The power-law component of the X-ray emissions from pulsar-wind nebulae and their pulsars

To look for possible phenomenological connections between pulsar timing properties and emissions from pulsar-wind nebulae and their pulsars, we studied the power-law component of the X-ray emissions from 35 pulsar-wind nebulae that have a detected pulsar in X-rays. Our major results are as follows. (1) The power-law components of the X-ray luminosities, in the energy range from 0.5–8 keV, of the nebulae and of the pulsar both show a strong correlation with the pulsar spin-down power ($\dot{E}$), consistent with earlier studies. However, equally significant correlations with the magnetic field strength at the light cylinder (Blc) are also found. The similar significance level of the correlations with $\dot{E}$ and with Blc suggests that not only $\dot{E}$ but also Blc plays an important role in understanding these power-law emissions. (2) Thermal X-ray emissions are detected in 12 pulsars among the 35 samples. With derived temperature as one additional variable, we found that the photon indices of a pulsar’s non-thermal X-ray power-law spectra can be well described by a linear function of log P, $\log \dot{P}$, and temperature logarithm log T. This indicates that the surface temperature of neutron stars plays an important role in determining the energy distribution of the radiating pair plasma in pulsar magnetospheres.