tokens: predictions. The luminosity of X-ray emissions ( L X ) from pulsars, sometimes mixed with their PWN, has indeed been found to strongly correlate with a pulsar’s spin-down power . In Seward Wang ( 1988 ), with Einstein data for nine pulsars, it was found that L X (0.2–4 keV) is proportional to , where the luminosity L X is contributed from both the pulsars and their nebulae. With ROSAT data of 27 pulsars, Becker Trümper ( 1997 ) reported that L X (0.1–2.4 keV) is about . This luminosity counts only the emissions from the pulsar. To reduce the contribution from surface thermal emissions, Possenti et al. ( 2002 ) considered an energy range of 2–10 keV and reported that , with a sample of 39 pulsars whose PWNe, if present, were not separated from their pulsars. Therefore, in that study, the luminosity includes a contribution from PWNe if they exist. Another relation of (2–10 keV) was reported in Mattana et al. ( 2009 ) for 14 TeV-emitting PWNe, some of which are mixed with the pulsar’s luminosity. In the works mentioned above, there seems to be an indication that the relation between the X-ray luminosity L X and the spin-down power has a larger power index when emissions from PWNe are included and a smaller one when only the emission from the pulsar is considered. Indeed, in Cheng et al. ( 2004 ), with a sample of 23 pulsars in the energy range between 2 and 10 keV, the non-pulsed luminosity was found to be , while the pulsed one was . In Li, Lu Li ( 2008 ), with 24 PWNe and 27 pulsars, it was reported that, at 2–10 keV, and , where L X, pwn is the luminosity from PWNe and L X, psr is that from pulsars. It is one of the purposes of this paper to examine these relations with a larger sample. The spectral photon indices Γ pwn and Γ psr in the power-law spectra of the non-thermal X-ray emissions from PWNe and from pulsars are another important property of the emission. With nine bright Crab-like pulsars, relations between Γ pwn and Γ psr , between Γ pwn and , and between Γ psr and were reported (Gotthelf 2003 ). These relations were, however, not confirmed in Li et al. ( 2008 ) with a larger sample of pulsars and their PWNe. None the less, Cheng et al. ( 2004 ) reported an indication of a positive correlation between Γ pwn and , and Li et al. ( 2008 ) found moderately strong positive correlations between Γ pwn and L X, pwn and between Γ pwn and . On the other hand, Γ psr was not found to correlate with luminosities or other pulsar timing properties (Cheng et al. 2004 ; Li et al. 2008 ). In this paper, we report correlations among properties of the PWN/pulsar power-law component of the X-ray emissions and of pulsar rotations, using a sample of 35 PWNe, all with detected pulsars whose X-ray emission can be separated from that of PWNe. To have a more uniform comparison basis, we consider the flux in the energy range from 0.5–8 keV for all the sources in the sample. This flux is derived from the power-law component of the corresponding best-fitting
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