------------------------------------------------------------------------ RM.tex ApJ Lett, Jun 2006, in press Message-ID: MIME-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="-679269273-559381838-1150482768=:31555" Content-ID: X-Virus-Scanned: ClamAV 0.88.2/1548/Fri Jun 16 10:53:47 2006 on phobos X-Virus-Status: Clean X-MailScanner-Information: Please contact postmaster@aoc.nrao.edu for more information X-MailScanner: Found to be clean X-MailScanner-SpamCheck: not spam, SpamAssassin (score=0, required 5, autolearn=disabled) X-MailScanner-From: jpm@astro.caltech.edu X-Spam-Status: No This message is in MIME format. The first part should be readable text, while the remaining parts are likely unreadable without MIME-aware tools. ---679269273-559381838-1150482768=:31555 Content-Type: TEXT/PLAIN; CHARSET=US-ASCII; FORMAT=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE Content-ID: %astro-ph/0606381 \documentclass[12pt,preprint]{aastex} \newcommand{\et}{{\it et al.}} \newfont{\myfont}{cmmib10} \newcommand{\bkappa}{\hbox{\myfont \symbol{20} }} \newcommand{\balpha}{\hbox{\myfont \symbol{11} }} \newcommand{\bdelta}{\hbox{\myfont \symbol{14} }} \newcommand{\bfeta}{\hbox{\myfont \symbol{17} }} \newcommand{\btheta}{\hbox{\myfont \symbol{18} }} \newcommand{\sinc}{\hbox{sinc}} \newcommand{\myemail}{jmacquar@aoc.nrao.edu} \shorttitle{Faraday Rotation towards Sgr A*} \shortauthors{Macquart et al.} \begin{document} \title{The Rotation Measure and 3.5\,mm Polarization of Sgr A*} \author{Jean-Pierre Macquart\altaffilmark{1}, Geoffrey C. Bower\altaffilmar= Heino Falcke\altaffilmark{3}} 87801, U.S.A. {\it jmacquar@nrao.edu} (Jansky Fellow)} \altaffiltext{2}{Astronomy Department and Radio Astronomy Laboratory, Unive= rsity of California, Berkeley, Berkeley, CA 94720, U.S.A.} \altaffiltext{3}{ASTRON, Postbus 2, 7990 AA Dwingeloo, The Netherlands and = Department of Astrophysics, Radboud Universiteit Nijmegen, Postbus 9010, 65= 00 GL Nijmegen, The Netherlands} \begin{abstract} We report the detection of variable linear polarization from Sgr A* at a w= avelength of $3.5\,$mm, the longest wavelength yet at which a detection has= been made. The mean polarization is $2.1 \pm 0.1$\% at a position angle o= f $16 \pm 2^\circ$ with rms scatters of 0.4\% and 9$^\circ$ over the five e= pochs. We also detect polarization variability on a timescale of days. C= ombined with previous detections over the range 150--400\,GHz (750--2000\,$= \mu$m), the average polarization position angles are all found to be consis= tent with a rotation measure of $-4.4 \pm 0.3 \times 10^5\,$rad\,m$^{-2}$. = This implies that the Faraday rotation occurs external to the polarized so= urce at all wavelengths. This implies an accretion rate $\sim 0.2 - 4 \tim= es 10^{-8}\, {\rm M}_\odot \,$yr$^{-1}$ for the accretion density profiles = expected of ADAF, jet and CDAF models and assuming that the region at which= electrons in the accretion flow become relativistic is within $10\,R_{\rm = S}$. The inferred accretion rate is inconsistent with ADAF/Bondi accretion= =2E The stability of the mean polarization position angle between disparate= polarization observations over the frequency range limits fluctuations in = the accretion rate to less than $5$\%. The flat frequency dependence of th= e inter-day polarization position angle variations also makes them difficul= t to attribute to rotation measure fluctuations, and suggests that both the= magnitude and position angle variations are intrinsic to the emission. \end{abstract} \keywords{galaxies: active --- Galaxy: center --- polarization --- radiatio= n mechanisms: nonthermal} %--------------------------------------------------------------------------= ------------------ \section{Introduction} \label{Introduction} % INTRODUCTION %--------------------------------------------------------------------------= ------------------ Linear polarization can be an important diagnostic of relativistic jets and= accretion flows associated with black hole systems. In the case of the ma= ssive black hole in the Galactic Center, Sgr A*, the properties of its mm-w= avelength linear polarization probes the accretion environment on scales in= accessible with other techniques (Bower et al.