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 \simeq - 3 b ) .
This translates into the relation L _ { x, ( 2 - 10 ) } = L _ { x,nor } \left ( { { { L } } _ { sd } / { erg s ^ { -1 } } } % \right ) ^ { 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 } ) \propto { { 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 { \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 ) } .