2023MNRAS.520.4068C

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_lc, the non-thermal X-ray luminosity in 0.5-8 keV, L_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_pc, of the pulsar. The spectral power index Γ_p of that power-law component is also found, for the first time in the literature, to strongly correlate with $\dot{E}$, B_lc, and E_pc, thanks to the large sample. In addition, we found that L_p can be well described by L_p ∝ T^5.96 ± 0.64^R2.24 ± 0.18^, where T and R are the surface temperature and the emitting-region radius of the surface thermal emission, represented by the blackbody component in the spectral model. Γ_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.