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

To look for possible phenomenological connections between pulsar's 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 which have a detected pulsar in X-rays. Our major results are in the following: (1) The power-law component of the X-ray luminosities, in the energy range from 0.5 keV to 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 ($B_{\rm lc}$) are also found. The similar significance level of the correlations with $\dot{E}$ and with $B_{\rm lc}$ suggests that not only $\dot{E}$ but also $B_{\rm lc}$ 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 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 $\log T$. It indicates that the surface temperature of neutron stars plays an important role in determining the energy distribution of the radiating pair plasma in pulsar's magnetospheres.