Abstract
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.
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