Runaway velocities of stellar components originating from disrupted binaries via asymmetric supernova explosions

We present analytical formulae to calculate the dynamical effects of asymmetric supernova explosions which disrupt a binary system. These formulae are applied to Monte Carlo simulations of asymmetric supernovae in a large number of binaries. The expected velocities of runaway neutron stars and companion stars are calculated as a function of separation and component masses, prior to the explosion and the amount of asymmetry involved (i.e. the magnitude of the kick velocity imparted to the neutron star during the explosion) assuming an isotropic distribution of kicks. We also discuss the effect of shell impact on the companion star. Furthermore, we demonstrate that no simple constraints on the pre-supernova parameter space can be derived from observations of single neutron stars if supernova explosions are asymmetric....