The spin period - eccentricity relation of double neutron stars: evidence for weak supernova kicks?

Double neutron stars (DNSs), binary systems consisting of a radio pulsar and a generally undetected second neutron star (NS), have proven to be excellent laboratories for testing the theory of general relativity. The seven systems discovered in our Galaxy exhibit a remarkably well-defined relation between the pulsar spin period and the orbital eccentricity. Here we show, using a simple model where the pulsar is spun up by mass transfer from a helium-star companion, that this relation can only be produced if the second neutron star received a kick that is substantially smaller (with a velocity dispersion of less than 50 km/s) than the standard kick received by a single radio pulsar. This demonstrates that the kick mechanism depends on the evolutionary history of the NS progenitor and that the orbital parameters of DNSs are completely determined by the evolution in the preceding helium star - neutron star phase. This has important implications for estimating the rates of NS-NS mergers, one of the major potential astrophysical sources for the direct detection of gravitational waves, and for short-period gamma-ray bursts.