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 upscattering 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 \gamma \gtrsim \gamma _ { KN } , where \gamma _ { KN } = 1 / 4 \epsilon _ { 0 } and \epsilon _ { 0 } = h \nu _ { 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 0.1 \gamma _ { KN } and changes the synchrotron spectral index relative to its Thomson limit value by as much as \Delta \alpha \sim 0.75 for q \gg 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 .