We propose a methodology to derive a black-hole mass for super-critical accretion flow .
Here , we use the extended disk blackbody ( extended DBB ) model , a fitting model in which the effective temperature profile obeys the relation T _ { eff } \propto r ^ { - p } , with r being the disk radius and p being treated as a fitting parameter .
We first numerically calculate the theoretical flow structure and its spectra for a given black-hole mass , M , and accretion rate , \dot { M } .
Through fitting to the theoretical spectra by the extended DBB model , we can estimate the black-hole mass , M _ { x } , assuming that the innermost disk radius is r _ { in } = 3 r _ { g } ( \propto M _ { x } ) , where r _ { g } is the Schwarzschild radius .
We find , however , that the estimated mass deviates from that adopted in the spectral calculations , M , even for low- \dot { M } cases .
We also find that the deviations can be eliminated by introducing a new correction for the innermost radius .
Using this correction , we calculate mass correction factors , M / M _ { x } , in the super-critical regimes for some sets of M and \dot { M } , finding that a mass correction factor ranges between M / M _ { x } \sim 1.2 – 1.6 .
The higher is \dot { M } , the larger does the mass correction factor tend to be .
Since the correction is relatively small , we can safely conclude that the black holes in ULXs which Vierdayanti et al .
( 2006 , PASJ , 58 , 915 ) analyzed are stellar-mass black holes with the mass being < 100 M _ { \odot } .