A mass of less than 15 solar masses for the black hole in an ultraluminous X-ray source

Most ultraluminous X-ray sources (ULXs) display a typical set of properties not seen in Galactic stellar-mass black holes (BHs): higher luminosity Lx > 3 10^39 erg/s, unusually soft X-ray components (kT < 0.3 keV) and a characteristic downturn in their spectra above ~ 5 keV. Such puzzling properties have been interpreted either as evidence of intermediate-mass BHs, or as emission from stellar-mass BHs accreting above their Eddington limit, analogous to some Galactic BHs at peak luminosity. Recently, a very soft X-ray spectrum has been observed in a rare and transient stellar-mass BH. Here we show that the X-ray source P13 in the galaxy NGC\,7793 is in a ~ 64 day period binary and exhibits all three canonical properties of ULXs. By modelling the strong optical and UV modulations due to X-ray heating of the B9Ia donor star, we constrain the BH mass to less than 15 solar masses. Our results demonstrate that in P13, soft thermal emission and spectral curvature are indeed signatures of supercritical accretion. By analogy, ULXs with similar X-ray spectra and luminosities of up to a few 10^40 erg/s can be explained by supercritical accretion onto massive stellar BHs.