Investigation of the timing and spectral properties of an Ultra-luminous X-ray pulsar NGC 7793 P13.

We perform both timing and spectral analyses using the archival X-ray data taken with Swift, XMM-Newton, NICER, and NuSTAR from 2016 to 2020 to study an ultra-luminous pulsar, NGC 7793 P13, that showed a long period of super-Eddington accretion. We use the Rayleigh test to investigate the pulsation at different epochs, and confirm the variation of the pulse profile with the finite Gaussian mixture modelling and two-sample Kuiper test. Taking into account the periodic variation of the spin periods caused by the orbital Doppler effect, we further determine an orbital period of ~65 d and show that no significant correlation can be detected between the orbital phase and the pulsed fraction. The pulsed spectrum of NGC7793 P13 in 0.5-20keV can be simply described using a power-law with a high energy exponential cutoff, while the broad-band phase-averaged spectrum of the same energy range requires two additional components to account for the contribution of a thermal accretion disk and the Comptonization photons scattered into the hard X-rays. We find that NGC 7793 P13 stayed in the hard ultra-luminous state and the pulsed spectrum was relatively soft when the source was faint in the end of 2019. Moreover, an absorption feature close to 1.3 keV is marginally detected from the pulsed spectra and it is possibly associated with a cyclotron resonant scattering feature.