Pair Production Multiplicities in Rotation‐powered Pulsars

Abstract

We discuss the creation of electron-positron cascades in the context of pulsar polar cap acceleration models and derive several useful analytic and semianalytic results for the spatial extent and energy response of the cascade. Instead of Monte Carlo simulations, we use an integrodi †erential equation that describes the development of the cascade energy spectrum in one space dimension quite well, when it is compared to existing Monte Carlo models. We reduce this full equation to a single integral equation, from which we can derive useful results, such as the energy loss between successive generations of photons and the spectral index of the response. We Ðnd that a simple analytic formula represents the pair cascade multiplicity quite well, provided that the magnetic Ðeld is below 1012 G and that an only slightly more complex formula matches the numerically calculated cascade at all other Ðeld strengths. Using these results, we Ðnd that cascades triggered by c-rays emitted through inverse Compton scattering of thermal photons from the neutron starÏs surface, both resonant and nonresonant, are important for the dynamics of the polar cap region in many pulsars. In these objects, the expected multiplicity of pairs generated by a single input particle is lower than previously found in cascades initiated by curvature emission, frequently being on the order of 10 rather than D1000 as usually quoted. Such pulsars also are expected to be less luminous in polar cap c-rays than when curvature emission triggers the cascade, a topic that will be the subject of a subsequent paper.

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The Variable Jet of the Vela Pulsar

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