IMPROVED REFLECTION MODELS OF BLACK HOLE ACCRETION DISKS: TREATING THE ANGULAR DISTRIBUTION OF X-RAYS

X-ray reflection models are used to constrain the properties of the accretion disk, such as the degree of ionization of the gas and the elemental abundances. In combination with general relativistic ray tracing codes, additional parameters like the spin of the black hole and the inclination to the system can be determined. However, current reflection models used for such studies only provide angle-averaged solutions for the flux reflected at the surface of the disk. Moreover, the emission angle of the photons changes over the disk due to relativistic light bending. To overcome this simplification, we have constructed an angle-dependent reflection model with the xillver code and self-consistently connected it with the relativistic blurring code RELLINE. The new model, relxill, calculates the proper emission angle of the radiation at each point on the accretion disk and then takes the corresponding reflection spectrum into account. We show that the reflected spectra from illuminated disks follow a limb-brightening law highly dependent on the ionization of disk and yet different from the commonly assumed form I alpha ln(1 + 1/mu). A detailed comparison with the angle-averaged model is carried out in order to determine the bias in the parameters obtained by fitting a typical relativistic reflection spectrum. These simulations reveal that although the spin and inclination are mildly affected, the Fe abundance can be overestimated by up to a factor of two when derived from angle-averaged models. The fit of the new model to the Suzaku observation of the Seyfert galaxy Ark 120 clearly shows a significant improvement in the constraint of the physical parameters, in particular by enhancing the accuracy in the inclination angle and the spin determinations.