The nature of ultra-luminous X-ray sources (ULXs) has long been plagued by an ambiguity about whether the central compact objects are intermediate-mass (IMBH, >~ 10^3 M_sun) or stellar-mass (a few tens M_sun) black holes (BHs). The high luminosity (~ 10^39 erg/s) and super-soft spectrum (T ~ 0.1 keV) during the high state of the ULX source X-1 in the galaxy M101 suggest a large emission radius (>~ 10^9 cm), consistent with being an IMBH accreting at a sub-Eddington rate. However, recent kinematic measurement of the binary orbit of this source and identification of the secondary as a Wolf-Rayet star suggest a stellar-mass BH primary with a super-Eddington accretion. If that is the case, a hot, optically thick outflow from the BH can account for the large emission radius and the soft spectrum. By considering the interplay of photons absorption and scattering opacities, we determine the radius and mass density of the emission region of the outflow and constrain the outflow mass loss rate. The analysis presented here can be potentially applied to other ULXs with thermally dominated spectra, and to other super-Eddington accreting sources.
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