Compton scattering of self-absorbed synchrotron emission

   Synchrotron self-Compton (SSC) scattering is an important emission mechanism in many astronomical sources, such as gamma-ray bursts (GRBs) and active galactic nuclei (AGN). We give a complete presentation of the analytical approximations for the Compton scattering of synchrotron emission with both weak and strong synchrotron self-absorption. All possible orders of the characteristic synchrotron spectral breaks (synchrotron absorption frequency ν_a, synchrotron typical frequency ν_m, and synchrotron cooling frequency ν_c) are studied.  

   In the strong absorption regime, i.e. ν_a > ν_c, heating of low-energy electrons due to synchrotron absorption leads to pile-up of electrons, and form a thermal component besides the broken power-law component. This leads to two-component (thermal + non-thermal) spectra for both the synchrotron and SSC spectral components. For ν_c < ν_a <ν_m, the spectrum is thermal (non-thermal) dominated if ν_a > sqrt(ν_mν_c ) (ν_a < sqrt(ν_mν_c)). Similar to the weak-absorption regime, the SSC spectral component is broader than the simple broken power-law approximation. We derive the critical condition for strong absorption (electron pile-up), and discuss a case of GRB reverse shock emission in a wind medium, which invokesν_a > max(ν_m, ν_c). More details can be seen in Fig. 2. 

 The work by He Gao, Wei-Hua Lei, Xue-Feng.Wu, & Bing Zhang has been accepted to be published in the MNRAS in 2013, please see MNRAS, 435, 2520–2531 for more details (http://mnras.oxfordjournals.org/content/435/3/2520).