Massive Pulsars and Ultraluminous X-ray Sources

The detection of 1.37$\,$s pulsations from NuSTAR J095551+6940.8 implies the existence of an accreting pulsar, which challenges the conventional understanding of ultraluminous X-ray source. This kind of sources are proposed to be massive pulsars in this paper. Considering the general relativistic effect, stronger gravity of massive pulsars could lead to a larger maximum luminosity, scaled as the Eddington luminosity. The pseudo-Newtonian potential is employed to simulate the gravitational field in general relativity, and the Eddington luminosity is calculated for self-bound stars (quark star and quark-cluster star) and for the Tolman IV solution. It is found that, for a massive pulsar with radius close to the Schwarszchild radius, the Eddington luminosity could be as high as $2\times10^{39} \, {\rm erg\, s}^{-1}$. It is able to account for the X-ray luminosity of NuSTAR J095551+6940.8 with reasonable beaming factor. It is also suggested that massive pulsar-like compact stars could form via this super-Eddington phase of ultraluminous X-ray source.