Research on the Magnetic Field of NGC 7793 P13 and Other Confirmed Pulsating Ultraluminous X-Ray Sources

A pulsating ultraluminous X-ray source (PULX) is a new kind of pulsar (PSR) whose characteristics are different from all known neutron stars. The magnetic field of PULX is suspected to be the main reason to support its supper Eddington luminosity of PULX. NGC 7793 P13, which is the second confirmed PULX, can be easily studied due to its nearby position and isolation from other sources in its host galaxy. In this paper, we calculate its magnetic field to be ~1.0 × 10¹² G based on the continued observations from 2016 to 2020. The magnetic field evolution of NGC 7793 P13 is analyzed, which shows that the source has spent about 10⁴ yr for the field decaying from the simulated initial strength 4.0 × 10¹⁴ G to the present value. In case of an assumed constant accretion and the limitation of the companion mass, it will be a recycled PSR whose magnetic field is ~10⁹ G and spin period is a few hundred milliseconds. We estimate the field strength of the other confirmed PULXs and find main range is 10¹³-10¹⁴ G. Their positions of the magnetic field and spin period are around or below the magnetars. This is because these PULXs are in the binary systems and are with the spin-up rate that are 2-3 orders higher than the normal binary pulsars. We suggest that PULXs are the accreting magnetars whose multi-pole strong magnetic field can support the supper Eddington luminosity. They would be helpful for studying the evolution of the magnetars, the formation of the binary PSRs above the Eddington spin-up line, and the millisecond PSRs with the magnetic field stronger than ~10⁹ G.