Detailed Atmosphere Model Fits to Disk-Dominated ULX Spectra
  We have chosen 6 Ultra-Luminous X-ray sources from the {\it XMM-Newton} archive whose spectra have high signal-to-noise and can be fitted solely with a disk model without requiring any power-law component. To estimate systematic errors in the inferred parameters, we fit every spectrum to two different disk models, one based on local blackbody emission (KERRBB) and one based on detailed atmosphere modelling (BHSPEC). Both incorporate full general relativistic treatment of the disk surface brightness profile, photon Doppler shifts, and photon trajectories. We found in every case that they give almost identical fits and similar acceptable parameters. The best-fit value of the most interesting parameter, the mass of the central object, is between 23 and 73 M$_\sun$ in 5 of the 6 examples. In every case, the best-fit inclination angle and mass are correlated, in the sense that large mass corresponds to high inclination. Even after allowing for this degeneracy, we find that, with $\gtrsim 99.9%$ formal statistical confidence, 3 of the 6 objects have mass $\gtrsim 25 M_\sun$; for the other 3, these data are consistent with a wide range of masses. A mass greater than several hundred $M_\sun$ is unlikely for the 3 best-constrained objects. These fits also suggest comparatively rapid black hole spin in the 3 objects whose masses are relatively well-determined, but our estimate of the spin is subject to significant systematic error having to do with uncertainty in the underlying surface brightness profile. 
Y. Hui and Julian H. Krolik