Klein-Nishina Effects in the Spectra of Non-Thermal Sources Immersed in External Radiation Fields

Abstract

We study Klein-Nishina (KN) effects in the spectrum produced by a steady state, non-thermal source where rapidly accelerated electrons cool by emitting synchrotron radiation and Compton upscattering ambient photons produced outside the source. We focus on the case where the radiation density inside the source exceeds that of the magnetic field. We show that the KN reduction in the electron Compton cooling rate causes the steady-state electron spectrum to harden at energies above \gamma_{KN}, where \gamma_{KN}= 1/4\epsilon_0 and \epsilon_0=h\nu_0/m_ec^2 is the characteristic ambient photon energy. The source synchrotron spectrum thus shows a high-energy ``bump'' or excess even though the electron acceleration spectrum has no such excess. In contrast, the low-energy Compton gamma-ray spectrum shows little distortion because the electron hardening compensates for the KN decline in the scattering rate. For sufficiently high electron energies, however, Compton cooling becomes so inefficient that synchrotron cooling dominates -- an effect omitted in most previous studies. The hardening of the electron distribution thus stops, leading to a rapid decline in Compton gamma-ray emission, i.e., a strong spectral break whose location does not depend on the maximum electron energy. This break can limit the importance of Compton gamma-ray pair production on ambient photons and implies that a source's synchrotron luminosity may exceed its Compton luminosity even though the source magnetic field energy density is smaller than the ambient radiation energy density. We discuss the importance of these KN effects in blazars, micro-quasars, and pulsar binaries.