X-ray spectra of young pulsars and their wind nebulae: Dependence on spin-down energy loss rate

An observational model is presented for the spectra of young rotation-powered pulsars and their nebulae based on a study of nine bright Crab-like pulsar systems observed with the Chandra X-ray observatory. A significant correlation is discovered between the X-ray spectra of these pulsars and that of their associated pulsar wind nebulae, both of which are observed to be a function of the spin-down energy loss rate, (E)over dot. The 2-10 keV spectra of these objects are well characterized by an absorbed power-law model with photon indices, C, in the range of 0.6 < Γ(PSR) < 2.1 and 1.3 < Γ(PWN) < 2.3, for the pulsars and their nebulae, respectively. A linear regression fit relating these two sets of indexes yields Gamma(PWN) = 0.91 +/- 0.18 +/- (0.66 +/- 0.11)Gamma(PSR), with a correlation coefficient of r = 0.97. The spectra of these pulsars are found to steepen as Gamma = Gamma(max) + alpha(E)over dot(-1/2), with Gamma(max) providing an observational limit on the spectral slopes of young rotation-powered pulsars. These results reveal basic properties of young pulsar systems, allow new observational constraints on models of pulsar wind emission, and provide a means of predicting the energetics of pulsars lacking detected pulsations.