Constraining the dipolar magnetic field of M82 X-2 by the accretion model

Recently, ultraluminous X-ray source (ULX) M82 X-2 has been identified to be an accreting neutron star, which has a $P=1.37$ s spin period, and is spinning up at a rate $\dot{P}=-2.0\times 10^{-10}~\rm s\,s^{-1}$. Interestingly, its isotropic X-ray luminosity $L_{\rm iso}=1.8\times 10^{40}~\rm erg\,s^{-1}$ during outbursts is 100 times the Eddington limit for a $1.4~\rm M_{\odot}$ neutron star. In this Letter, based on the standard accretion model we attempt to constrain the dipolar magnetic field of the pulsar in ULX M82 X-2. Our calculations indicate that the accretion rate at the magnetospheric radius must be super-Eddington during outbursts. To support such a super-Eddington accretion, a relatively high multipole field ($\ga 10^{13}$ G) near the surface of the accretor is invoked to produce an accreting gas column. However, our constraint shows that the surface dipolar magnetic field of the pulsar should be in the range of $1.0-3.5\times 10^{12}$ G. Therefore, our model supports that the neutron star in ULX M82 X-2 could be a low magnetic field magnetar (proposed by Tong) with a normal dipolar field ($\sim 10^{12}$ G) and relatively strong multipole field. For the large luminosity variations of this source, our scenario can also present a self-consistency interpretation.