Angular Momentum Transport in Accretion Disks and its Implications for Spin Estimates in Black Hole Binaries

Abstract

The accretion flow in the disk dominated state of black hole binaries has peak temperature and luminosity which vary together in such a way as to indicate an approximately constant emitting area. The association of this with the last stable orbit gives one of the few ways to estimate spin when the mass of the black hole is known. However, deriving this radius requires knowledge of how the disk spectrum is modified by radiative transfer through the vertical structure of the disk, as well as special and general relativistic effects on the propagation of this radiation. Here we investigate the extent to which differences in vertical structure change the derived disk spectra by calculating these for a range of different stress prescriptions. We find that at a given mass accretion rate the spectra are almost identical for accretion rates of L/L_Edd <~ 0.1. The spectra are remarkably similar even up to the highest luminosities considered (L/L_Edd ~ 0.6) as long as the stresses do not dissipate more than about 10 per cent of the gravitational energy above the effective photosphere. This is exceeded only by classic alpha disks with alpha >~ 0.1, but these models give spectral variation which is incompatible with existing data. Therefore, we conclude that disk spectral modelling can place interesting constraints on angular momentum transport, but still provide a robust estimate of the spin of the black hole.