Role of emission angular directionality in spin determination of
  accreting black holes with broad iron line
  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. 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. Precision of spectra fitting procedure could be
compromised by inappropriate account of 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. We study how sensitive
the spin determination is to the assumptions about the intrinsic angular
distribution of the emitted photons. We find that the uncertainty of the
directional emission distribution translates to 20% uncertainty in
determination of the marginally stable orbit. 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 to determine the directionality of
outgoing X-rays in the 2-10 keV energy band. 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 usage of limb darkening
can partly mimic a steeper profile of radial emissivity. We demonstrate these
results on the case of XMM-Newton observation of the Seyfert galaxy
MCG-6-30-15, for which we construct confidence levels of chi squared
statistics, and on the simulated data for the future X-ray IXO mission.
