We present a detailed analysis of archival Hubble Space Telescope data that we use to measure 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 ) .
Combining data from 47 observations spanning > 10 yr with two different instruments , and using the best available measurement techniques and latest distortion models , we are able to demonstrate that our measurement is robust and has an uncertainty of only \pm 0.4 \mbox { mas } \mbox { yr } ^ { -1 } on each component of the proper motion .
However , we then consider the various uncertainties that arise from the need to correct the proper motion that we measure to the local standard of rest at the position of the pulsar and find \mu _ { \alpha } = -11.8 \pm 0.4 \pm 0.5 \mbox { mas } \mbox { yr } ^ { -1 } and \mu _ { \delta } = \mbox { +4.4 } \pm 0.4 \pm 0.5 \mbox { mas } \mbox { yr } ^ { -1 } relative to the pulsar ’ s standard of rest , where the two uncertainties are from the measurement and the reference frame , respectively .
If we then wish to compare this proper motion to the symmetry axis of the pulsar wind nebula , we must consider the unknown velocity of the pulsar ’ s progenitor ( assumed to be \sim 10 \mbox { km } \mbox { s } ^ { -1 } ) , and hence add an additional uncertainty of \pm 2 \mbox { mas } \mbox { yr } ^ { -1 } to each component of the proper motion , although this could be a factor of 10 larger if the pulsar ’ s progenitor had an anomalously high velocity ( > 100 \mbox { km } \mbox { s } ^ { -1 } ) .
This implies a projected misalignment with the nebular axis of 14 \arcdeg \pm 2 \arcdeg \pm 9 \arcdeg , consistent with a broad range of values including perfect alignment .
We use our proper motion to derive an independent estimate for the site of the supernova explosion with an accuracy that is 2–3 times better than previous estimates .
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 .