Cyclo-Synchrotron Emission and Comptonization in Optically Thin Hot Accretion Flows

Soft cyclo-synchrotron photons produced by thermal electrons moving in a magnetic field can be subsequently Comptonized to produce hard X-ray and $\gamma$-ray emission. An accurate determination of the amount of soft cyclo-synchrotron photons produced from such plasmas is clearly necessary. We present the complete solution to the cyclo-synchrotron problem. We calculate the emission produced by an isotropic distribution of thermal electrons moving in a magnetic field, for temperatures ranging from $5\times10^8$K to $3.2\times10^{10}$K. The applicability of the standard synchrotron formula is evaluated, and we provide convenient fitting functions for the emission spectra within this range of temperatures. We discuss how the Comptonized spectra, for various temperatures and optical depths, are affected by the new results.