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 \sim 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 .