Spectral Hardening in Black Hole Accretion: Giving Spectral Modelers an f

By fitting synthetic spectral models computed via the TLUSTY code, we examine how the spectra from thin accretion disks are expected to vary in accreting black hole systems. We fit color-corrected blackbody models to our synthetic spectra to estimate the spectral hardening factor f, which parameterizes the departure from blackbody and is commonly used to help interpret multitemperature blackbody fitting results. We find we can define a reasonably robust f value to spectra when the effects of Compton scattering dominate radiation transfer. We examine the evolution of f with black hole mass and accretion rate, typically finding a moderate variation (f ~ 1.4-2) for accretion rates between 1% and 100% of the Eddington rate. Consistent with most previous work, we find f tends to increase with accretion rate, but we also infer a weaker correlation of f with black holes mass. We find that f is rarely much larger than 2 unless the disk becomes photon starved, in contention with some previous calculations. Significant spectral hardening (f > 2) is only found when the disk mass surface density is lower than expected for alpha-disk models unless alpha is near unity or larger.