\,1999a,b; Aitken et al.\,200= 1; Bower et al.\,2001; Bower et al.\,2003; Marrone et al.\,2006). The appa= rent absence of linear polarization at wavelengths exceeding 2.7\,mm and sh= arp rise in polarization fraction at shorter wavelengths sets an upper limi= t to the rotation measure (RM). This limits the mass accretion rate to $\s= im 10^{-7} {\rm M}_\sun {\rm\ yr^{-1}}$ at distances of $10 - 1000$ Schwarz= schild radii from the black hole, which eliminates certain classes of accre= tion flow (Quataert \& Gruzinov 2000; Agol 2000), but is consistent with CD= AF and jet models (e.g. Falcke, Mannheim and Biermann 1993). The RM measur= es the accretion rate by serving as a proxy for the electron column density= once coupled with assumptions about the magnetic field. Equipartition bet= ween kinetic, magnetic and gravitational energy is often assumed to relate = the electron density and magnetic field (e.g. Bower et al. 1999a; Melia \& = Falcke 2001; Marrone et al. 2006). The discovery of variations in both the polarization angle (Bower et al.\,2= 005) and fraction (Marrone et al.\,2006) suggests two potential sources of = variability. The variations may be intrinsic and, therefore, offer evidenc= e on the nature and structure of the emission region on a scale of $\sim 10= R_s$. Changes in the RM along the line of sight may also induce external = polarization variability. Structure in the accretion region on all scales w= ithin the Bondi radius can contribute to RM variations. There is thus stro= ng motivation to accurately characterize the RM, its fluctuations, and the = intrinsic variability of the polarized source. In \S2 we present the detection of linear polarization of Sgr A* at 3.5\,mm= , showing that it varies on short timescales as well as relative to histori= cal non-detections. Combining this in \S3 with other data, our detection y= ields the best constraints so far on the RM. We discuss the nature of the= accretion flow and on the intrinsic source properties in \S4.=20 %Our conclusions follow in \S5. %--------------------------------------------------------------------------= ------------------ \section{Observations} \label{Observations} % OBSERVATIONS %--------------------------------------------------------------------------= ------------------ Sgr A* was observed with the BIMA array at 3.5 mm between 28 March and 01 A= pril 2004 UT. All five observations were obtained in identical LST time ra= nges that corresponded roughly to 11 to 16 UT. Observations were obtained in a polarimetric mode that pro= duced Stokes $I$, $Q$, $U$ and $V$ images, with the two frequency bands cen= tered on 82.76 and 86.31\,GHz, each with 800 MHz bandwidth. Data were cal= ibrated assuming that the flux density of J1733-130 was steady at its mean = value of 2.7\,Jy. J1733-130 was observed for 5 minutes every 30 minutes. Observations were o= btained in the B configuration giving a resolution of $8.6 \times 2.6\arcse= c$ in position angle (p.a.) $7^\circ$. The data were filtered to remove sp= acings shorter than 20\,k$\lambda$, similar to the processing of previous S= gr A* polarization experiments. This $u$--$v$ distance cutoff gives a tot= al flux estimate accurate to better than 10\% from 8.4 to 86 GHz (Bower et = al.