Compton Scattering of Self-Absorbed Synchrotron Emission

Abstract

Synchrotron self-Compton (SSC) scattering is an important emission mechanism in many astronomical sources, such as gamma-ray bursts (GRBs) and active galactic nuclei (AGNs). 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 (${\nu }_{\mathrm{a}}$, ${\nu }_{\mathrm{m}}$, and ${\nu }_{\mathrm{c}}$) are studied. In the weak self-absorption regime, i.e., ${\nu }_{\mathrm{a}}<{\nu }_c$, 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 ${\nu }_{\mathrm{a}}$; 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. ${\nu }_{\mathrm{a}}>{\nu }_{\mathrm{c}}$, 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 ${\nu }_{\mathrm{c}}<{\nu }_{\mathrm{a}}<{\nu }_{\mathrm{m}}$, the spectrum is thermal (non-thermal) -dominated if ${\nu }_a>\sqrt{{\nu }_m{\nu }_c}$ (${\nu }_a<\sqrt{{\nu }_m{\nu }_c}$). 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 invokes ${\nu }_{\mathrm{a}}>\max ({\nu }_{\mathrm{m}},{\nu }_{\mathrm{c}})$.

Accepted for publication in MNRAS

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