1 Introduction

Good quality gamma-ray data for three pulsars - Vela, Crab, and Geminga - acquired with EGRET aboard the CGRO tempts to analyse the properties of pulsar high-energy radiation as a function of photon energy and phase of rotation. Gamma-ray spectra of pulsed radiation from these sources (as well as from three other EGRET pulsars: B1706-44, B1951+32, and B1055-52) extend up to $\la$10 GeV. All three pulsars feature gamma lightcurves characterised by two strong peaks separated by 0.4 to 0.5 in rotational phase. These double-peak pulses are asymmetrical and their profiles change with energy. Above $\sim$100 MeV the leading peak (LP) is stronger than the trailing peak (TP) in the case of the Vela and the Crab pulsars, and the opposite is true for Geminga. However, for all three pulsars their leading peaks exhibit lower energy cutoffs - around $\sim$5 GeV - than the trailing peaks (TP). In other words, the trailing peaks dominate over the leading peaks above $\sim$5 GeV (Thompson 2001). In the case of the Vela pulsar and Geminga, this effect is accompanied by the softening of the spectrum of the leading peak (Fierro et al. 1998; Kanbach 1999). The potential importance of the double-peak pulse asymmetry in the case of Vela was already acknowledged - at the time when the COS-B data became available - by Morini (1983) who attempted to explain the asymmetry with a hybrid model, with two different mechanisms responsible for the formation of the leading and the trailing peak.

High-energy cutoffs in pulsar spectra are interpreted within polar cap models as due to one-photon absorption of gamma-rays in strong magnetic field with subsequent $e^\pm$-pair creation. A piece of observational support for such an interpretation comes from a strong correlation between the inferred "spin-down" magnetic field strength and the position of the high-energy cutoff (Baring & Harding 2000; Baring 2001). This in turn opens a possibility that the observed asymmetry between LP and TP, i.e. the dominance of LP over TP above $\sim$5 GeV, is a direct consequence of propagation effects (which eventually lead to stronger magnetic photon absorption for photons forming LP than TP) rather than due to some inherent property of the gamma-ray emission region itself.

The aim of this paper is to investigate the role of pulsar rotation in a built-up of such asymmetry in the double-peak pulse profiles. We consider purely rotational effects: due to presence of rotation-induced electric field $\vec E$, aberration of photon direction and slippage of magnetosphere under the photon's path. In Sect. 2 we compare them with some other effects which may be responsible for the asymmetry (like various distortions of the magnetic field structure). In Sect. 3 we show that the rotation effects result in an asymmetric pair production rate for the leading and the trailing part of the magnetosphere even in the case when the magnetic field structure and the population of radiating particles are symmetric around the magnetic pole. In Sect. 4 asymmetric pulse profiles are calculated as a function of photon energy and then the model predictions of the ratio of fluxes in the leading and trailing peaks are compared with the inferred ratio for Vela at different energy bins. In Sect. 5 we address the significance of rotation-driven asymmetry across the pulsar parameter space. Our main results are discussed in Sect. 6.