Introduction

The mechanism for converting rotational energy of pulsars to electromagnetic radiation has long been the subject of active research in pulsar physics. The recent observation of seven pulsars by the instruments aboard CGRO provides even more challenge to the current pulsar theory. These pulsars radiate high-energy photons with apparently high efficiency (Ulmer 1994; Thompson et al. 1994). One possible way to convert the rotational energy to electromagnetic radiation is through particle acceleration by the rotation-induced electric field in the pulsar's magnetosphere. There are several sites for gap acceleration, which include the polar gap (Ruderman & Sutherland 1975; Arons & Scharlemann 1979; Michel 1974; Fawley, Arons & Scharlemann 1977), the slot gap (Arons 1983), and the outer gap (Cheng, Ho & Ruderman 1986). In the polar gap model, the acceleration region is located near the polar cap while in the outer gap model, the acceleration occurs near the light cylinder. In the slot gap model, the acceleration is at the boundary between the open and closed field lines.

There is observational evidence that polar caps of young pulsars can be hot with effective temperature (Ögelman 1991; Greiveldinger et al. 1996). Although the exact value of T is rather uncertain, and may depend on the model of the atmosphere above the polar cap (Romani 1987), the hot polar cap appears to be a plausible consequence of polar cap heating as the result of particle acceleration (Cheng & Ruderman 1977; Arons & Scharlemann 1979; Luo 1996). One of the important consequences of hot polar caps is that it provides an alternative mechanism for controlling the gap, i.e. mainly through pair cascades initiated by Compton scattered photons (Sturner 1995; Luo 1996). Inverse Compton scattering in the polar cap region is strongly modified by the magnetic field in that the scattering cross section is enhanced by the cyclotron resonance (Herold 1979), i.e. in the electron rest frame, soft photons have energies close to the cyclotron energy in with the critical field. This process is referred to as resonant inverse Compton scattering (RICS). Because of the resonance, the effective cross section is greatly enhanced in comparison with the ordinary Compton scattering. For gap acceleration, we can define its efficiency as the ratio of the total voltage across the gap to the maximum voltage across the polar cap (i.e. for an empty magnetosphere). The efficiency of the gap acceleration is controlled by the pair production and thus strongly depends on the effective temperature of the polar caps.

In this paper, we consider the constraint imposed by RICS on the efficiency of polar gap acceleration. We assume that free emission of charges from polar caps is allowed, and consider both the polar region in which the outflowing charges are electrons () and that in which the outflowing charges are heavy ions or positrons (). In the polar gap at which , since the energy loss of ions due to RICS is negligibly small, they can be accelerated by the full potential drop across the gap. We derive the condition for the ions to carry most of the particle luminosity. Accelerated ions may produce pairs in the anisotropic thermal photon field. We calculate numerically the distance from the polar cap at which the ions start to produce pairs and compare it to the gap length constrained by pair production by RICS.

© Copyright Astronomical Society of Australia 1997