Photon-conserving Comptonization in simulations of accretion discs 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 supercritical black hole accretion discs. We find that blackbody Comptonization underestimates the gas and radiation temperature by up to a factor of 2 compared to photon-conserving Comptonization. This discrepancy could be serious when computing spectra. The photon-conserving simulation indicates that the spectral colour correction factor of the escaping radiation in the funnel region of the disc could be as large as 5.