Re-examining the X-ray versus spin-down luminosity correlation of rotation powered pulsars

Abstract

The empirical relation between the X-ray luminosity (in the 2-10 keV band) and the rate of spin-down energy loss L_sd of a sample of 39 pulsars is re-examined considering recent data from ASCA, RXTE, BeppoSAX, Chandra, and XMM-Newton and including statistical and systematic errors. The data show a significant scatter around an average correlation between L_x, (2-10) and L_sd. By fitting a dependence of L_x, (2-10) on the period P and period derivative dot P of the type L_x, (2-10)propto P^a dot P^b, we obtain a=-4.00 and b=+1.34 (i.e. a =~ -3b). This translates into the relation L_x, (2-10)=L_x, nor (L_sd/erg s^-1)^1.34 with a normalization L_x, nor=10^-15.3 ergs^-1 . However, the reduced chi² is large (=7.2) making the fit unacceptable on statistical ground. All the X-ray luminosities lie below a critical line L_xcrit: the corresponding efficiency of conversion of rotational energy into 2-10 keV X-rays is eta_x = (L_xcrit/L_sd)~ L_sd^0.48 and varies, within the sample, between 0.1 and 80%. The large dispersion of L_x below L_xcrit indicates that other physical parameters uncorrelated with P and dot P need to be included to account for the observed emission at X-ray energies. We indicate a few possibilities that all conspire to reduce L_x, (2-10).