Initial accelerations of pulsars caused by external kicks

TL;DR

This paper derives a relation between initial pulsar acceleration, velocity, and magnetic field using energy conservation, and concludes that external forces causing such accelerations are likely physically infeasible.

Contribution

It introduces a theoretical relation linking pulsar acceleration, velocity, and magnetic field, highlighting the unlikelihood of external forces causing observed accelerations.

Findings

External forces of the derived magnitude are physically unlikely.

Realistic magnetic fields do not support the required accelerations.

The relation constrains possible mechanisms for pulsar acceleration.

Abstract

Using energy conservation we show that if a sudden external force of unknown nature causes a newborn pulsar of mass $M=1.4 M_\odot$ and radius R=10 km to have the acceleration $a_0$ then we can derive the relation $a_0\simeq k^{-1}vB_0^{-2/3},$ where $v$ is the velocity of the pulsar, $B_0$ its initial magnetic field and $k\approx 10^{-17}$G$^{-2/3}$s. This relation predicts that a newborn pulsar with $v=450$ km experienced the acceleration $a_0\simeq10^{13}$g when $B_0\simeq10^{13}$G. An external force producing such an acceleration seems not to be physically feasible. This pulsar could have experienced the more realistic acceleration $a_0\simeq10^{9}$g if $B_0\simeq10^{18}$G. But this huge magnetic field seems to be unrealistic.