Neutron Star Kicks II: Revision and further testing of the conservation of momentum "kick" model

In Bray and Eldridge (2016) we proposed a simple neutron star kick formula, v kick = {\alpha} ( M ejecta / M remnant ) + {\beta} to explain the observed 2D velocities of young single neutron stars. However, in light of the recent analysis by Janka (2017), we have revisited our basic assumptions and our new analysis has led to best fit kick values of alpha = 100 km per second and beta = -170 km per second. While the changes appear significant, the revised values do not change our three fundamental findings, namely that there is no statistically significant preference for any of the three kick orientations nor for any of the three initial mass function (IMF) slopes tested, and that populations including binary stars reproduced the kick distribution better than single star only populations. The reduction of beta to a negative value, means both alpha and beta can be explained by processes widely accepted to be present in supernovae, namely conservation of momentum and gravitational attraction. To further test the validity of the new kick, we have created synthetic populations of runaway star and double neutron star (DNS) binaries at solar metallicity (Z=0.020) using our best-fit kick. We find our new kick values create runaway star velocities and DNS period distributions in agreement with the comparable observational distributions with only the DNS eccentricities in tension with the observations. From our DNS and BH-BH datasets we estimate a predicted DNS merger rate at Solar metallicity of 3944 (+1570/-2371) per cubic Gpc per yr and a BH-BH merger rate of 3 (+40/-1) per cubic Gpc per yr.