Neutron star kicks – II. Revision and further testing of the conservation of momentum ‘kick’ model

In Bray & Eldridge, we proposed a simple neutron star (NS) ‘kick’ formula, |vkick=α \, (Mejecta\, /\, Mᵣₑₘₙₐₙₜ) + β \,| to explain the observed 2D velocities of young single NSs. Using this kick we found that there is no statistically significant preference for a kick orientation 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. However, recent analysis by Janka prompted us to revisit our basic assumptions and our new analysis has led to revised ‘best-fitting’ kick values of |α =100\ km\, s⁻¹| and |β =-170\ km\, s⁻¹|⁠. The reduction of β to a negative value is due to using the 2D observed kick velocity distribution rather than the modelled 3D velocity distribution for NSs. 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-fitting 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 black hole–black hole (BH–BH) data sets we estimate a predicted DNS merger rate at solar metallicity of 3864|+1,570-2,371| Gpc−3 yr−1 and a BH–BH merger rate of 5|⁺⁴⁰₋₁| Gpc−3 yr−1.