The Inverse Compton Thermostat in Hot Plasmas near Accreting Black Holes

Abstract

The X-ray spectra of accreting black hole systems generally contain components (sometimes dominating the total emission) which are well-fit 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: ΘτT ≃ 0.1(l h /ls) 1/4 ; and α ≃ 1.6(ls/l h ) 1/4 . Here the hot plasma heating rate compactness is l h , the seed photon compactness is ls, the temperature in electron rest mass units is Θ, and the Thomson optical depth is τT . The coefficient in the first expression is weakly-dependent on plasma geometry; the second expression is independent of geometry. Only when ls/l h is a few tenths or greater is there a weak secondary dependence in both relations on τT .Because α is almost independent of everything but ls/l h , the observed power law index may be used to estimate ls/l h . In both AGN and stellar black holes, the mean value estimated this way is ls/l h ∼ 0.1, although there is much greater sample dispersion among stellar black holes than among AGN. 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 ΘτT ≃ 0.1 -0.2, depending primarily on plasma geometry. It is possible to construct coronal models (i.e. models in which ls/l h ≃ 0.5) which fit the observed spectra, but they are tightly constrained: τT must be ≃ 0.08 and Θ ≃ 0.8.

Two Different Long‐Term Behaviors in Black Hole Candidates: Evidence for Two Accretion Flows?

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A Comprehensive Spectral and Variability Study of Narrow‐Line Seyfert 1 Galaxies Observed by ASCA . II. Spectral Analysis and Correlations

“…Generally, the feedback consists of reprocessing of radiation from the hot phase by the cool phase, which increases the luminosity of the cool phase, as well as pair creation in the hot phase which alters the optical depth. Pietrini & Krolik (1995) Ðnd that the plasma parameters can be described by two scaling laws that are weak functions of the ratio of hard and soft luminosity :…”

Disk-Corona Models and X-Ray Emission from Seyfert Galaxies

“…We recall that the optical depth does not appear explicitly but is related to the temperature by the balance equation for the corona (see also Pietrini and Krolik 1995). Values of T C in the range 30-300 keV, as suggested by observations (Maisak et al 1993, Johnson et al 1993, Madejski et al 1995, correspond to optical depths between 1 and 0.1.…”