A Precise Proper Motion for the Crab Pulsar, and the Difficulty of Testing Spin-Kick Alignment for Young Neutron Stars

Abstract

We present a detailed measurement of the proper motion of the Crab pulsar, with the primary goal of comparing the direction of its proper motion with the projected axis of its pulsar wind nebula (the projected spin axis of the pulsar). We demonstrate that our measurement is robust and has an uncertainty of only +/-0.4 mas/yr on each component of the proper motion. We find mu_alpha = -11.7+/-0.4+/-0.5 mas/yr and mu_delta = +4.2+/-0.4+/-0.5 mas/yr relative to the pulsar's standard of rest, where the two uncertainties are from the measurement and the ncertainties in correcting the proper motion reference frame, respectively. Comparing this proper motion to the symmetry axis of the pulsar wind nebula, we must also consider the unknown velocity of the pulsar's progenitor (assumed to be ~10 km/s), and hence add an additional uncertainty of +/-2 mas/yr to each component of the proper motion, although this could be significantly larger. This implies a projected misalignment with the nebular axis of 14+/-2+/-9 degrees. We conclude that the precision of individual measurements which compare the direction of motion of a neutron star to a fixed axis will often be limited by fundamental uncertainties regarding reference frames and progenitor properties. The question of spin-kick (mis)alignment, and its implications for asymmetries and other processes during supernova core-collapse, is best approached by considering a statistical ensemble of such measurements, rather than detailed studies of individual sources. [abriged]