Compton scattering in a converging fluid flow - II. Radiation-dominated shock

Abstract

The problem of Compton scattering in an optically thick fluid flow in which bulk motion is the dominant source of photon heating is illus-trated by analysing a radiation-dominated, plane-parallel shock of speed u with photon to electron ratio greatly exceeding ~ (^p/^ e)-I n traversing the shock (of thickness ~ (c/u) Thomson optical depths), a typical photon experiences {c/u) 2 scatterings, each one giving a secular fractional energy increase ~ (u/c) 2 and a total average increase of order unity. In a converging fluid flow, an exponentially small number of photons are accelerated to an exponentially large energy. Thus, a power-law spectrum will be transmitted at high frequencies. For a shock of Mach number M, bulk acceleration pro-duces a spectral index a = (M 2 — Vi) (M 2 + 6) (M 2 — l) -2 , which tends to unity for a strong shock. The applicability of these results to quasars and the micro-wave background is briefly discussed.