Observational connection of non-thermal X-ray emission from pulsars with their timing properties and thermal emission

The origin and radiation mechanisms of high energy emissions from pulsars have remained mysterious since their discovery. Here we report, based on a sample of 68 pulsars, observational connection of non-thermal X-ray emissions from pulsars with their timing properties and thermal emissions, which may provide some constraints on theoretical modeling. Besides strong correlations with the spin-down power $\dot{E}$ and the magnetic field strength at the light cylinder $B_{\rm lc}$, the non-thermal X-ray luminosity in 0.5 - 8 keV, $L_{\rm p}$, represented by the power-law component in the spectral model, is found to be strongly correlated with the highest possible electric field strength in the polar gap, $E_{\rm pc}$, of the pulsar. The spectral power index $\Gamma_{\rm p}$ of that power-law component is also found, for the first time in the literature, to strongly correlate with $\dot{E}$, $B_{\rm lc}$ and $E_{\rm pc}$, thanks to the large sample. In addition, we found that $L_{\rm p}$ can be well described by $L_{\rm p}\propto T^{5.96\pm 0.64}R^{2.24\pm 0.18}$, where $T$ and $R$ are the surface temperature and the emitting-region radius of the surface thermal emission, represented by the black-body component in the spectral model. $\Gamma_{\rm p}$, on the other hand, can be well described only when timing variables are included, and the relation is $\Gamma_{\rm p} = \log(T^{-5.8\pm 1.93}R^{-2.29\pm 0.85}P^{-1.19\pm 0.88}\dot{P}^{0.94\pm 0.44})$ plus a constant. These relations strongly suggest the existence of connections between surface thermal emission and electron-positron pair production in pulsar magnetospheres.