On the Spectral Hardening Factor of the X-Ray Emission from Accretion Disks in Black Hole Candidates

Radiation spectrum and the spectral hardening factor of an accretion disk around a Schwarzschild black hole with a mass of 1.4, 3, and 10 solar mass are determined by solving the vertical structure and radiative transfer self-consistently. When a viscous parameter alpha is approximately 0.1, for accretion rates close to Eddington limit, the local spectrum can be described by the diluted blackbody spectrum with the spectral hardening factor f approximately 1.8 - 2.0 which is almost independent of a radial position and black hole mass. For approximately 10% of the Eddington rate, the local spectrum emitted from an inner region can be approximated by the diluted blackbody with f approximately 1.7. For accretion rates lower than 1% of the Eddington limit, the local spectrum cannot be fitted with any f. For accretion rates close to the Eddington limit, f increases with an increase of alpha in an inner region for alpha is greater than 0.1, and the radial dependence of f also becomes large gradually. We have applied our results to the observations of LMC X-3, and have estimated the mass of the black hole in LMC X-3 as greater than or equal to 7 solar mass.