Constraint on AGN corona size with fully relativistic modeling of 3D corona

The ``lamp-post'' scenario was usually used to describe AGN corona, in which the corona is assumed to be an infinitesimal point source on the symmetry axis. In some AGNs, especially NLS1s, the broad iron line profile requires extremely compact corona. On the other hand, the corona must be large enough to intercept enough seed photons to be able to produce the observed X-ray continuum and reflection spectrum. One attempt to constrain AGN corona size was made by Dovciak & Done 2016, in which the corona size was estimated by conservation of photons during Comptonization process. They found out that for one NLS1 1H 0707-495, the size of the corona must be substantially larger than 1 GM/c ^{2}. In that work, the Comptonized spectrum was evaluated assuming lamp-post geometry and the corona size was estimated under the assumption that the emission of the corona is homogeneous. To calculate the spectrum of 3D corona (i.e., the corona is extended and with finite height) self-consistently, we perform a fully relativistic Monte Carlo calculation of energy and polarization spectrum of AGNs of disk-corona geometry, taking into account propagation of null geodesic in Kerr space-time and Compton scattering process. With the calculated spectra, we are able to put constraint on AGN corona size for an AGN sample with simultaneous XMM-Newton X-ray/UV observations.