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 pulsar's variability is a direct
manifestation of an SGT state and the emission mechanism is linear (either
direct or indirect), with no evidence for nonlinear mechanisms like
modulational instability and wave collapse which produce power-law field
statistics. Stringent constraints are placed on nonlinear 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.Comment: 11 pages, 12 figures. Accepted by Monthly Notices of the Royal
Astronmical Society in April 200
