Constraining the Size of the Corona with Fully Relativistic Calculations of Spectra of Extended Coronae. I. The Monte Carlo Radiative Transfer Code

The size and geometry of the X-ray-emitting corona in an active galactic nucleus (AGN) are still not well constrained. Dovciak & Done proposed a method based on calculations assuming a point-like lamp-post corona. To perform more self-consistent calculations of energy spectra of extended coronae, we develop MONK, a Monte Carlo radiative transfer code dedicated to calculations of Comptonized spectra in the Kerr spacetime. In MONK we assume a Klein-Nishina scattering cross section and include all general relativistic effects. We find that for a corona located above the disk, the spectrum is not isotropic, but has harder and less luminous spectra toward observers at lower inclinations, owing to anisotropic illumination of the seed photons. This anisotropy also leads to an underestimated size for the corona if we assume it to be a point-like, isotropic source located on the rotation axis of the black hole, demonstrating the necessity for more self-consistent calculations. We also study the effect of motion and geometry of the corona on the emergent spectrum. Finally, we discuss the implication of anisotropic coronal emission for the reflection spectrum in AGNs as well as black hole X-ray binaries (BHXRBs). We find that by assuming the coronal emission to be isotropic, one may underestimate the soft excess in AGNs, and the reflection continuum and iron K fluorescent line flux in BHXRBs.