  The X-ray spectra of accretion discs of eight stellar-mass black holes have
been analyzed 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.
