Gas heating inside radio sources to mildly relativistic temperatures via induced Compton scattering

The measured brightness temperatures of the low-frequency synchrotron radia tion from intense extragalactic sources reach 10(11)-10(12) K. If there is some amount of nonrelativistic, ionized gas within such sources, it must be heated through induced Compton scattering of the radiation. If cooling via inverse Compton scattering of the same radio radiation counteracts this he ating, then the plasma can be heated up to mildly relativistic temperatures kT similar to 10-100 keV. In this case, the stationary electron velocity d istribution can be either relativistic Maxwellian or quasi-Maxwellian (with the high-velocity tail suppressed), depending on the efficiency of Coulomb collisions and other relaxation processes. We derive several simple approx imate expressions for the induced Compton heating rate of mildly relativist ic electrons in an isotropic radiation field, as well as for the stationary electron distribution function and temperature. We give analytic expressio ns for the kernel of the integral kinetic equation (one as a function of th e scattering angle, and the other for an isotropic radiation field), which describes the photon redistribution in frequency through induced Compton sc attering in thermal plasma. These expressions can be used in the parameter range hv much less than kT less than or similar to 0.1mc(2) [in contrast to the formulas written out previously in Sazonov and Sunyaev (2000), which a re less accurate]. (C) 2001 MAIK "Nauka/Interperiodica".