Intrinsic variability and field statistics for the Vela pulsar - II. Systematics and single-component fits

Individual pulses from pulsars have intensity-phase profiles that differ widely from pulse to pulse, from the average profile, and from phase to phase within a pulse. Widely accepted explanations do not exist for this variability or for the mechanism producing the radiation. The variability corresponds to the field statistics, particularly the distribution of wave field amplitudes, which are predicted by theories for wave growth in inhomogeneous media. This paper shows that the field statistics of the Vela pulsar (PSR B0833-45) are well-defined and vary as a function of pulse phase, evolving from Gaussian intensity statistics off-pulse to approximately power-law and then lognormal distributions near the pulse peak to approximately power-law and eventually Gaussian statistics off-pulse again. Detailed single-component fits confirm that the variability corresponds to lognormal statistics near the peak of the pulse profile and Gaussian intensity statistics off-pulse. The lognormal field statistics observed are consistent with the prediction of stochastic growth theory (SGT) for a purely linear system close to marginal stability. The simplest interpretations are that the variability of the pulsar is a direct manifestation of an SGT state and the emission mechanism is linear (either direct or indirect), with no evidence for non-linear mechanisms like modulational instability and wave collapse which produce power-law field statistics. Stringent constraints are placed on non-linear mechanisms: they must produce lognormal statistics when suitably ensemble-averaged. Field statistics are thus a powerful, potentially widely applicable tool for understanding variability and constraining mechanisms and source characteristics of coherent astrophysical and space emissions.