Slim disk or medium-sized black hole?
Two interpretations arise. The first is to assume the low-temperature accretion disk constituent as expected and the power function spectrum constituent that explains the remaining high-energy side (at left in Fig.2). Even in star-sized black holes, there is a power function spectrum constituent that is athermal and present in the high-energy side away from the accretion disk constituent. This is to apply the two-constituent model. According to this interpretation, the black hole’s mass that can be estimated by the low-temperature accretion disk spectrum is hundreds to thousands of times the solar mass. The other interpretation is that, since the mass-accretion ratio rises so high in the ULX that the standard accretion-disk model collapses (right in Fig. 2), the disks transform to a different physical state called the “slim disk.” In fact, the slim-disk model is theoretically predicted. When the disk’s brightness approaches the Eddington limit, gravity energy is not thermalized locally and is transported to the inside by advection. The calculation of energy spectrum anticipated from slim disks is complex. According to the recent studies, however, it seems that temperature becomes considerably higher than that of standard accretion disks, which is consistent with ULX observation results. Further, since the slim disks are literally not too thin and not too thick, which allows them to escape from the assumption of spherical symmetry, they can emit up to 10 times the Eddington limit.
As described in Fig. 2, both models can fit the observed spectrum. I am not convinced of the former model, however, for the following reasons.
(1) With star-sized black holes, temporal variation of the power-function constituent in the high-energy side fluctuates greatly. Meanwhile, with ULX, the fraction of the low-temperature disk constituent and the power-function constituent is almost always constant. This is unnatural. Is this because the form of the slim disks is forced to fit the phenomenological two-constituent model?
(2) With star-sized black holes, there is strong evidence that the radius of the inner boundary of the disks is constant even though the disks’ brightness and temperature vary largely, which links the radius of the accretion disks with the Schwarzschild radius (Fig. 1). No such evidence is found with ULX.
I am in favor of the latter model and, in cooperation with accretion-disk theorists, I am now trying to discover the parameters of black holes by applying the slim disks’ spectrum to ULX. In our model, the mass of black holes in ULX is around 30 times the solar mass, i.e., a very heavy star-sized black hole. Accretion disks are transformed to slim disks, shining at several times the Eddington luminosity. This can explain the observed brightness of around 1040 erg/sec without problems. “Medium-sized black holes” with mass of hundreds to thousands of times the solar mass are not required in our model.
I think that, with further advance of observation and theory, our model will be proved to be correct in the near future, ending discussion on real identity of ULX. Alternatively, our model may be wrong and evidence indicating the existence of medium-sized black holes may be discovered. In that case, we will have to apologize. But if such black holes actually exist in the universe, it is very exciting and interesting. The universe seldom reveals its real figure, so I sometimes feel tantalized. For the time being, however, we can enjoy the problem-solving game on the ULX.