In ( ) 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 .
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 ( ) , prompted us to revisit our basic assumptions and our new analysis has led to revised “ best-fit ” kick values of \alpha = 100 { km s ^ { -1 } } and \beta = -170 { km s ^ { -1 } } .
The reduction of \beta to a negative value is due to using the 2D observed kick velocity distribution rather than the modelled 3D velocity distribution for neutron stars ( NS ) .
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 3,864 ^ { +1 , 570 } _ { -2 , 371 } Gpc ^ { -3 } yr ^ { -1 } and a BH-BH merger rate of 5 ^ { +40 } _ { -1 } Gpc ^ { -3 } yr ^ { -1 } .