The Magnetic Field Evolution of ULX NuSTAR J095551+6940.8 in M82--A
  Legacy of Accreting Magnetar
  Ultra-luminous X-ray sources are usually believed to be black holes with mass
about $10^{2-3}M_{\odot}$. However, the recent discovery of NuSTAR
J095551+6940.8 in M82 by Bachetti et al. shows that it holds the spin period
$P=1.37\rm\,s$ and period {\bf derivative}
$\dot{P}\approx-2\times10^{-10}\rm\,s\,s^{-1}$, which provides a strong
evidence that some ultra-luminous X-ray sources could be neutron stars. We
obtain that the source may be an evolved magetar, according to our simulation
by employing the model of accretion induced the polar magnetic field decay and
standard spin-up torque of an accreting neutron star. The results show that
NuSTAR J095551+6940.8 is still in the spin-up process, and the polar magnetic
field decays to about $4.5\times10^{12}\rm\,G$ after accreting $\sim
10^{-2.5}$\ms, while the strong magnetic field exists in the out-polar region,
which could be responsible for the observed low field magnetar. The ultra
luminosity of the source can be explained by the beaming effort and two kinds
of accretion--radial random accretion and disk accretion. Since the birth rate
of magnetars is about ten percent of the normal neutron stars, we guess that
several ultra-luminous X-ray sources should share the similar properties to
that of NuSTAR J095551+6940.8.
