Slim-disk model for ultraluminous X-ray sources

The ultraluminous X-ray sources (ULXs) are unique in exhibiting moderately bright X-ray luminosities, L-x similar to 10(38)-10(40) ergs s(-1), and relatively high blackbody temperatures, T(in)similar to1.0-2.0 keV. From the constraint that L-x cannot exceed the Eddington luminosity, L-E, we require relatively high black hole masses, M similar to 10-100 M-. however, for such large masses the standard disk theory predicts lower blackbody temperatures, T-in <1.0 keV. To understand a cause of this puzzling fact, we carefully calculate the accretion flow structure shining at <similar to>L-E, 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 ((M) over dot greater than or similar to 30L(E)/c(2)) an apparently compact region with a size of R-in similar or equal to (1-3)r(g) (with r(g) being the Schwarzschild radius) is shining with a blackbody temperature of T-in similar or equal to 1.8(M/10 M-.)(-1/4) keV even for the case of a nonrotating black hole. Furthermore, R-in decreases as increases, in (M) over dot 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 L-x and T-in both on the logarithm 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 similar to 10-30 M-., and high accretion rates, (M) over dot greater than or similar to 10L(E)/c(2). Interestingly, IC 342 source 1, in particular, was observed to move along the constant M line (not constant R-in line) in our simulations. This provides firm evidence that at least some ULXs are shining at greater than or similar toL(E) and contain black holes with M similar or equal to 10-100 M-..