General Relativistic Polar Particle Acceleration and Pulsar Death

Abstract

I summarize the theory of acceleration of non-neutral particle beams by starvation electric fields along the polar magnetic field lines of rotation powered pulsars, including the effect of dragging of inertial frames which dominates the acceleration of a space charge limited beam. I apply these acceleration results to a new calculation of the radio pulsar death line, under the hypotheses that pulsar ``death'' corresponds to cessation of pair creation over the magnetic poles and that the magnetic field has a locally dipolar topology. While the frame dragging effect in star centered dipole geometry does improve comparison of the theory with observation, an unacceptably large fraction of the observed stars outside the bounds of pair creation theory still persists. Offsetting the dipole improves the correspondence between theory and observation. The result is a ``death valley'' for pulsars; acceptable comparison of observation and theory occurs if the boundary of death valley corresponds to offsets of the dipole center from the stellar center $\sim (0.7-0.8) R_*$. I also point out that pulsars are absent for magnetic moments corresponding to star centered polar fields in excess of $\sim 4 \times 10^{13}$ Gauss, and I suggest that this absence is due to pairs forming as bound positronium atoms in such strong fields, creating a neutral, relativistically outflowing gas which cannot participate in low altitude collective radio emission processes in such strongly magnetized objects.