Inflow-Outflow Solution with Stellar Winds and Conduction near Sgr A*
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
INFLOW-OUTFLOW SOLUTION WITH STELLAR WINDS AND CONDUCTION NEAR SGR A*
Roman V. Shcherbakov , Frederick K. Baganoff Draft version November 9, 2018
ABSTRACTWe propose a 2-temperature radial dynamical model of plasma flow near Sgr A* and fit thebremsstrahlung emission to extensive quiescent X-Ray Chandra data. The model extends from sev-eral arcseconds to black hole (BH) gravitational radius, describing the outer accretion flow togetherwith the infalling region. The model incorporates electron heat conduction, relativistic heat capacityof particles and feeding by stellar winds. Stellar winds from each star are considered separately assources of mass, momentum and energy. Self-consistent search for the stagnation and sonic points isperformed. Most of gas is found to outflow from the region. The accretion rate is limited to below 1%of Bondi rate due to the effect of thermal conduction enhanced by entropy production in a turbulentflow. The X-Ray brightness profile proves too steep near the BH, thus a synchrotron self-Comptonpoint source is inferred with luminosity L ∼ · erg/s. We fit the sub-mm emission from the innerflow, thus aiming at a single model of Sgr A* accretion suitable at any radius. Subject headings: accretion, accretion disks, Galaxy: center INTRODUCTION
Our Galaxy is known to host a supermassive black hole (BH) with mass M ≈ . · M ⊙ at a distance R ≈ . ∼ K andemit bremsstrahlung X-Rays, observed by Chandra (Baganoff et al. 2003). A small fraction of mass accretes ontothe black hole is thus producing the emission in sub-mm and other wavebands. However, the inferred accretion ratewithin several Schwarzschild radii is 2 orders of magnitude lower (Marrone 2007) than the inferred Bondi accretionrate (Bondi 1952) at several arcseconds. This disparity is resolved in a present work with a point source revealedcoincident with Sgr A*. A brief account of observations is made in §
2. The dynamical model is outlined in §
3. Theresults are discussed in § OBSERVATIONS
We analyze ∼ ′′ . Having the extensive data we are able to perform the subpixel spatial binning in rings 0 . ′′ thicknessowing to dithering of spacecraft. The counts from four 90 deg ring segments centered at Sgr A* are compared in orderto test the viability of the radial model. It appears that within 2 ′′ the counts do not differ significantly between ringsegments, but the variation was found at > ′′ . The point spread function (PSF) is extracted by observing the nearbybinary J174540.9-290014. STELLAR WINDS AND DYNAMICAL MODEL
Feeding of the black hole should be a starting point of any accretion model. This approach helps to eliminate anumber of arbitrary boundary conditions. A set of ∼
30 wind emitters is believed to supply almost all the matterinto the feeding region of Sgr A*. Following Cuadra et al. (2008), we identify the important wind emitters, findthe wind speeds and ejection rates. We obtain the orbital data from Paumard et al. (2006); Martins et al. (2007);Lu et al. (2009), assuming the stars either belong to the disk or taken to have the minimum eccentricities. As weare constructing the radial model, the radial feeding function q ( r ) is produced by smoothing wind inputs over radiusbetween the apocenter and the pericenter for each star (see Fig. 1). The averaged wind velocity is found as a root-mean-square average over stars weighed with the ejection rate. We do not account for orbital velocities of stars inenergy input as feeding is dominated by only a few stars close to the BH. S2 star is included into the calculation as itmay eject more matter (Martins et al. 2008), than falls onto the BH.The dynamical model has sources of mass, radial momentum and energy due to winds (Lamers & Cassinelli 1999).The main feature of the model is the electron thermal conduction proportional to the temperature gradient withconductivity κ = 0 . p k B T e /m e n e r (Johnson & Quataert 2007). Here we have included the factor of 5 inhibition of Electronic address: [email protected] Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Center for Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA - - - - - - Distance r from BH in arcsec at 8kpc M s un (cid:144) yea r Feeding rate 4 Π r q H r L per unit radius 0.1 0.2 0.5 1.0 2.0 5.0 10.010001500 Distance r from BH in arcsec at 8kpc k m (cid:144) s RMS "wind" velocity v w Fig. 1.—