\,2001). A priori amplitude calibration using system temperature and de= fault gain information was applied to J1733-130. Both sources were phase s= elf-calibrated. Polarization leakage terms from observations of 3C279 on 1= 1 November 2003 were applied. Numerous sources of error contribute to the accuracy with which we can meas= ure the polarization fraction and p.a.. In addition to statistical errors = that include noise from the sky and the telescope, the leakage of polarizat= ion from one polarization handedness to the other is an important effect. = This converts a fraction of the total intensity into a false polarization s= ignal. Leakage calibration uses observations of a bright calibrator sourc= e and simultaneously solves for the polarization of the source and the leak= age terms appropriate for individual antennas. Imperfect correction leaves= a residual false polarization signal and introduces errors that exist in t= he calibrator observation. BIMA leakage solutions at 1.3\,mm were found to= be stable over periods of months to years; variability in the solutions we= re due to changes in receiver orientation (Bower, Wright \& Forster, 2002).= Typical variations in antenna leakage terms were $\sim 1.5\%$ over 2 years= , indicating a $\sim 0.5\%$ variation in the average leakage solution for t= he 9 BIMA antennas. Solutions at 3.5\,mm are expected to have the same cha= racteristics although this has not been studied in depth. In addition to v= ariations in the leakage error, statistical errors in the calibrator data i= ntroduce errors. A comparison of actual measured p.a.s of=20 3C 279 at 3.5\,mm and 1.3\,mm from BIMA with measured p.a.s at 1.3\,cm and = 0.7\,cm from the VLA indicate excursions of 10$^\circ$-- 20$^\circ$ (Bower = et al.\,2002). These deviations exceed those expected from leakage correct= ions and statistical errors. They are possibly real source effects but may= also be uncorrected instrumental errors. The average flux densities of Sgr A* and linear polarization E-vectors are = listed in Table \ref{FluxTable}.=20 In the polarization fraction and p.a. errors we include the effect of a 0.5= \% polarization leakage error. This error propagation is accurate in the c= ase of the high SNR detections in the LSB but presents a lower limit to the= errors in the low SNR detections in the USB. Inter-day flux density varia= tions are detected at a significant level, with a reduced-$\chi^2$ of 4.9 f= or the hypothesis of constant flux density for Sgr A* for 4 degrees of free= dom. The mean flux density is $1.93 \pm 0.07\,$Jy and the rms variability = amplitude is $0.18\,$Jy.=20 %We do not have strong confidence in flux deviations on shorter timescales = than a day. Gain calibration was also considered to be too unreliable to p= lace significant limits on circular polarization. Polarization was detected in all five epochs, making this the first detecti= on of polarization at 3.5\,mm, the longest wavelength at which polarization= has been detected in Sgr A*. The mean polarization fraction is $2.1 \pm 0.1$\% and its mean p.a.~is $16 \pm 2^{\circ}$. The p= olarization fraction and p.a.~vary from day to day. The detection of polar= ization is more robust in the LSB (82.8 GHz) than in the USB (86.3 GHz). T= he origin of this difference is unclear. It may be due to changes in the l= eakage corrections and/or poor phase stability at the higher frequency. We= have previously seen data from BIMA in which polarization results in one s= ideband were more reliable than in the other=20 (Bower et al.