THE INVERSE COMPTON THERMOSTAT IN HOT PLASMAS NEAR ACCRETING BLACK-HOLES

The X-ray spectra of accreting black hole systems generally contain components (sometimes dominating the total emission) which are well fitted by thermal Comptonization models with temperatures similar to 100 keV. We demonstrate why, over many orders of magnitude in heating rate and seed photon supply, hot plasmas radiate primarily by inverse Compton scattering, and find equilibrium temperatures within a factor of a few of 100 keV. We also determine quantitatively the (wide) bounds on heating rate and seed photon supply for which this statement is true. Plasmas in thermal balance in this regime obey two simple scaling laws: Theta tau(T) similar or equal to 0.1(l(h)/l(s))(1/4); and alpha similar or equal to 1.6(l(s)/l(h))(1/4). Here the hot plasma heating rate compactness is l(h), the seed photon compactness is l(s), the temperature in electron rest-mass units is Theta, and the Thomson optical depth is tau(T). The coefficient in the first expression is weakly dependent on plasma geometry; the second expression is independent of geometry. Only when l(s)/l(h) is a few tenths or greater is there a weak secondary dependence in both relations on tau(T). Because alpha is almost independent of everything but l(s)/l(h) the observed power-law index may be used to estimate l(s)/l(h). In both active galactic nuclei (AGNs) and stellar black holes, the mean value estimated this way is l(s)/l(h) similar to 0.1, although there is much greater sample dispersion among stellar black holes than among AGNs. This inference favors models in which the intrinsic (as opposed to reprocessed) luminosity in soft photons entering the hot plasma is small, or in which the hard X-ray production is comparatively distant from the source of soft photons. In addition, it predicts that Theta tau(T) similar or equal to 0.1-0.2, depending primarily on plasma geometry. It is possible to construct coronal models (i.e., models in which l(s)/l(h) similar or equal to 0.5) which fit the observed spectra, but they are tightly constrained: tau(T) must be similar or equal to 0.08 and Theta similar or equal to 0.8.