  Supernova explosions are inherently asymmetric and can accelerate new-born
neutron stars (NSs) to hundreds of km/s. Two prevailing theories to explain NS
kicks are ejecta asymmetries (e.g., conservation of momentum between NS and
ejecta) and anisotropic neutrino emission. Observations of supernova remnants
(SNRs) can give us insights into the mechanism that generates these NS kicks.
In this paper, we investigate the relationship between NS kick velocities and
the X-ray morphologies of 18 SNRs observed with the Chandra X-ray Observatory
and the Rontgen Satellite (ROSAT). We measure SNR asymmetries using the
power-ratio method (a multipole expansion technique), focusing on the dipole,
quadrupole, and octupole power-ratios. Our results show no correlation between
the magnitude of the power-ratios and NS kick velocities, but we find that for
Cas A and G292.0+1.8, whose emission traces the ejecta distribution, their NSs
are preferentially moving opposite to the bulk of the X-ray emission. In
addition, we find a similar result for PKS 1209-51, CTB 109, and Puppis A;
however their emission is dominated by circumstellar/interstellar material, so
their asymmetries may not reflect their ejecta distributions. Our results are
consistent with the theory that NS kicks are a consequence of ejecta
asymmetries as opposed to anisotropic neutrino emission. In the future,
additional observations to measure NS proper motions within ejecta-dominated
SNRs are necessary to constrain robustly the NS kick mechanism.
