  We have analyzed the archival XMM-Newton data of the bright Ultra-Luminous
X-ray Source (ULX) M82 X-1 with an 105 ksec exposure when the source was in the
steady state. Thanks to the high photon statistics from the large effective
area and long exposure, we were able to discriminate different X-ray continuum
spectral models. Neither the standard accretion disk model (where the radial
dependency of the disk effective temperature is T(r) \propto r^-3/4) nor a
power-law model gives a satisfactory fit. In fact, observed curvature of the
M82 X-1 spectrum was just between those of the two models. When the exponent of
the radial dependence (p in T(r) \propto r^-p) of the disk temperature is
allowed to be free, we obtained p =0.61^+0.03_-0.02. Such a reduction of p from
the standard value 3/4 under extremely high mass accretion rates is predicted
from the accretion disk theory as a consequence of the radial energy advection.
Thus, the accretion disk in M82 X-1 is considered to be in the Slim disk state,
where an optically thick Advection Dominant Accretion Flow (ADAF) is taking
place. We have applied a theoretical slim disk spectral model to M82 X-1, and
estimated the black hole mass ~ 19-32 M_odot. We propose that M82 X-1 is a
relatively massive stellar black hole which has been produced through evolution
of an extremely massive star, shining at a super-Eddington luminosity by
several times the Eddington limit.
