Initial accelerations of pulsars caused by external kicks

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.