Electron thermalization and photon emission from magnetized compact sources

We present detailed calculations of the electron thermalization by synchrotron self-absorption accounting for cooling by Compton scattering. For the first time, we solve coupled kinetic equations for electrons and photons without any approximations on the relevant cross-sections and compute self-consistently the resulting electron and photon distributions. The results presented in this contribution may be applied to the magnetized coronae around Galactic black hole accretion disks.