4 Correlation of flux in the two peaks

Patt et al. (1999) report that the X-ray flux in the two peaks of the integrated profile of Fig. 1 are uncorrelated. Their integrated profile consists of 16 samples, in which the two peaks are defined as covering phases 1 to 4 plus 15 and 16, and phases 5 to 11, respectively, (Fig. 1 of Patt et al. 1999). They obtain the covariance between the number of photons in these two peaks to be $-7.7 \times 10^{-4}$, which they claim is consistent with zero. In this work the dotted curves of Fig. 1 are the models for the two peaks. The X-ray flux in each period was multiplied by the two curves, to obtain the flux in the two peaks, respectively. A normalized correlation coefficient (in contrast to the covariance of Patt et al. 1999) was computed for these two fluxes, across all 1868112 periods; the result is 3.5 ($\pm$10.0 $) \times 10^{-4}$, which is consistent with zero. Therefore it is concluded that the X-ray fluxes of Crab pulsar in the two peaks of its integrated profile are indeed uncorrelated.