Long-term evolution of the X-ray flux of the Crab pulsar

Purpose In order to carry out in-orbit calibration, the hard X-ray modulation telescope satellite (HXMT) has made a number of observations of Crab pulsar. We study the long-term evolution of the X-ray flux of the Crab pulsar with these observational data.
Methods We use nearly four years Crab pulsar’s data obtained by HXMT and the neutron star interior composition of explorer to test whether L_\textrmx \propto L_\textrmsd^\alpha holds for an individual pulsar, where L_\textrmx is the pulsed X-ray luminosity and L_\textrmsd is its spin-down luminosity. We also combine the earlier results obtained with PCA and HEXTE data (Yan et al. in ApJ 865:21, 2018) to get the long-term evolution characteristics of the Crab pulsar.
Results We find the X-ray flux evolution can be fitted by a linear correlation: L_\textrmx \propto L_\textrmsd^1.42\pm 0.18 . In soft X-ray energy band (1–10 keV) and hard X-ray energy band (27–250 keV), \alpha does not change significantly with either energy or phase. However, this will need to be confirmed in future. For example, the interpulse component of hard X-ray may follow L_\textrmx\propto L_\textrmsd^0.96\pm 0.34 , which may be different from the correlation of soft X-rays and main pulse component. On the other hand, the hard X-ray flux evolution shows that the performance of high energy X-ray telescope (HE) onboard HXMT, such as effective area, is stable.
Conclusion We conclude that the X-ray luminosity of the Crab pulsar closely correlates with its spin-down luminosity. However, the emission mechanism responsible for these phenomena remains not fully understood.