Model of peak separation in the gamma light curve of the Vela pulsar

The separation Delta (peak) between two peaks in the gamma-ray pulse profile is calculated as a function of energy for several polar cap models with curvature-radiation induced cascades. The Monte Carlo results are interpreted with the help of analytical approximations and discussed in view of the recent data analysis for the Vela pulsar. We find that the behaviour of Delta (peak) as a function of photon energy epsilon depends primarily on local values of the magnetic field, B-local, in the region where electromagnetic cascades develop. For low values of B-local, (<10(12) G), <Delta>(peak) (epsilon) is kept constant. However, for stronger magnetic fields (greater than or similar to 10(12) G) in the hollow-column model, Delta (peak) decreases with increasing photon energy at a rate dependent on the maximum energy of the beam particles, as well as on viewing geometry. There exists a critical photon energy epsilon (turn) above which the relation Delta (peak) (epsilon) changes drastically: for epsilon > epsilon (turn), in hollow-column models the separation Delta (peak) increases (whereas in the filled-column model it decreases) rapidly with increasing epsilon, at a rate of similar to 0.28 of the total phase per decade of photon energy. The existence of critical energy epsilon (turn) is a direct consequence of one-photon magnetic absorption effects. In general, epsilon (turn) is located close to the high-energy cut-off of the spectrum, thus photon statistics at epsilon (turn) should be very low. This will make it difficult to verify the existence of epsilon (turn) in real gamma-ray pulsars. Spectral properties of the Vela pulsar would favour those models that use low values of magnetic field in the emission region (B-local less than or similar to 10(11) G), which in turn implies a constant value of the predicted Delta (peak) within the range of EGRET.