Revising Natal Kick Prescriptions in Population Synthesis Simulations

Abstract

Natal kicks are a matter of debate and they significantly affect the merger rate density of compact objects. Here, we present a new simple formalism for natal kicks of neutron stars (NSs) and black holes (BHs). We describe the magnitude of the kick as , where f H05 is a normalization factor, drawn from a Maxwellian distribution with one-dimensional rms velocity σ  = 265 km s −1 , m ej is the mass of the supernova (SN) ejecta, and m rem is the mass of the compact object. This formalism matches the proper motions of young Galactic pulsars and can naturally account for the differences between core-collapse SNe of single stars, electron-capture SNe and ultra-stripped SNe occurring in interacting binaries. Finally, we use our new kick formalism to estimate the local merger rate density of binary NSs ( R BNS ), BH–NS binaries ( R BHNS ), and binary BHs ( R BBH ), based on the cosmic star formation rate density and metallicity evolution. In our fiducial model, we find R BNS  ∼ 600 Gpc −3  yr −1 , R BHNS  ∼ 10 Gpc −3  yr −1 , and R BBH  ∼ 50 Gpc −3  yr −1 , fairly consistent with the numbers inferred from the LIGO–Virgo collaboration.