A Magnetic α ω Dynamo in Active Galactic Nuclei Disks - NMT Physics

– 25 –The energy emitted from the unit surface of the one side of the disk per unit time is(Q = 3 GM√ )( )( )3rg0.18πṀ R 3 1 − = 7.6 · 10 8 erg cm −2 s −1 lE×rǫ 0.1( ) (r −3√ )10 −2 M8 2 3rg1 − . (A9)pcrThe effective temperature near the surface of the disk isQ = ac( ) 0.1 1/4 ( ) 1/44 T s 4 , T lEs = 1900K×ǫ 0.1( ) (r −3/4√ ) 1/410 −2 M 1/2 3rg8 1 − . (A10)pcrThe article by Shakura & Sunyaev (1973) contains the solution of the radiative transport equationin the vertical direction of an optically thick disk with assumed local thermodynamic equilibriumfor each z in the disk. Volume emission due to viscous heating is included in the solution. Using thissolution with the Thomson opacity κ T = 0.4cm 2 g −1 one obtains (section 2a of Shakura & Sunyaev1973) the temperature at the midplane of the disk(Tmpd 4 = T s4 1 + 3 )16 κ TΣ . (A11)Since the disk is very opaque for Thomson scattering one can neglect 1 in the expression (A11) andobtains( ) 0.01 1/4 ( ) −1/4 lE ( ǫ) 1/4T mpd = T s · 41.3×α ss 0.1 0.1( ) (r 3/8√ ) −1/410 −2 M −3/8 3rg8 1 − . (A12)pcrUsing expression (A10) for the effective surface temperature T s and substituting for T s in theequation (A12) one obtains( ) 0.01 1/4 ( )T mpd = 7.9 · 10 4 r −3/8Kα ss 10 −2 M 1/88 . (A13)pcNote that the terms describing the dependence on the accretion rate cancel out as well as generalrelativistic correction term. Therefore, T mpd in the inner parts of accretion disk does not depend onthe accretion rate, but is determined by the mass of the central black hole and viscosity parameterα ss . Radiation pressure in the midplane of the disk in the zone (a) isP r = 1 3 aT mpd 4 = 1.07 · 105 erg cm −30.01( )M 1/2 r −3/28α ss 10 −2 . (A14)pc