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 ∼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: ΘθT ≃ 0.1(lh/ls)¼; and α ≃ 1.6(ls/lh)¼. Here the hot plasma heating rate compactness is lh, the seed photon compactness is ls, the temperature in electron rest-mass units is Θ, and the Thomson optical depth is θT. The coefficient in the first expression is weakly dependent on plasma geometry; the second expression is independent of geometry. Only when ls/lh is a few tenths or greater is there a weak secondary dependence in both relations on θT. Because α is almost independent of everything but ls/lh, the observed power-law index may be used to estimate ls/lh. In both active galactic nuclei (AGNs) and stellar black holes, the mean value estimated this way is ls/lh ∼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 ΘθT ≃0.1-0.2, depending primarily on plasma geometry. It is possible to construct coronal models (i.e., models in which ls/lh ≃ 0.5) which fit the observed spectra, but they are tightly constrained: θT must be ≃0.08 and Θ ≃ 0.8.