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We present a statistical study of the non-thermal X-ray emission of 29 young rotation powered pulsars (RPPs) and 22 pulsar wind nebulae (PWNe) by using Chandra and XMM-Newton observations, which with the high spatial resolutions enable us to spatially resolve pulsars from their surrounding PWNe. We obtain the X-ray luminosities and spectra separately for RPPs and PWNe, and then we investigate their distribution and relation to each other and also relations with other rotational parameters. In the pair-correlation analysis we find that: (1) the nonthermal pulsar X-ray luminosity Lx,psr is strongly correlated with the pulsar period P, period derivative ˙ P, characteristic age τ, and spin-down power ˙E, Lx,psr = 10−3.7E ˙ 1.0±0.1; (2) the pulsar photon spectral index Γpsr is negatively correlated with ˙ P and ˙ E but positively correlated with τ; (3) the PWN X-ray luminosity Lx,pwn shows weak correlation with ˙ P and strong correlation with τ and ˙ E, Lx,pwn = 10−19.0E ˙ 1.4±0.2; (4) the PWN photon spectral index Γpwn is positively correlated with Lx,pwn and Lx,pwn / ˙ E. The statistic study of PWN spectral properties supports the particle wind model in which the X-ray emitting electrons are accelerated by the termination shock of the wind.
Li et al. (2008) studied this question.