The above-discussed Galactic black-holes in XBs have the masses around 10M0. Recently, there has been increasing attention to a possible presence of more massive black holes in external galaxies (e.g., [11,16, 36]). They are ultraluminous X-ray sources (ULXs) with Lx in the range 1039- >1040 erg s-1, located off-center of the galaxies (hence not AGN). Liu and Mirabel  published a catalogue of 229 ULXs. The observed spectra are either the MCD-type or of a power-law shape. Their luminosities are at least comparable to or well exceed the Eddington limit of a — 10M0 black hole. The detected time variabilities argue that they are compact objects. This has led to the concept that ULXs are accreting black holes significantly more massive than 10M0, ranging to as high as 100M0 [17,36]. On the other hand, an alternative possibility has been considered that they are ordinary black-hole XBs radiating anisotropically . In our Galaxy, no black-hole XB has been found to remain persistently super-Eddington, although a few of them temporarily exceeded the Eddington limit around the peak luminosity (see 126.96.36.199).
The slim disk concept allows for super-Eddington luminosities when M > LEdd/c2. Numerical simulations show that the luminosity may go up to several times LEdd [56,57]. Watarai et al.  analyzed the ULXs having the MCD-type spectra with the slim disk model, and found that they are mostly consistent with —10M0 black holes at extremely high accretion rates (M > LEdd/c2). Another effect at M > LEdd/c2 is that the radiation is expected to become anisotropic, i.e., stronger towards the disk axis . Hence, if viewed at a small inclination angle, the luminosity assuming isotropy may be a considerable overestimate.
Even though most of ULXs may be explained as —10 M0 black holes at very high accretion rates, the existence of intermediate-mass black holes exceeding several tens M0 is by no means excluded at present. For an example, a variable offcenter source in M 82  can be a strong candidate for an intermediate-mass black hole. It brightened to Lx — 1041 erg s-1 corresponding to the Eddington limit for an object of several hundred M0. If a class of intermediate-mass black holes were confirmed by future observations, the origin of them should be a challenging problem since such massive black holes could not be produced by supernovae.
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