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Astron. Astrophys. 357, 301-307 (2000)

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1. Introduction

Electrons accelerated near the polar cap of pulsars interact with the thermal radiation emitted by the photosphere via non-resonant and (cyclotron) resonant inverse Compton collisions (e.g. Kardashev et al. 1984). Several groups have examined how these processes affect the end energies of electrons and the production of gamma rays. For the electron acceleration model of Michel (1974) important results have been published by Sturner (1993), Sturner & Dermer (1994), Sturner et al. (1995), Sturner & Dermer (1995), and Sturner (1995). Results concerning the Ruderman & Sutherland model (1975) have been published by Xia et al. (1985), Daugherty & Harding (1989), Chang (1995), Zhang & Qiao (1996), and others.

Zhang & Qiao (1996) compared inverse Compton scattering (ICS) with curvature radiation (CR) under the condition of gap sparking initiated by pair cascading in the strong magnetic field. Both reduce the height of the gap and the end energy of the electrons. Zhang & Qiao found in some cases the ICS much more important than the CR.

Among the publications based on the acceleration model of Michel (1974) the most recent and most extension work of Sturner (1995) used Monte Carlo simulations to calculate the energy transfer caused by ICS. Additionally he investigated CR and triplet pair production. The calculations revealed ICS as the dominant energy loss process for electron energies [FORMULA] below a few [FORMULA]. Above this threshold energy loss by CR dominates whereas triplet pair production was generally found to be unimportant (for typical gamma-ray pulsar parameters), except for very low electron energies with [FORMULA].

Using Monte Carlo Methods Sturner calculated the limiting energy of electrons for two magnetic field strength ([FORMULA] and [FORMULA]) and four temperatures between 2.0 and [FORMULA]. Additionally, he fixed the rotation period of the neutron star to 0.150 seconds.

In this paper, we present an analytical treatment of the ICS problem including CR in the case of Michel's acceleration model and show results of numerical integrations of the developed differential equations. The anisotropy of the distribution of the thermal photons originating from the hot thermal cap is explicitely considered. The relevant parameters like magnetic field strength, thermal temperature of the hot polar cap and rotation period of the neutron star have been varied within a wide range of pulsar parameter values. In addition, we briefly discuss to what extent our results are relevant for other polar cap acceleration models, like the one described by Arons & Scharlemann (1979) which explicitly considers the effect of the divergence of the magnetic field lines or the model of Muslimov & Tsygan (1992) which describes the influence of the general relativistic frame dragging effect on the acceleration field.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000