Natal supernova kicks, the linear momentum compact remnants receive during their formation, are an essential part of binary population synthesis (BPS) models. Although these kicks are well-supported by evidence, their underlying distributions and incorporation into BPS models is uncertain. In this work, we investigate the nature of natal kicks using a previously proposed analytical prescription where the strength of the kick is linearly proportional to the ejecta-remnant mass ratio. We vary the free parameters over large ranges of possible values, comparing these synthetic populations simultaneously against four constraints: the merger rate of compact binary neutron star (BNS) systems, the period-eccentricity distribution of galactic BNSs, the velocity distribution of single-star pulsars, and the likelihood for low-ejecta mass supernovae to produce low-velocity kicks. We find that different samples of the parameter space satisfy each tests, and only 1 per cent of the models satisfy all four constraints simultaneously. Although we cannot identify a single best kick model, we report 𝛼 = 80 ± 30 km s −1 , 𝛽 = 0 ± 20 km s −1 as the center of the region of the parameter space that fulfils all of our constraints, and expect 𝛽 ≥ 0 km s −1 as a further constraint. We also suggest further observations that will enable future refinement of the kick model. A sensitive test for the kick model will be the redshift evolution of the BNS merger rate since this is effectively a direct measure of the delay-time distribution for mergers. For our best fitting values, we find that the peak of the BNS merger rate is the present-day.

The recent discovery of an unambiguous quiescent BH and main sequence O star companion in VFTS 243 opens the door to new constraints on theoretical stellar evolution and population models looking to reproduce the progenitors of black hole - black hole binaries. Here we show that the Binary Population and Spectral Synthesis fiducial models (BPASSv2.2.1) natively predict VFTS 243-like systems: We find that VFTS 243 likely originated from a binary system in a ∼15 day orbit with primary mass ranging from 40 to 50  M⊙ and secondary star with initial mass 24–25 M⊙. Additionally we find that the death of the primary star must have resulted in a low energy explosion E < 1050 ergs. With a uniform prior we find that the kick velocity of the new-born black hole was ≤10  km s−1. The very low eccentricity reported for VFTS 243 and the subsequent conclusion by the authors that the SN kick must have been very small is in line with the peak in the posterior distribution between 0 and 5  km s−1 found from our numerical simulations performed with a uniform prior. Finally, the reduced Hobbs kick distribution commonly used in black hole population synthesis is strongly disfavoured, whereas the Bray kick with the most recent parameter calibration predicts 4.2 ± 3.4  km s−1, which is very consistent with the posterior velocity distributions obtained for our matching VFTS 243-like models using a uniform kick prior.

Natal supernova kicks, the linear momentum compact remnants receive during their formation, are an essential part of binary population synthesis (BPS) models. Although these kicks are well-supported by evidence, their underlying distributions and incorporation into BPS models is uncertain. In this work, we investigate the nature of natal kicks using a previously proposed analytical prescription where the strength of the kick is given by $v_\text{k}=\alpha \frac{m_\text{ejecta}}{m_\text{remnant}}+\beta \, km~s^{-1}$, for free parameters α and β. We vary the free parameters over large ranges of possible values, comparing these synthetic populations simultaneously against four constraints: the merger rate of compact binary neutron star (BNS) systems, the period-eccentricity distribution of galactic BNSs, the velocity distribution of single-star pulsars, and the likelihood for low-ejecta mass supernovae to produce low-velocity kicks. We find that different samples of the parameter space satisfy each tests, and only 1 per cent of the models satisfy all four constraints simultaneously. Although we cannot identify a single best kick model, we report $\alpha =115^{+40}_{-55}\, km~s^{-1}, \beta =15^{+10}_{-15}\, km~s^{-1}$ as the center of the region of the parameter space that fulfils all of our constraints, and expect β ≥ 0 km s−1 as a further constraint. We also suggest further observations that will enable future refinement of the kick model. A sensitive test for the kick model will be the redshift evolution of the BNS merger rate since this is effectively a direct measure of the delay-time distribution for mergers. For our best fitting values, we find that the peak of the BNS merger rate is the present-day.