\,2001). The bandwidth used in these observations is sufficie= ntly small that the linear polarization is not depolarized by rotation of t= he polarization vector across the observing band, as discussed below. %Figure x shows the Stokes $I$ light curve, the polarization %fraction light curve and the polarization position angle light curve. %--------------------------------------------------------------------------= ------------------ \section{The Rotation Measure} \label{RMSect} % DISCUSSION %--------------------------------------------------------------------------= ------------------ %Values to be plotted:=20 % A00 JCMT data at 230, 350, 450 GHz. Table \ref{PolnTable} lists the mean polarization p.a.s for all previous de= tections of linear polarization in Sgr A*. Due to systematic errors from p= olarization leakage calibration, the poor quality of upper sideband data at= 3.5\,mm, and the relatively small spacing between the two sidebands, we ar= e unable to compute a meaningful RM estimate from the 3.5\,mm data alone. = The combined average polarization data are consistent with a single RM of $= -4.4 \pm 0.3 \times 10^5\,$rad\,m$^{-2}$ and an intrinsic polarization p.a.= ~$\chi_0=3D168 \pm 8^\circ$. Fig.\,1 plots the best RM fit to the mean pol= arization p.a. data. The best fit, with a reduced-$\chi^2$ of 29 computed = using the errors quoted in Table \ref{PolnTable}, is obtained if the 85\,GH= z p.a. is rotated by $-180^\circ$. A fit to the unwrapped 85\,GHz p.a. yie= lds a reduced-$\chi^2$ of 54 and ${\rm RM}=3D-2.0 \pm 0.4 \times 10^5\,$rad= \,m$^{-2}$, while an extra $-180^\circ$ wrap yields ${\rm RM}=3D-6.9 \pm 0.= 4 \times 10^5\,$rad\,m$^{-2}$ with an associated reduced-$\chi^2$ of 64. The reduced-$\chi^2$ for the best fit is unacceptably high because of the u= nrealistically small errors associated with the Aitken et al.\,(2001) obser= vations. These single-epoch low-resolution measurements predate the identi= fication of polarization variability in Sgr A*. We therefore fit only to = interferometric observations spanning multiple epochs. The resulting fit p= roperties depend on whether one regards measurements from the two sidebands= at $\nu> 216\,$GHz, where available, as being mutually independent. If so= , the reduced-$\chi^2$ for a fit including the two -180$^\circ$-wrapped 3.5= \,mm points is 0.9, but is 3.6 for the unwrapped 3.5\,mm polarization pas. = If not, the two $\chi^2$ values are 0.8 and 2.1 respectively. In both ca= ses, the solution involving the wrapped 3.5\,mm points is preferred. We r= egard these cases as bounding the true significance of the RM. For the cas= e of independent sideband measurements, the associated best fit is $\chi_0 = =3D 163 \pm 2^\circ$ and ${\rm RM}=3D -4.38 \pm 0.06 \times 10^5\,$rad\,m$^= {-2}$. We adopt the RM $=3D-4.4 \pm 0.3 \times 10^5\,$rad\,m$^{-2}$ derived from all of the multi-epoch data. Given the variability of the p.a.~and the unc= ertain=20 systematics of different measurements, we consider the use of all data to p= rovide the most=20 conservative estimate of the RM. %--------------------------------------------------------------------------= ------------------ \section{Discussion} \label{Discussion} % DISCUSSION %--------------------------------------------------------------------------= ------------------ The accretion rate implied by this RM depends on density and magnetic profi= les assumed. Following the prescription outlined by Marrone et al.\,(2006)= ,\footnote{Note the typographical error in eq.\,(9) of Marrone et al.\,(200= 6) in which one should have RM$ \propto r_{\rm in}^{-7/4}$.} we write $n \p= ropto r^{-\beta}$, for $r_{\rm in} < r 3= \, r_{\rm in}$ and $1/2<\beta < 3/2$. The fact that a single RM accounts for the frequency dependence of all mean= polarization p.a.s implies that the Faraday rotation occurs external to th= e polarized source. Internal rotation would cause the RM to vary as a func= tion of frequency. The emission is optically thick at all frequencies at w= hich polarization is detected (Falcke et al.