Constraining the Accretion Flow in Sgr A* by GR Dynamical and Radiative Modeling
aa r X i v : . [ a s t r o - ph . H E ] D ec Draft version November 9, 2018
Preprint typeset using L A TEX style emulateapj v. 08/13/06
CONSTRAINING THE ACCRETION FLOW IN SGR A* BYGR DYNAMICAL AND RADIATIVE MODELING
Roman V. Shcherbakov , Robert F. Penna Draft version November 9, 2018
ABSTRACTWe present the combination of dynamical accretion model based on 3D GRMHD simulations andgeneral relativistic (GR) polarized radiative transfer. We write down the formalism of and perform theGR ray-tracing of cyclo-synchrotron radiation through the model of accretion flow in Sagittarius A*.GR polarimetric imaging is presented as well as the results for spectrum for a probable set of spinsand orientations. Precise fitting formulae for Faraday rotation and Faraday conversion coefficientsare employed for thermal plasma. The axisymmetic flow pattern and the magnetic field geometrycorrespond to averaged 3D GRMHD simulations near the black hole, whereas the analytic model wasused far from the black hole. The density scaling is found by fitting the sub-mm flux. Spin a = 0 . θ = 0 . Subject headings: GR POLARIZED RADIATIVE TRANSFER AND DYNAMICS
We come up with the formalism in several stages. First, we write down the standard propagation equations ofStokes parameters
I, Q, U, V in the uniform thermal plasma (Melrose & McPhedran 1991) in a locally flat co-movingreference frame with synchrotron emissivities/absorptivities from Melrose (1971). We take Faraday rotation/conversioncoefficients from Shcherbakov (2008), as the other published derivation of Faraday conversion coefficients (Huang et al.2009) is a very crude approximation. Second, we parallel propagate the basis vectors along the null geodesic from theobserver’s plane to account for GR rotation of the basis. Third, with proper gauges on wave vector potential we writedown the covariant equations of polarized radiative transfer. Following Huang et al. (2009), we assume that the matrixof absorptivities and propagation coefficients generalizes in the polarized transfer analogously to the unpolarized case.The dynamical model used in the transfer starts with adiabatic 3D GRMHD simulations of thick accretion flowonto the Kerr black hole (BH) with spins a = 0 , . , . , . . We average the flow velocity, magnetic field, RMSmagnetic field, gas density and pressure for the quasi-steady period of the developed accretion and separate the electrontemperature T e from the proton temperature T p by applying the heating prescription from Sharma et al. (2007). Thedynamical model is smoothly extended to large radii r > M to take into account the Faraday rotation effect at largedistances from the BH.
10 20 50 100 200 500 1000 20000.51.02.0 Ν ,GHz F Ν , Jy Fig. 1.—
Specific flux F ν in comparison to observations (Yuan, Quataert & Narayan 2004; Marrone 2007) (dots) on the left panel. Imageof specific flux F ν in logarithmic scale with contrast 8 at ν = 345 GHz on the right panel. In both calculations spin a = 0 . , inclinationangle θ = 0 . . Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA RESULTS
We perform the GR polarized radiative transfer for each spin for a set of inclination angles θ and compare the specificfluxes, linear polarization fractions (LP), and circular polarization fractions (CP) to observations. We find, that theextreme spins a = 0 . , a = 0 .
98 do not fit all the observations well. They require lower density n < · cm − near BHto fit the flux at 220 GHz, but Faraday depolarization fails at these densities leading to high LP at 86 GHz comparedto the observed value (Macquart et al. 2006). The preferred value of the inclination angle θ = 0 . a = 0 . a = 0 produces goodfits as well. Imaging produces some unexpected results. As our simulation appears to be substantially sub-Keplerianand have significant thermal support, the Innermost Stable Circular Orbit (ISCO) loses its importance and the blackhole shadow is not always seen.Supported by NASA ESSF to RVS.= 0 produces goodfits as well. Imaging produces some unexpected results. As our simulation appears to be substantially sub-Keplerianand have significant thermal support, the Innermost Stable Circular Orbit (ISCO) loses its importance and the blackhole shadow is not always seen.Supported by NASA ESSF to RVS.