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Slim-Disk Model for Ultraluminous X-Ray Sources

The ultraluminous X-ray sources (ULXs) are unique in exhibiting moderately bright X-ray luminosities, LX ~ 1038-1040 ergs s-1, and relatively high blackbody temperatures, Tin ~ 1.0-2.0 keV. From the constraint that LX cannot exceed the Eddington luminosity LE, we require relatively high black hole masses, M ~ 10-100 M☉; however, for such large masses the standard disk theory predicts lower blackbody temperatures, Tin < 1.0 keV. To understand a cause of this puzzling fact, we carefully calculate the accretion flow structure shining at ~LE, fully taking into account the advective energy transport in the optically thick regime and the transonic nature of the flow. Our calculations show that at high accretion rate ( ≳ 30LE/c2) an apparently compact region with a size of Rin ≃ (1-3)rg (with rg being the Schwarzschild radius) is shining with a blackbody temperature of Tin ≃ 1.8(M/10 M☉)-1/4 keV even for the case of a nonrotating black hole. Furthermore, Rin decreases as increases, contrary to the canonical belief that the inner edge of the disk is fixed at the radius of the marginally stable last circular orbit. Accordingly, the loci of a constant black hole mass on the H-R diagram (representing the relation between LX and Tin both on the logarithmic scales) are not straight but bent toward the lower M-direction in the frame of the standard disk relation. We also plot the ASCA data of some ULXs on the same H-R diagram, finding that they all fall on the regions with relatively high masses, M ~ 10-30 M☉, and high accretion rates, ≳ 10LE/c2. Interestingly, IC 342 source 1, in particular, was observed to move along the constant M line (not constant Rin line) in our simulations. This provides firm evidence that at least some ULXs are shining at ≳LE and contain black holes with M ≃ 10-100 M☉.