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X-ray continuum spectra of super-Eddington accretion flow are studied bymeans of Monte Carlo radiative transfer simulations based on the radiationhydrodynamic simulation data, in which both of thermal and bulk Comptonscatterings are taken into account. We compare the calculated spectra ofaccretion flow around black holes with masses of $M_{\rm BH} = 10, 10^2, 10^3$,and $10^4 M_\odot$ for a fixed mass injection rate (from the computationalboundary at $10^3 r_{\rm s}$) of $10^3 L_{\rm Edd}/c^2$ (with $r_{\rm s}$,$L_{\rm Edd}$, and $c$ being the Schwarzschild radius, the Eddingtonluminosity, and the speed of light, respectively). The soft X-ray spectraexhibit mass dependence in accordance with the standard-disk relation; themaximum surface temperature is scaled as $T \propto M_{\rm BH}^{-1/4}$. Thespectra in the hard X-ray bands, by contrast, look quite similar amongdifferent models, if we normalize the radiation luminosity by $M_{\rm BH}$.This reflects that the hard component is created by thermal and bulk Comptonscattering of soft photons originating from an accretion flow in theover-heated and/or funnel regions, the temperatures of which have no massdependence. The hard X-ray spectra can be reproduced by a Wien spectrum withtemperature of $T\sim 3$ keV accompanied by a hard excess at photon energyabove several keV. The excess spectrum can be well fitted with a power law witha photon index of $\Gamma \sim 3$. This feature is in good agreement with thatof the recent NuSTAR observations of ULX (Ultra-Luminous X-ray sources).

Theoretical modeling of Comptonized X-ray spectra of super-Eddington accretion flow: origin of hard excess in Ultraluminous X-Ray Sources