Is the Link Between the Observed Velocities of Neutron Stars and their Progenitors a Simple Mass Relationship?

While the imparting of velocity `kicks' to compact remnants from supernovae is widely accepted, the relationship of the `kick' to the progenitor is not. We propose the `kick' is predominantly a result of conservation of momentum between the ejected and compact remnant masses. We propose the `kick' velocity is given by v _kick = α(M _ejecta/M _remnant)+β, where α and β are constants we wish to determine. To test this we use the BPASS v2 (Binary Population and Spectral Synthesis) code to create stellar populations from both single star and binary star evolutionary pathways. We then use our Remnant Ejecta and Progenitor Explosion Relationship (REAPER) code to apply `kicks' to neutron stars from supernovae in these models using a grid of α and β values, (from 0 to 200 km s<sup>-1</sup> in steps of 10 km s<sup>-1</sup>), in three different `kick' orientations, (isotropic, spin-axis aligned and orthogonal to spin-axis) and weighted by three different Salpeter initial mass functions (IMF's), with slopes of -2.0, -2.35 and -2.70. We compare our synthetic 2D and 3D velocity probability distributions to the distributions provided by Hobbs et al. (1995).