Polarization of Inverse Compton Scattering without Ultrarelativistic Approximation*

Inverse Compton (IC) scattering is an essential radiative process in many high-energy astrophysical setups. Typical calculations on the differential cross-section adopted isotropic or ultrarelativistic approximations. We develop a new formalism to compute IC scattering without the above assumptions and with improved numerical stability compared to previous results. Our calculations can be employed in extensive astrophysical scenarios. An application is for computing the differential polarization of photons after anisotropic IC scattering, which is seldom explored with numerical approaches and is often inconsistent in previous contexts. This work is timely for current and future high-energy missions with polarimetry capability.