\,1998; Zhao et al.\,2003, Yuan= et al.\,2003), so if any internal Faraday rotation did occur, the diminuat= ion of opacity effects with frequency, which increases the depth down to wh= ich one observes emission, would cause a corresponding increase in the Fara= day rotation path length. %In the context of jet models (Falcke et al.\,1993), where the magnetic fie= ld is typically orthogonal to the jet axis, the polarization pa derived her= e favors a jet aligned along the N-S axis. % NNNN % changes shows that the -> shows the % An interpretation of the p.a.~jitter observed at 85\,GHz in terms of RM var= iability would imply rms deviations of $1.2 \times 10^4\,$rad\,m$^{-2}$, fa= r smaller than the $\sim 2 \times 10^5\,$rad\,m$^{-2}$ rms deviations impli= ed by the 340\,GHz Marrone et al.\,(2006) fluctuations interpreted similarl= y. However, the absence of a clear frequency dependence in the inter-day jitte= r makes it difficult to ascribe to RM fluctuations, and hence variations in= the accretion rate. Table 2 shows the rms p.a. deviations for the multi-e= poch observations at 85, 216, 230 and 340\,GHz. These are inconsistent wit= h the $\nu^{-2}$ dependence expected of RM fluctuations from a magnetoionic= medium external to the source, suggesting instead that the jitter reflects= changes in the intrinsic source polarization p.a.. Nonetheless, the fact = that the fluctuations at these frequencies were not observed simultaneously= , coupled with the short time span of the 85\,GHz observations compared to = the $>2\,$month -- albeit sporadic -- sampling of the 230 and 340\,GHz meas= urements, still admits the possibility that the p.a.~dispersion observed at= 85\,GHz is unrepresentative of its long-term average. This appears unlike= ly.=20 If the $\approx 20^\circ$ rms p.a. variations observed at 216--230\,GHz wer= e associated with RM fluctuations we would expect $\approx 150^\circ$ fluct= uations at 85\,GHz and would not expect to find $\chi \propto \lambda^2$ ov= er a set of disparate measurements.=20 %Thus, even if the position angle variations occur on a timescale substanti= ally greater than five days, it is improbable that the observed mean positi= on angle should coincide with its long-term mean value=20 % and thus that we obtained an RM consistent with the Marrone et al.\,(2006= ) determination.=20 Moreover, the presence of intrinsic p.a. changes is unsurprising given that= the polarization fraction is also intrinsically variable, as discussed bel= ow. % NNNNNN % Note changes in this paragraph!!! % NNNNNN The lack of p.a.~jitter attributable to RM fluctuations can be interpreted = in terms of an upper limit in accretion rate fluctuations. The absence of = clearly identifiable inter-day RM fluctuations suggests it is uniform on in= ter-day timescales. The consistency of the observations over a large number= of disjoint epochs and frequencies with a single RM further suggests that = the underlying accretion rate is constant on the timescale over which the o= bserved polarization pas were averaged.=20 The uncertainty in our RM fit places an upper bound on the accretion rate v= ariations using ${\rm RM} \propto \dot{M}^{3/2}$, valid under the assumptio= n of equipartition between magnetic, kinetic and gravitational energy (e.g.= Marrone et al.\,2006). The 7\% uncertainty in the RM implies $\dot{M}$ fl= uctuations less than $5$\%. The limit on $\dot{M}$ variations is largely c= onsistent with the limits imposed by source flux density variations. In th= e jet model the flux density scales as $\dot{M}^{17/12}$ (Falcke et al.\,19= 93). The standard deviation of the 3.5\,mm fluxes is 10\%, comparable to t= he errors on the individual measurements, which imposes an upper limit of 1= 4\% on $\dot{M}$ fluctuations. Marrone et al.