Measuring black hole spin by the continuum-fitting method: effect of deviations from the Novikov-Thorne disc model

Abstract

The X‐ray spectra of accretion discs of eight stellar mass black holes have been analysed to date using the thermal continuum‐fitting method, and the spectral fits have been used to estimate the spin parameters of the black holes. However, the underlying model used in this method of estimating spin is the general relativistic thin‐disc model of Novikov & Thorne, which is only valid for razor‐thin discs. We therefore expect errors in the measured values of spin due to inadequacies in the theoretical model. We investigate this issue by computing spectra of numerically calculated models of thin accretion discs around black holes, obtained via three‐dimensional general relativistic magnetohydrodynamic (GRMHD) simulations. We apply the continuum‐fitting method to these computed spectra to estimate the black hole spins and check how closely the values match the actual spin used in the GRMHD simulations. We find that the error in the dimensionless spin parameter is up to about 0.2 for a non‐spinning black hole, depending on the inclination. For black holes with spins of 0.7, 0.9 and 0.98, the errors are up to about 0.1, 0.03 and 0.01, respectively. These errors are comparable to or smaller than those arising from current levels of observational uncertainty. Furthermore, we estimate that the GRMHD simulated discs from which these error estimates are obtained correspond to effective disc luminosities of about 0.4–0.7 Eddington, and that the errors will be smaller for discs with luminosities of 0.3 Eddington or less, which are used in the continuum‐fitting method. We thus conclude that use of the Novikov–Thorne thin‐disc model does not presently limit the accuracy of the continuum‐fitting method of measuring black hole spin.

heroic: 3D general relativistic radiative post-processor with comptonization for black hole accretion discs

“…The latter has no viscous heating inside the ISCO, whereas the former does (the heating rates outside the ISCO are also modestly different because of non-zero stress at the ISCO). The GRMHD model thus predicts a larger luminosity than the equivalent Novikov & Thorne (1973) model (see Penna et al 2010;Kulkarni et al 2011;Noble et al 2011;Zhu et al 2012). However, the shape of the spectrum is very similar, suggesting that efforts to measure BH spin by fitting the continuum spectrum of the disc are likely to be reasonably accurate (McClintock et al 2014).…”

“…Typically, geodesic paths are traced backwards from a distant observation plane until they hit the accretion flow (see, e.g., Rauch & Blandford 1994;Broderick & Blandford 2003;Dovčiak et al 2004;Dexter & Agol 2009;Kulkarni et al 2011;Psaltis & Johannsen 2012;Zhu et al 2012). This yields a transfer function that allows one to map the local Comptonized disc emission to the spectrum as measured by the distant observer.…”

Black Hole Spin: Theory and Observation

“…The combination of these two effects leads to the emission peaking at smaller radii than Novikov-Thorne discs giving both a higher peak temperature and larger emitted flux (and which extends to outside of the plunging region: Zhu et al 2012). By fitting the simulated spectra with KERRBB (Kulkarni et al 2011) and BHSPEC (Zhu et al 2012), the spin is found to be systematically overestimated as a result of the increased disc brightness. Crucially, the typical error resulting from use of the Novikov-Thorne profile is far less than the errors associated with the system parameters of mass, inclination and distance (see Gou et al 2009;Steiner et al 2010); the spin values derived from GRAD based models are therefore reliable where the errors on the system parameters dominate.…”

“…Dexter & Quateart (2012) quantify the likely effect, finding that the impact depends on the model used to account for the hard tail accompanying the disc emission . In practice, they determine that the errors can be far larger than those resulting from deviation from the Novikov-Thorne prescription resulting from a finite disc thickness (Kulkarni et al 2011) except in the most disc dominated states (with a disc fraction 0.95 or σ T 0.15).…”

A tilted and warped inner accretion disc around a spinning black hole: an analytical solution

“…This means we do not make any specific assumption about this boundary condition. For example, we do not assume a zero torque at R = Rin, which, although often used (but not always; see, for example, Balbus 2012;Penna et al 2012;Kulkarni et al 2011;Zhu et al 2012), is an ad hoc assumption (e.g., McClintock et al 2014). Moreover, a zero torque at R = Rin is unlikely because of the frame-dragging effect.…”