Role of emission angular directionality in spin determination of accreting black holes with a broad iron line

Aims: The spin of an accreting black hole can be determined by spectroscopy of the emission and absorption features produced in the inner regions of an accretion disc. In this work, we discuss the method employing the relativistic line profiles of iron in the X-ray domain, where the emergent spectrum is blurred by general relativistic effects.
Methods: Precision of the spectra fitting procedure could be compromised by inappropriate accounting for the angular distribution of the disc emission. Often a unique profile is assumed, invariable over the entire range of radii in the disc and energy in the spectral band. An isotropic distribution or a particular limb-darkening law have been frequently set, although some radiation transfer computations exhibit an emission excess towards the grazing angles (i.e., the limb brightening). By assuming a rotating black hole in the centre of an accretion disc, we perform radiation transfer computations of an X-ray irradiated disc atmosphere (NOAR code) to determine the directionality of outgoing X-rays in the 2-10 keV energy band. Based on these computations, we produce a new extension to the KY software package for X-ray spectra fitting of relativistic accretion discs.
Results: We study how sensitive the spin determination is to the assumptions about the intrinsic angular distribution of the emitted photons. The uncertainty of the directional emission distribution translates to ≃20% uncertainty in the determination of the marginally stable orbit. We implemented the simulation results as a new extension to the KY software package for X-ray spectra fitting of relativistic accretion disc models. Although the parameter space is rather complex, leading to a rich variety of possible outcomes, we find that on average the isotropic directionality reproduces our model data to the best precision. Our results also suggest that an improper use of limb darkening can partly mimic a steeper profile of radial emissivity. We demonstrate these results in the case of XMM-Newton observation of the Seyfert galaxy MCG-6-30-15, for which we construct confidence levels of χ² statistics, and on the simulated data for the future X-ray IXO mission. Our simulations, with the tentative IXO response, show a significant improvement that can qualitatively enhance the accuracy of spin determination.