  Ultra-luminous Compact X-ray Sources (ULXs) in nearby spiral galaxies and
Galactic superluminal jet sources share the common spectral characteristic that
they have unusually high disk temperatures which cannot be explained in the
framework of the standard optically thick accretion disk in the Schwarzschild
metric. On the other hand, the standard accretion disk around the Kerr black
hole might explain the observed high disk temperature, as the inner radius of
the Kerr disk gets smaller and the disk temperature can be consequently higher.
However, we point out that the observable Kerr disk spectra becomes
significantly harder than Schwarzschild disk spectra only when the disk is
highly inclined. This is because the emission from the innermost part of the
accretion disk is Doppler-boosted for an edge-on Kerr disk, while hardly seen
for a face-on disk. The Galactic superluminal jet sources are known to be
highly inclined systems, thus their energy spectra may be explained with the
standard Kerr disk with known black hole masses. For ULXs, on the other hand,
the standard Kerr disk model seems implausible, since it is highly unlikely
that their accretion disks are preferentially inclined, and, if edge-on Kerr
disk model is applied, the black hole mass becomes unreasonably large (> 300
M_solar). Instead, the slim disk (advection dominated optically thick disk)
model is likely to explain the observed super-Eddington luminosities, hard
energy spectra, and spectral variations of ULXs. We suggest that ULXs are
accreting black holes with a few tens of solar mass, which is not unexpected
from the standard stellar evolution scenario, and that their X-ray emission is
from the slim disk shining at super-Eddington luminosities.