Mass input into the central region around the BH on the left panel. Root-mean-square wind velocity v w on the right panel. conductivity in turbulent magnetic field (Narayan & Medvedev 2001). So computed heat flux appears to be belowthe saturated flux (Cowie & McKee 1976). In reality the inner accretion flow is collisionless and the outer accretion isweakly collisional, however, the single prescription for conductivity gives the reasonable approximation. The realisticbehavior of electrons in the inner flow is achieved by using their relativistic heat capacity in the equations of motion,which naturally leads to the ratios T p /T e up to 10 even in adiabatic flows. For completeness of the theory we add thedirect energy transfer into electrons and protons equivalent to the entropy production, which happens due to viscosityin the rotating flow or due to dissipation of turbulence (Shcherbakov 2008). We assume that the fractions f e and f i ofavailable gravitational energy goes to electrons and protons. The Coulomb collisions are included for numerical stabilityto balance the electron and proton temperature in the outer flow, though they do not have the significant dynamicaleffect. The effect of gas composition is accounted for by introducing the effective mass m av ≈ . m H per electronand correspondent reduction in ion gas pressure. These numbers are taken for the solar abundance of elements, whichseems to be reasonable for stellar winds (Najarro et al. 2004). Paczhynski-Wiita gravitational potential is employed.The proposed system of equations has no artificial boundary conditions, but it appears to have an unmatchedcomplexity. We self-consistently solve for the positions of the stagnation point, where gas velocity is zero, and theinner isothermal sonic point (Quataert 2004). The heat flux is set to zero at the point, where dT e /dr = 0 in the Bondisolution near the BH. The outer boundary is either taken to be the isothermal sonic point in the outflow or the pointwith slightly higher density (for numerical stability). The relaxation technique is used for the 2-temperature systembetween the inner boundary and the stagnation point, whereas only shooting works outside the stagnation point. RESULTS
Having produced a bunch of dynamical models, we convert the temperature and density radial profiles into thesurface brightness profile. We take the up-to-date bremsstrahlung emissivities (see (Gould 1980) and errata) andaccount for emission by heavy elements, excluding iron. We calculate the spectrum along each ray and convert it to S , c oun t s p i xe l - S , c oun t s p i xe l - Fig. 2.—
Plots of surface brightness S in observed counts per pixel squared (1 pixel=0 . ′′ ). Blue curve with error bars shows theobservations. Extended emission model is on the left panel: the green curve shows brightness smoothed by PSF. The model of a pointsource with L = 3 · erg/s (red) and the residual (green) are on the right panel. counts by applying the solar metallicity interstellar absorption (Morrison & McCammon 1983) with hydrogen column N H = 10 cm − and convolving with the response of Chandra. Then we apply the PSF blurring and compare withthe observed surface brightness profile. The outer surface brightness profile can be reasonably fitted by a model with f e = 0 . , f i = 0 . , which also leads to the ratio T p /T e ≈
15 near the BH. However, we find that the inner partof surface brightness curve is too steep for any extended emission. There should be a point source in the centeraccounting for to of central surface brightness and having the unabsorbed luminosity about L = 3 · erg/sof monoenergetic 4 keV photons. About the same luminosity is expected from the synchrotron self-Compton (SSC)process near the BH. The search for the best model with the point source continues. We want the best model toreproduce the observed Faraday rotation measure RM ≈ − (Marrone 2007) and optically thick flux F R = 1 .
73 Jyat 86 GHz (Krichbaum et al. 2006). An order of magnitude consistency is achieved on the way. The accretion rateappears to be self-consistently limited to <
1% of Bondi value, thus the connection between the inner accretion flowand the outer accretion flow is established. The future versions will include the angular momentum and use X-Rayspectral information.The author is grateful to Mikhail Medvedev and Ramesh Narayan for fruitful discussions, Daniel Wang and FengYuan for comments.1% of Bondi value, thus the connection between the inner accretion flowand the outer accretion flow is established. The future versions will include the angular momentum and use X-Rayspectral information.The author is grateful to Mikhail Medvedev and Ramesh Narayan for fruitful discussions, Daniel Wang and FengYuan for comments.