\,(2006) detect 10\% rms intensity variations at 340\,GHz. T= he five intensity measurements from Bower et al.\,(2005) at 216--230\,GHz e= xhibit 29\% modulations, implying $\dot{M}$ fluctuations of 40\%. Variabil= ity in polarization fraction is detected by all multi-epoch observations (F= ig.\,\ref{FigPolnlabel}), at 85, 230 and 340\,GHz, and presumably occurs at= 112\,GHz, where it was not detected at the 1.8\% (1-$\sigma$) level by a p= revious search (Bower et al. 2001). A previous limit of 1\% linear polariz= ation at 86\,GHz (Bower et al.\,1999b) demonstrates that it also varies on = long timescales. Since the Faraday screen is external to the source the polarization amplitu= de fluctuations must be intrinsic. Instrumental depolarization effects are= too low to explain the variability: bandwidth depolarization is only impor= tant for RMs greater than $2.7 \times 10^7\,$rad\,m$^{-2}$ at 85\,GHz, whil= e beam depolarization is similarly improbable given the sub-mas size of Sg= r A* at mm wavelengths (Bower et al. 2004; Shen et al. 2005). Spatial vari= ation in the RM across the transverse extent of the source could depolarize= the emission, but at even 85\,GHz this requires RM fluctuations $\delta {\= rm RM} \ga 7 \times 10^5\,$rad\,m$^{-2}$ (Quataert \& Gruzinov 2000). Both the high variability of the mm and sub-mm emission (Zhao et al.\,2004= ; Wright \& Backer 1993; Tsuboi et al.\,1999) and the linearly polarized em= ission of Sgr A* are possibly associated with its excess sub-mm emission (S= erabyn et al.\,1997; Falcke et al.\,1998; Melia et al.\,2001). ADAF models= that fit the cm to-sub-mm spectrum include at least two distinct populatio= ns of radiating particles (Yuan et al.\,2003), with the second important at= $\nu \ga 100\,$GHz in order to explain the sub-mm bump. The model of Yuan et al.\,(2003), in which the sub-mm emission is dominated= by thermal electrons, overpredicts the polarization fraction at 85\,GHz (c= f. Fig.\,\ref{FigPolnlabel}). In this model the degree of linear polarizat= ion ranges from 32\% at 85\,GHz to 70\% at 400\,GHz assuming a uniform magn= etic field and that Faraday depolarization intrinsic to the source is unimp= ortant (see their Fig.\,3b). In the context of this model the ratio of the = predicted to observed polarization levels can only be attributed to magneti= c field inhomogeneity intrinsic to the source. This ratio is a factor of 3= higher at 85\,GHz relative to the fraction in the range $150-400\,$GHz, ov= er which it is constant within the errors. It is hard to account for such = an increase in magnetic field inhomogeneity at 85\,GHz, particularly if the= source size only scales $\propto \nu^{-1}$, as expected if its emission is= self-absorbed. On the other hand, including synchrotron self-absorption e= ffects, Goldston, Quataert \& Igumenshchev (2005) show that the polarizatio= n fraction is expected to increase by a factor of three over the range $85-= 200\,$GHz. The quasi-spherical accretion polarization model of Melia, Liu \& Coker (20= 00) and the two-component model of Agol (2000) predict a 90$^\circ$ p.a.