rule out the existence of a second component in the past: a synchrotron component at the epoch of the Krichbaum \etal (1993) observations is likely to have decayed significantly by the epoch of our observations. If the intrinsic size adds in quadrature with the scattering size to form the apparent size, the major and minor axes of the intrinsic source must be less than 0.48 mas. For a galactocentric distance of 8.5 kpc, this corresponds to 4.1 AU. We infer a lower limit to the brightness temperature of $4.9 \times 10^9$ K. This limit is less than the limit of $1.4 \times 10^{10}$ K found by Backer \etal \markcite{backe93} (1993) at 7 mm $\lambda$ and Rogers \etal \markcite{roger94} (1994) at 3 mm $\lambda$ principally due to the lower flux in our epoch of observation. The morphology and size of Sgr A* did not change from the Backer \etal \markcite{backe93} (1993) observations despite a factor of two decrease in the flux. The upper limit to source expansion over this epoch is $0.04 {\rm\ mas\ y^{-1}} \approx 2 {\rm ~km~s^{-1}}$. The constant size also supports the hypothesis that the apparent source is scattered radiation from the intrinsic source. An unobscured, homogeneous synchrotron source with constant magnetic field, spectral index and peak frequency would show a 40\% increase in its angular size with a doubling in flux density (Marscher \markcite{marsc83} 1983). Only a conspiracy of parameter changes could keep the size from changing significantly. The constant ellipticity as a function of wavelength indicates a coherent magnetic field over 0.02 to $3 \times 10^{-5}$ pc for a scattering screen near the Galactic Center. Detection of a change in the ellipticity with wavelength would be indicative of a turbulent magnetic field on these scales (e.g., Wilkinson, Narayan \& Spencer \markcite{wilki94} 1994). At 7 mm $\lambda$ the refractive time scale is on the order of 2 years. Hence, future observers might expect to see a change in the ellipticity of Sgr A*. These results are consistent with the hypothesis that the radio emission from Sgr A* results from synchrotron or cyclo-synchrotron radiation of gas in the vicinity of a black hole. Both radial and rotating flow models predict the mass of the black hole on the order of $10^6 M_{\sun}$ and the accretion rate in the range $10^{21}$ to $10^{22} {\rm\ g\ s^{-1}}$ (Melia \markcite{melia94} 1994, Narayan \etal \markcite{naray95} 1995). The radio emission may originate in a spherical cloud or in a low-power inhomogeneous jet. However, the absence of any external feature at any wavelength argues against the jet model. What will shorter wavelength VLBI observations reveal in Sgr A*? Future global VLBI arrays at 1.3 mm $\lambda$ will have an angular resolution of 20 $\mu$as (Wright \& Bower \markcite{wrigh97} 1997), which is on the scale of a few Schwarzschild radii for a $10^6 M_{\sun}$ black hole. At this wavelength scattering will not dominate since the expected scattering size is 27 $\mu$as. However, recent measurements of the centimeter to submillimeter spectrum indicate the presence of two compact sources on two different size scales (Serabyn \etal \markcite{serab97} 1997, Falcke \etal \markcite{falck97} 1997). If the intrinsic source responsible for the centimeter to millimeter wavelength spectrum has a spectral turnover near 3 mm $\lambda$, then this component may be forever invisible to VLBI. \acknowledgements The authors thank H. Falcke and K. Kellermann for useful discussions. \begin{references} \renewcommand{\etal}{{\it et al.}} \reference{backe96} Backer, D. C., 1996, in IAU Symp. 169, L. Blitz and P. Teuben, eds., 193 \reference{backe93} Backer, D. C., Zensus, J. A., Kellermann, K. I., Reid, M., Moran, J. M. \& Lo, K. Y., 1993, Sci., 262, 1414 \reference{brigg95} Briggs, D.S., 1995, \baas, 187, 112.02 \reference{falck97} Falcke, H., Goss, W. M., Matsuo, H., Teuben, P., Zhao, J.-H. \& Zylka, R., 1997, \apjl, submitted \reference{falck93} Falcke, H., Mannheim, K. \& Biermann, P. L., 1993, \aap, 278, L1 \reference{genze97} Genzel, R., Eckart, A., Ott, T. \& Eisenhauer, F., 1997, \mnras, in press \reference{krich93} Krichbaum, T. P. \etal, 1993, \aap, 274, L37 \reference{maoz97} Maoz, E., 1997, \apjl, in press \reference{marsc83} Marscher, A. P., 1983, \apj, 264, 296 \reference{melia94} Melia, F., 1994, \apj, 426, 577 \reference{naray95} Narayan, R., Yi, I., \& Mahadevan, R., 1995, \nat, 374, 623 %\reference{pears91} Pearson, T. J., 1991, \baas, 23, 991 \reference{roger94} Rogers, A. E. E. \etal, 1994, \apjl, 434, L59 \reference{serab97} Serabyn, E., Carlstrom, J., Lay, O., Lis, D. C., Hunter, T. R., Lacy, J. H. \& Hills, R. E., 1997, \apjl, 490, L77 \reference{thomp91} Thompson, A. R., Moran, J. M. \& Swenson, G. W., Jr., 1991, Interferometry and Synthesis in Radio Astronomy, John Wiley, New York \reference{vanla91} van Langevelde, H. J. \& Diamond, P. J., 1991, \mnras, 249, 7 \reference{wilki94} Wilkinson, P. N., Narayan, R., \& Spencer, R. E., 1994, \mnras, 269, 67 \reference{wrigh97} Wright, M. C. H. \& Bower, G. C., 1997, BIMA Memos, 55 \reference{yusef94} Yusef-Zadeh, F., Cotton, W., Wardle, M., Melia, F. \& Roberts, D., 1994, \apjl, 434, L63 \end{references} \newpage \figcaption[robust.ps]{A uniformly-weighted image of Sgr A*. The beam is shown in the lower left hand corner. The contours are -0.01, 0.01, 0.03, 0.10, 0.30, 0.60 and 0.90 times the peak intensity of 0.87 Jy/beam. \label{fig:sgra}} \figcaption[robust_super.ps]{An image of Sgr A* in which the CLEAN components are convolved with a beam with FWHM of 0.400 mas, shown in the lower left hand corner. The contours are -0.01, 0.01, 0.03, 0.10, 0.30, 0.60 and 0.90 times the peak intensity of 0.66 Jy/beam. \label{fig:sgrasup}} \figcaption[best_modbias.ps]{Visibility amplitude as a function of $uv$ distance for Sgr A*. The solid lines indicate the expectation for a circular Gaussian with a zero baseline flux of 1.28 Jy and FWHM of 0.694, 0.727 and 0.760 mas. The dashed lines indicate the expectation for a circular Gaussian with zero baseline fluxes of 1.38 Jy and 1.18 Jy with FWHM of 0.760 and 0.694 mas, respectively. The noise bias is added in quadrature to the model. The large triangles indicate the median flux in a 35 M$\lambda$ bin. The errors indicate the scatter in the data. \label{fig:sgrauvd}} \figcaption[paperfig.ps]{Closure phase on 3 triangles for Sgr A*. The solid line is the Krichbaum \etal model. \label{fig:sgracp1}} \end{document}