Thermal synchrotron radiation and its Comptonization in compact X-ray sources

We investigate the process of synchrotron radiation from thermal electrons at semirelativistic and relativistic temperatures. We find an analytic expression for the emission coefficient for random magnetic fields with an accuracy significantly higher than those derived previously. We also present analytic approximations to the synchrotron turnover frequency, treat Comptonization of self-absorbed synchrotron radiation, and give simple expressions for the spectral shape and the emitted power. We also consider modifications of the above results by bremsstrahlung. We then study the importance of Comptonization of thermal synchrotron radiation in compact X-ray sources. We first consider emission from hot accretion flows and active coronae above optically thick accretion discs in black hole binaries and active galactic nuclei (AGNs). We find that for plausible values of the magnetic field strength, this radiative process is negligible in luminous sources, except for those with hardest X-ray spectra and stellar masses. Increasing the black hole mass results in a further reduction of the maximum Eddington ratio from this process. Then, X-ray spectra of intermediate-luminosity sources, e.g. low-luminosity AGNs, can be explained by synchrotron Comptonization only if they come from hot accretion flows, and X-ray spectra of very weak sources are always dominated by bremsstrahlung. On the other hand, synchrotron Comptonization can account for power-law X-ray spectra observed in the low states of sources around weakly magnetized neutron stars.