~fl= ip at $\sim 280\,$GHz which is at variance with the measured p.a.s at 150, = 230 and 340\,GHz. %--------------------------------------------------------------------------= ------------------ %\section{Conclusions} \label{Conclusions} % CONCLUSIONS %--------------------------------------------------------------------------= ------------------ We have reported here the detection of linear polarization in Sgr A* at 3.5= \,mm. This enables us to calculate the rotation measure and set a limit on= the accretion rate. The lack of frequency dependence for position angle f= luctuations indicates that they are intrinsic to the source. Our result favors RIAF/CDAF accretion mo= dels, with a shallow density distribution, over ADAF and Bondi-Hoyle accret= ion flows, which have a steep profile and are more likely to produce rapid = RM variations. Future wide bandwidth simultaneous observations with CARMA and the SMA will= fully characterize intrinsic and extrinsic changes in the polarization pro= perties of Sgr A* and allow us to investigate the accretion environments of= other nearby low luminosity AGN, such as M81* (Brunthaler, Bower \& Falcke= 2006). %Inter-day variable polarization is detected in Sgr A* at 3.5\,mm. When co= mbined with measurements at higher frequencies, the scaling of the mean pol= arization position angles implies a rotation measure ${\rm RM} =3D -4.4 \pm= 0.3 \times 10^5\,$rad\,m$^{-2}$ and that the Faraday rotation occurs exter= nal to the source. This implies an accretion rate $\sim 0.2 - 4 \times 10^= {-8}\, {\rm M}_\odot \,$yr$^{-1}$ assuming that the region at which electro= ns in the accretion flow become relativistic (Quataert \& Gruzinov 2000; Ma= rrone et al. 2006) is within $10\,R_{\rm S}$. Larger accretion rates are a= llowed if the latter restriction is relaxed. %The position angle variations do not exhibit the frequency dependence expe= cted from fluctuations in the Faraday rotation measure, suggesting that the= y are instead intrinsic to the source. The absence of RM fluctuations limi= ts variations in the accretion rate to less than 5\%. Our result favors RI= AF/CDAF accretion models, with a shallow density distribution, over ADAF an= d Bondi-Hoyle accretion flows, which have a steep profile and are more like= ly to produce rapid RM variations. %Future wide bandwidth simultaneous observations with CARMA and the SMA, ca= pable of separating RM-induced position angle fluctuations from intrinsic v= ariability, will place better limits on accretion rate fluctuations. Improv= ed sensitivity at mm wavelengths will soon render it possible to pursue the= technique used here to investigate the accretion environments of other nea= rby low luminosity AGN, such as M81* (Brunthaler, Bower \& Falcke 2006). %\acknowledgments %We thank the referee Dan Marrone for suggesting several improvements to th= e manuscript. \begin{thebibliography}{} \bibitem[Agol(2000)]{Ag00} Agol, E. 2000, \apj, 538, L121 \bibitem[Aitken et al.(2001)]{Aik01} Aitken, D.K., Greaves, J., Chrysostomo= u, A., Jenness, T., Holland, W., Hough, J.H., Pierce-Price, D. \& Richer, = J. 2001, \apj, 534, L176 \bibitem[Bower et al.(1999a)]{Bow99a} Bower, G.C., Backer, D.C., Zhao, J.-H= =2E, Goss, W.M. \& Falcke, H. 1999a, \apj, 521, 582 \bibitem[Bower et al.(2004)]{Bow04} Bower, G.C., Falcke, H., Herrnstein, R.= M., Zhao, J.-H., Goss, W. 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R.M., Bower, G= =2EC., Goss, W.M. \& Lui, S.M. 2004, \apj, 603, L85 \end{thebibliography} \clearpage \begin{table} \begin{tabular}{cccccccc} \tableline UT Day (2004) & $I$\,(Jy) & $I_{\rm err}$\,(Jy) & $Q$\,(mJy)= & $U$\,(mJy) & $\sigma$\,(mJy) & P (mJy) & $\chi$ ($^\circ$) = \\ LSB \qquad \qquad \qquad & \null & \null & \null & \null & \null & \null & = \null \\ \tableline 88.5 & 1.94 & 0.11 & 20 & 34 & 5 & $39 \pm 5$ & $ 29 \pm 3$ \\ 89.5 & 1.96 & 0.20 & 31 & 9 & 4 & $32 \pm 4$ & $8 \pm 3$ \\ 90.5 & 1.71 & 0.20 & 29 & 16 & 8 & $33 \pm 8$ & $14 \pm 6$ \\ 91.5 & 1.69 & 0.20 & 29 & 18 & 8 & $34 \pm 8$ & $15 \pm 6$ \\ 92.5 & 2.12 & 0.14 & 55 & 21 & 4 & $58 \pm 4$ & $10.0 \pm 1.0$ \\ USB \qquad \qquad \quad & \null & \null & \null & \null & \null & \null & \= null \\ \tableline=20 88.5 & 1.98 & 0.12 & -10 & 11 & 5 & $14 \pm 5$ & $66 \pm 9$ \\ 89.5 & 1.97 & 0.18 & 7 & -15 & 4 & $16 \pm 4$ & $-32 \pm 6$ \\ 90.5 & 1.68 & 0.19 & 3 & 3 & 7 & $4 \pm 7$ & $22 \pm 47$ \\ 91.5 & 1.76 & 0.16 & 9 & 6 & 7 & $10 \pm 7$ & $16 \pm 18$ \\ 92.5 & 2.25 & 0.09 & 30 & 19 & 4 & $35 \pm 4$ & $16 \pm 3$ \\ % 88.5 & 1.94 & 0.11 & 20 & 34 & 5 & $40 \pm 5$ & $30 \pm 4$\\ % 89.5 & 1.96 & 0.20 & 31 & 9 & 4 & $32 \pm 4$ & $8 \pm 4$ \\ % 90.5 & 1.71 & 0.20 & 29 & 16 & 8 & $34 \pm 8$ & $14 \pm 7$ \\ % 91.5 & 1.69 & 0.20 & 29 & 18 & 8 & $35 \pm 8$ & $16 \pm 7$ \\ % 92.5 & 2.12 & 0.14 & 55 & 21 & 4 & $59 \pm 4$ & $10 \pm 2$ \\ \tableline \end{tabular} \caption{The daily average flux densities of Sgr A*. $I_{\rm err}$ is de= termined from=20 the flux density scatter determined on short timescales for each day. $\si= gma$ is the statistical error for $Q$ and $U$; errors in the polarization f= raction and p.a.~include the effects of 0.5\% leakage error.} \label{FluxTa= ble} \end{table} \clearpage \begin{table} \begin{tabular}{cccccc} \tableline $\nu$ (GHz) &=09$P_l$(\%) & $\sigma_{P}$ (\%) & $\chi$ ($^\circ$) = & $\sigma_\chi$ ($^\circ$) & Measurement epochs \\ \tableline 82.8 =09& 2.1 & 0.4 =09& 15.2 & 8.2 & 5 \\ 86.3 & 0.8 & 0.5 & 18 & 35 & 5 \\ 150$^a$ =09=09& 12 & $ \null_{-4}^{+9}$ =09& 83 & 3 & 1\\ 222$^a$ =09=09& 11 & $\null_{-2}^{+3}$ =09& 88 & 3 & 1\\ 216$^{b}$ =09& 10 & 1 =09& 115 & 13 & 2 \\=20 230$^{b}$=09& 9 & 3=09& 117 & 24 & 7 \\=20 340$^{c}$=09& 6.1 & 2.0 =09& 145 & 9 & 6 \\ 350$^a$=09=09& 13 & $\null_{-4}^{+10}$ =09& 161 & 3 & 1\\ 400$^a$ =09=09& 22 & $\null_{-9}^{+25}$ =09& 169 & 3 & 1\\ \tableline \end{tabular} \caption{Mean polarization fractions and p.a.s from measurements of $^a$A= itken et al. 2001,$^b$Bower et al. 2003 \& 2005, and $^c$Marrone et al. 200= 6. The quantities $\sigma_P$ and $\sigma_\chi$ denote the rms variation in= the polarization fractions and p.a.s respectively except in the case of th= e single-epoch measurements, where they denote the estimated error of the m= easurement.} \label{PolnTable} \end{table} \clearpage \begin{figure} % \includegraphics[angle=3D0,scale=3D0.8]{SgrARMlambda2.eps} \includegraphics[angle=3D0,scale=3D0.8]{f1.eps} \caption{The mean polarization p.a.~of Sgr A* as a function of wavelength. = The 85\,GHz points have been derotated by $-180^\circ$. Diamonds denote m= easurements for which polarization variability is detected, and their error= bars denote the standard error of the mean of the p.a.~variations. Triang= les denote single epoch measurements only. The dashed line shows the best = fit to all data, the solid line to all points excluding the Aitken et al. (= 2001) data, and the dot-dashed line to the unwrapped 85\,GHz points, denote= d by stars.} \label{Figlabel} \end{figure} \begin{figure} % \includegraphics[angle=3D0,scale=3D0.8]{MdotFig2.eps} \includegraphics[angle=3D0,scale=3D0.8]{f2.eps} \caption{The accretion rate implied by our measurement of the RM for variou= s accretion models using $M_{\rm bh} =3D 2.6 \times 10^6\,$M$_\odot$ (Ghez = et al.\,1998). Two choices for $r_{\rm out}$ are shown: one in which the o= uter scale is large (effectively infinite) and another in which it is only = three times larger than the inner cutoff radius.} \label{FigMdotlabel} \end{figure} \begin{figure} % \includegraphics[angle=3D0,scale=3D0.8]{SgrAPoln.eps} \includegraphics[angle=3D0,scale=3D1.0]{f3.eps} \caption{The mean polarization fraction of Sgr A*. The error bars plotted = are those of Table \ref{PolnTable}. Previous 86 and 112\,GHz non-detection= s are marked with arrows. The error bars in the Aitken et al.\,(2001) meas= urements, marked with triangles, reflect uncertainty in the contribution fr= om dust emission rather than variability associated with the source.} \labe= l{FigPolnlabel} \end{figure} \end{document} ---679269273-559381838-1150482768=:31555--