Klein–Nishina effects in the spectra of non‐thermal sources immersed in external radiation fields

We provide a systematic numerical and analytical study of 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 up‐scattering ambient photons produced outside the source. We focus on the case where q , the ratio of the ambient radiation field to source magnetic field energy densities, significantly exceeds unity. We show that the KN reduction in the electron Compton cooling rate causes the steady‐state electron spectrum to harden at energies γ≳γ KN , where γ KN = 1/4ε 0 and ε 0 = h ν 0 / m e c 2 is the characteristic ambient photon energy. This hardening becomes noticeable in the synchrotron radiation from electrons with energies as low as 0.1γ KN and changes the synchrotron spectral index relative to its Thomson limit value by as much as Δα∼ 0.75 for q ≫ 1. 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 q > 1. We discuss the importance of these KN effects in blazars, micro‐quasars and pulsar binaries.