Spatial Distribution of Pair Production over the Pulsar Polar Cap

TL;DR

This paper analytically investigates the spatial distribution of pair production over pulsar polar caps, revealing that it occurs only on a fraction of the cap for aligned rotators, with results matching simulations and implications for pulsar emission models.

Contribution

It introduces an analytic, general relativistic framework to determine where pair production occurs on pulsar polar caps, aligning with simulation results and enhancing understanding of pulsar magnetospheres.

Findings

Pair production occurs on a limited fraction of the polar cap.

Results agree with force-free simulation data.

Implications for pulsar emission observations.

Abstract

Using an analytic, axisymmetric approach that includes general relativity, coupled to a condition for pair production deduced from simulations, we derive general results about the spatial distribution of pair-producing field lines over the pulsar polar cap. In particular, we show that pair production on magnetic field lines operates over only a fraction of the polar cap for an aligned rotator for general magnetic field configurations, assuming the magnetic field varies spatially on a scale that is larger than the size of the polar cap. We compare our result to force-free simulations of a pulsar with a dipole surface field and find excellent agreement. Our work has implications for first-principles simulations of pulsar magnetospheres, and for explaining observations of pulsed radio and high-energy emission.