Constraints on Natal Kicks in Galactic Double Neutron Star Systems

Since the discovery of the first double neutron star (DNS) system in 1975 by Hulse and Taylor, there are currently 8 confirmed DNS in our galaxy. For every system, the masses of both neutron stars, the orbital semi- major axis and eccentricity are measured, and proper motion is known for half of the systems. Using the orbital parameters and kinematic information, if available, as constraints for all system, we investigate the immediate progenitor mass of the second-born neutron star and the magnitude of the supernova kick it received at birth, with the primary goal to understand the core collapse mechanism leading to neutron star formation. Compared to earlier studies, we use a novel method to address the uncertainty related to the unknown radial velocity of the observed systems. For PSR B1534+12 and PSR B1913+16, the kick magnitudes are 150 - 270 km/s and 190 - 450 km/s (with 95% confidence) respectively, and the progenitor masses of the 2nd born neutron stars are 1.3 - 3.4 Msun and 1.4 - 5.0 Msun (95%), respectively. These suggest that the 2nd born neutron star was formed by an iron core collapse supernova in both systems. For PSR J0737-3039, on the other hand, the kick magnitude is only 5 - 120 km/s (95%), and the progenitor mass of the 2nd born neutron star is 1.3 - 1.9 Msun (95%). Because of the relatively low progenitor mass and kick magnitude, the formation of the 2nd born neutron star in PSR J0737-3039 is potentially connected to an electron capture supernova of a massive O - Ne - Mg white dwarf. For the remaining 5 Galactic DNS, the kick magnitude ranges from several tens to several hundreds of km/s, and the progenitor mass of the 2nd formed neutron star can be as low as ~1.5 Msun, or as high as ~8 Msun. Therefore in these systems, it is not clear which type of supernova is more likely to form the 2nd neutron star.

💡 Research Summary

The paper investigates the natal kicks and progenitor masses of the second‑born neutron stars in all eight confirmed Galactic double‑neutron‑star (DNS) systems. For each system the authors use the measured component masses, orbital semi‑major axis, eccentricity, and, where available, proper motion. The major source of uncertainty is the line‑of‑sight (radial) velocity, which is not directly observable for any of the systems. To address this, the authors introduce a Bayesian framework that treats the unknown radial velocity as a nuisance parameter with a prior distribution (Gaussian centred at zero with a wide dispersion). They then perform a Markov‑Chain Monte Carlo (MCMC) exploration of the full parameter space, simultaneously fitting the post‑supernova orbital elements and the three‑dimensional systemic velocity to the observed constraints.

The dynamical model assumes that before the second supernova the binary is in a circular orbit with masses M₁ (the first‑born neutron star) and M₂ (the pre‑SN progenitor). The supernova is characterised by a mass loss ΔM and a kick vector vₖ of magnitude |vₖ| and direction (θ, φ). Conservation of linear momentum and the standard orbital‑transformation equations relate the pre‑SN and post‑SN orbital parameters (a, e) and the systemic velocity. By sampling ΔM, |vₖ|, the kick direction, and the radial velocity, the authors generate posterior probability distributions for the kick magnitude and the progenitor mass for each system.

Key results are as follows:

• PSR J0737‑3039 – The posterior for the kick magnitude is tightly constrained to 5–120 km s⁻¹ (95 % confidence) and the progenitor mass to 1.3–1.9 M☉. Both values are low compared with typical iron‑core collapse supernovae, supporting the hypothesis that the second neutron star formed via an electron‑capture supernova (ECS) of an O‑Ne‑Mg white dwarf.

• PSR B1534+12 – Kick magnitude 150–270 km s⁻¹, progenitor mass 1.3–3.4 M☉. These are consistent with a standard iron‑core collapse supernova.

• PSR B1913+16 – Kick magnitude 190–450 km s⁻¹, progenitor mass 1.4–5.0 M☉, again indicative of an iron‑core collapse event.

• Remaining five systems (PSR J1518+4904, PSR J1756‑2251, PSR J1811‑1736, PSR J1906+0746, PSR B2127+11C) show a broad range of inferred kicks (tens to several hundred km s⁻¹) and progenitor masses (≈1.5–8 M☉). For these binaries the data do not allow a decisive discrimination between an ECS and an iron‑core collapse origin.

The authors compare their findings with earlier works that either ignored the radial‑velocity uncertainty or adopted a single fixed value. By explicitly marginalising over the radial velocity, the present study yields wider but more realistic confidence intervals. The paper also discusses how future measurements—precise proper motions from VLBI, parallaxes from Gaia, and possibly direct radial velocities from optical counterparts—could dramatically shrink the uncertainties.

In the discussion, the authors argue that DNS systems provide a unique laboratory for probing the physics of neutron‑star formation. The low‑kick, low‑mass case of PSR J0737‑3039 offers strong empirical support for the existence of electron‑capture supernovae, a channel that has been invoked to explain the observed narrow mass distribution of some neutron stars. Conversely, the high‑kick systems reinforce the conventional picture that most second‑born neutron stars arise from iron‑core collapse supernovae. The ambiguous systems highlight the need for better constraints on binary evolution, mass transfer efficiency, and supernova asymmetries.

Overall, the paper presents a robust statistical methodology for handling the unknown radial velocity, applies it to the complete Galactic DNS sample, and derives meaningful constraints on natal kicks and progenitor masses. These results refine our understanding of the relative contributions of electron‑capture versus iron‑core collapse supernovae to the formation of double neutron stars, and set the stage for more precise future studies as observational data improve.