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

摘要

Aims. The spin of an accreting black hole can bedetermined byspectroscopy of the emission and absorption features produced in theinner regions of an accretion disc. In this work, we discuss the methodemploying 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 procedurecould becompromised by inappropriate accounting for the angular distribution ofthe disc emission. Often a unique profile is assumed, invariable overtheentire range of radii in thedisc and energy inthespectral band. An isotropic distribution or a particular limb-darkeninglaw have been frequently set, although some radiation transfercomputations exhibit an emission excess towards the grazing angles(i.e., thelimb brightening). By assuming a rotating blackhole inthe centre of an accretion disc, we perform radiation transfercomputations of an X-ray irradiated disc atmosphere (NOAR code) todetermine thedirectionality of outgoing X-rays in the2-10keV energy band. Based on these computations, we produceanew extension to theptmmscky software package for X-rayspectrafitting of relativistic accretion discs. Results. We study how sensitive the spindetermination is to theassumptions about theintrinsic angular distribution oftheemitted photons. Theuncertainty ofthedirectionalemission distribution translates to 20%uncertainty in the determination of themarginally stableorbit.We implemented the simulation results as a new extension to theptmmscky software package for X-ray spectra fitting of relativisticaccretion disc models. Although the parameter space is rather complex,leading to a rich variety of possible outcomes, we find that on averagethe isotropic directionality reproduces our model data to the bestprecision. Our results also suggest that an improper use of limbdarkening can partly mimic asteeper profile of radialemissivity.We demonstrate these results in the case of XMM-Newton observation ofthe Seyfert galaxy MCG-6-30-15, for which we construct confidencelevels of statistics, and on thesimulated data for thefutureX-rayIXO mission. Our simulations, with thetentative IXO response,show a significant improvement that can qualitatively enhancetheaccuracy of spin determination. Key words: accretion, accretion discs - black holephysics - galaxies: active - X-rays: binaries