Measuring Black Hole Masses from X-ray Observations of Accretion Disk Spectra

We present a new approach to the theory of the atmosphere in which the Thomson scattering plays the dominating role. This situation includes, in particular, inner parts of accretion disks around black holes. Energy spectra from the accretion disks are calculated and applied for the LMC X-3 data taken with the GINGA satellite. Approximation of the electron scattering dominance is justified whenever the local luminosity of the disk is close to the local Eddington limit. In accordance with the standard theory of accretion, l equiv L/L_Edd ~ 1 holds in the zone responsible for the bulk of X-ray emission. We carried out self-consistent numerical calculations for the atmosphere with Thomson scattering and photoelectric absorption. Analytical theory also reproduced the numerical results fairly well. We found that the color temperature of the emerging spectrum, T_col, turns out to be essentially larger than the effective temperature, T_eff. The ratio of T_eff/T_col is found to be a strong function of l = 0.94 (1 - [He]/2), [He] being the He abundance, with a weak dependence on the radial coordinate. We calculated emergent spectra from accretion disks by radially integrating the local spectra. As an application, model fitting was carried out to LMC X-3 data by making only the mass, M, and the accretion rate, dot M, free parameters. In spite of the large intensity variations, the M is fairly constant and spectral variation is explained by change of dot M alone. The constant value of M is consistent with the fiducial mass obtained from observations of the binary motion, supporting the validity of our accretion disk model. () NAS/NRC Senior Research Associate