Model of peak separation in the gamma lightcurve of the Vela pulsar

Abstract

The separation $\del$ 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 (Kanbach 1999). We find that the behaviour of $\del$ as a function of photon energy $\epsilon$ depends primarily on local values of the magnetic field, $B_{\rm local}$, in the region where electromagnetic cascades develop. For low values of $B_{\rm local}$ ($< 10^{12}$ G), $\del(\epsilon)$ is kept constant. However, for stronger magnetic fields ($\ga 10^{12}$ G) in the hollow-column model $\del$ decreases with increasing photon energy at a rate dependent on maximum energy of beam particles as well as on viewing geometry. There exists a critical photon energy $\et$ above which the relation $\del(\epsilon)$ changes drastically: for $\epsilon > \et$, in hollow-column models the separation $\del$ increases (whereas in filled-column model it decreases) rapidly with increasing $\epsilon$, at a rate of $\sim 0.28$ of the total phase per decade of photon energy. The existence of critical energy $\et$ is a direct consequence of one-photon magnetic absorption effects. In general, $\et$ is located close to the high-energy cutoff of the spectrum, thus photon statistics at $\et$ should be very low. That will make difficult to verify the existence of $\et$ in real gamma-ray pulsars. Spectral properties of the Vela pulsar would favour those models which use low values of magnetic field in the emission region ($B_{\rm local} \simless 10^{11}$ G) which in turn implies a constant value of the predicted $\del$ within EGRET range.