Photon-conserving Comptonization in simulations of accretion disks around black holes

We introduce a new method for treating Comptonization in computational fluid dynamics. By construction, this method conserves the number of photons. Whereas the traditional "blackbody Comptonization" approach assumes that the radiation is locally a perfect blackbody and therefore uses a single parameter, the radiation temperature, to describe the radiation, the new "photon-conserving Comptonization" approach treats the photon gas as a Bose-Einstein fluid and keeps track of both the radiation temperature and the photon number density. We have implemented photon-conserving Comptonization in the general relativistic radiation magnetohydrodynamical code KORAL and we describe its impact on simulations of mildly super-critical black hole accretion disks. We find that blackbody Comptonization underestimates the gas and radiation temperature by up to a factor of two compared to photon-conserving Comptonization. This discrepancy could be serious when computing spectra. The photon-conserving simulation indicates that the spectral color correction factor of the escaping radiation in the funnel region of the disk could be as large as 5.