Intrinsic variability and field statistics for the Vela pulsar — III. Two-component fits and detailed assessment of stochastic growth theory

The variability of the Vela pulsar (PSR B0833–45) corresponds to well-defined field statistics that vary with pulsar phase, ranging from Gaussian intensity statistics off-pulse to approximately power-law statistics in a transition region and then lognormal statistics on-pulse, excluding giant micropulses. These data are analysed here in terms of two superposed wave populations, using a new calculation for the amplitude statistics of two vectorially combined transverse fields. Detailed analyses show that the approximately power-law and lognormal distributions observed are well fitted at essentially all on-pulse phases by Gaussian–lognormal and double-lognormal combinations, respectively. The good fits found, plus the smooth but significant variations in fitting parameters across the source, provide strong evidence that the approximately power-law statistics observed in the transition region are not intrinsic. Instead, the data are consistent with the normal emission of the pulsar having lognormal statistics whenever the pulsar is detectable. This is consistent with generation in an inhomogeneous source obeying stochastic growth theory (SGT) and with the emission mechanism being purely linear (either direct or indirect), with no evidence for non-linear processes. A non-linear mechanism is viable only if it produces lognormal statistics when suitably ensemble-averaged. Variations in the SGT fit parameters with phase are consistent with the radiation being relatively more variable near the pulse edges than near the centre, consistent with earlier work. In contrast, the giant micropulses of Vela come from a very restricted phase range and have power-law statistics with indices (6.7 ± 0.6) not inconsistent with non-linear wave collapse. These results are consistent with normal pulses coming from a source and generation mechanism different from giant micropulses, as suggested previously on other grounds. Analysis of field statistics thus emphasizes the richness of pulsar physics, the apparently widespread applicability of SGT, and connections between variability and the generation mechanism.