Theoretical modeling of Comptonized X-ray spectra of super-Eddington accretion flow: Origin of hard excess in ultraluminous X-ray sources

X-ray continuum spectra of super-Eddington accretion flow are studied by means of Monte Carlo radiative transfer simulations based on the radiation hydrodynamic simulation data, in which both thermal- and bulk-Compton scatterings are taken into account. We compare the calculated spectra of accretion flow around black holes with masses of M_BH = 10, 10², 10³, and 10⁴ M_⊙ for a fixed mass injection rate (from the computational boundary at 10³ r_s) of 10³ L_Edd/c² (with r_s, L_Edd, and c being the Schwarzschild radius, the Eddington luminosity, and the speed of light, respectively). The soft X-ray spectra exhibit mass dependence in accordance with the standard-disk relation; the maximum surface temperature is scaled as T ∝ M_{ BH}^{ -1/4}. The spectra in the hard X-ray band, by contrast with soft X-ray, look to be quite similar among different models, if we normalize the radiation luminosity by M_BH. This reflects that the hard component is created by thermal- and bulk-Compton scatterings of soft photons originating from an accretion flow in the overheated and/or funnel regions, the temperatures of which have no dependence on mass. The hard X-ray spectra can be reproduced by a Wien spectrum with the temperature of T ∼ 3 keV accompanied by a hard excess at photon energy above several keV. The excess spectrum can be fitted well with a power law with a photon index of Γ ∼ 3. This feature is in good agreement with that of the recent NuSTAR observations of ULXs (ultra-luminous X-ray sources).