Kinematic constraints on the ages and kick velocities of Galactic neutron star binaries

The systems creating binary neutron stars (BNSs) experience systemic kicks when one of the components goes supernova. The combined magnitude of these kicks is still a topic of debate, and has implications for the eventual location of the transient resulting from the merger of the binary. For example, the offsets of short-duration gamma-ray bursts (SGRBs) resulting from BNS mergers depend on the BNS kicks. We investigated Galactic BNSs, and traced their motion through the Galaxy. This enabled us to estimate their kinematic ages and construct a BNS kick distribution, based on their Galactic trajectories. We used the pulsar periods and their derivatives to estimate the characteristic spin-down ages of the binaries. Moreover, we used a Monte Carlo estimation of their present-day velocity vector in order to trace back their trajectory and estimate their kinematic ages. These trajectories, in turn, were used to determine the eccentricity of their Galactic orbit. Based on simulations of kicked objects in the Galactic potential, we investigated the relationship between this eccentricity and kick velocity, in order to constrain the kicks imparted to the binaries at birth. We find that the Galactic BNSs are likely older than $\sim40$ Myr, which means their current (scalar) galactocentric speeds are not representative of their initial kicks. However, we find a close relationship between the eccentricity of a Galactic trajectory and the experienced kick. Using this relation, we constrained the kicks of the Galactic BNSs, depending on the kind of isotropy assumed in estimating their velocity vectors. These kick velocities are well-described by a log-normal distribution peaking around $\sim40-50$ km/s, and coincide with the peculiar velocities of the binaries at their last disc crossing.