Klein-Nishina Effects on Optically Thin Synchrotron and Synchrotron Self-Compton Spectrum

TL;DR

This paper develops analytical models for synchrotron and SSC spectra considering Klein-Nishina effects, revealing spectral hardening and discontinuities in cooling frequencies relevant for astrophysical sources like GRBs.

Contribution

It provides new analytical approximations for synchrotron and SSC spectra including Klein-Nishina effects, applicable to various astrophysical sources.

Findings

Spectra can be described by broken power-laws with specific break frequencies.

Klein-Nishina effects cause hardening of the synchrotron spectrum below injection energy.

Discontinuous changes in cooling frequency can occur due to synchrotron and SSC cooling transition.

Abstract

We present analytic approximations to the optically thin synchrotron and synchrotron self-Compton (SSC) spectra when Klein-Nishina (KN) effects are important and pair production and external radiation fields can be neglected. This theory is useful for analytical treatment of radiation from astrophysical sources, such as gamma-ray bursts (GRBs), active galactic nuclei and pulsar wind nebula, where KN effects may be important. We consider a source with a continuous injection of relativistic electrons with a power-law energy distribution above some typical injection energy. We find that the synchrotron-SSC spectra can be described by a broken power-law, and provide analytic estimates for the break frequencies and power-law indices. In general, we show that the dependence of the KN cross-section on the energy of the upscattering electron results in a hardening of the energy distribution of fast cooling electrons and therefore in a hardening of the observed synchrotron spectrum. As a result the synchrotron spectrum of fast cooling electrons, below the typical injection energy, can be as hard as $F_\nu \propto \nu^0$, instead of the classical $\nu^{-1/2}$ when KN effects are neglected. The synchrotron energy output can be dominated by electrons with energy above the typical injection energy. We solve self-consistently for the cooling frequency and find that the transition between synchrotron and SSC cooling can result in a discontinuous variations of the cooling frequency and the synchrotron and SSC spectra. We demonstrate the application of our results to theory by applying them to prompt and afterglow emission models of GRBs.