Revising Natal Kick Prescriptions in Population Synthesis Simulations

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 nu kick alpha f(H05) m(ej) m(rem)(1), where f(H05) is a normalization factor, drawn from a Maxwellian distribution with one-dimensional rms velocity sigma = 265 km s(-1), m(ej) is m(rem) the mass of the supernova (SN) ejecta, and mrem 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 ultrastripped 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 similar to 600 Gpc(-3)yr(-1), R-BHNS similar to 10 Gpc(-3)yr(-1), and R-BBH similar to 50 Gpc(-3) yr(-1), fairly consistent with the numbers inferred from the LIGO-Virgo collaboration.