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

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 Lx;(2-10) and L-sd. By fitting a dependence of Lx;(2-10) on the period P and period derivative (P) over dot of the type Lx;(2-10) proportional to P-a (P) over dot(b), we obtain a = 4.00 and b = +1.34 (i.e. a similar or equal to 3b). This translates into the relation Lx;(2-10) = L-x;nor (L-sd/erg s(-1))(1.34) with a normalization L-x;nor = 10(-15.3) erg s(-1). However, the reduced chi(2) is large (=7.2) making the fit unacceptable on statistical ground. All the X-ray luminosities lie below a critical line L-x;crit: the corresponding efficiency of conversion of rotational energy into 2-10 keV X-rays is eta(x) = (L-x;crit/L-sd) proportional to L-sd(0.48) and varies, within the sample, between 0.1 and 80%. The large dispersion of L-x below L-x;crit indicates that other physical parameters uncorrelated with P and (P) over dot need to be included to account for the observed emission at X-ray energies. We indicate a few possibilities that all conspire to reduce Lx;(2-10)