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. 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 (νa, νm and νc) are studied. In the weak self-absorption regime, i.e. νa < νc, the electron energy distribution is not modified by the self-absorption process. The shape of the SSC component broadly resembles that of synchrotron, but with the following features: The SSC flux increases linearly with frequency up to the SSC break frequency corresponding to the self-absorption frequency νa; and the presence of a logarithmic term in the high-frequency range of the SSC spectra makes it harder than the power-law approximation. In the strong absorption regime, i.e. νa > νc, 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 νc < νa < νm, the spectrum is thermal (non-thermal) dominated if νa > √ νmνc (νa < √ νmνc). 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 invokes νa > max(νm, νc).