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

Abstract

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 χ 2 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.

Broad iron line in the fast spinning neutron-star system 4U 1636−53

“…2 and 5, where one of the models significantly deviated from the other two (see Table 6). It is interesting to mention that kyrline with a * =1 and laor, that are based on the same Kerr metric showed in general significantly different values for the Fe line parameters (see Svoboda et al 2009, for a detail comparison between the models). Very similar to that, also for kyrline with a * =0 and diskline we noticed discrepancies in the modelling of the line profile, although less significant.…”

Black Hole Spin: Theory and Observation

“…The grids in the KERRBB model allow for a range of spin, inclination and BH mass whilst assuming a standard disc structure with constant f col (= 1.7, although this value can be changed in the model) and allows for limb-darkening (e.g. Svoboda et al 2009). …”

Relativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit

“…A commonly accepted slope for the radial emissivity is q = 3 [31]. Following Svoboda et al [29], for the angular emissivity we consider two possible choices: the linear limb darkening and the limb brightening laws, expressed in Eqs. (2.3).…”

“…(2.3) with linear limb darkening or limb brightening alternatives. The first one is the classical linear approximation for the limb darkening and is widely used in literature [6,9,36], while the second one was proposed by Haardt [28] in order to model external sources of X-ray photons [29] reflected by the disk. Of course, the right choice of emissivity law depends on the specific origin of the X-ray sources.…”