On the role of supernova kicks in the formation of Galactic double neutron star systems

In this work we focus on a group of Galactic double neutron star (DNS) systems with long orbital periods of $ \gtrsim 1$ day and low eccentricities of $\lesssim 0.4$. The feature of these orbital parameters is used to constrain the evolutionary processes of progenitor binaries and the supernova (SN) kicks of the second born NSs. Adopting that the mass transfer during primordial binary evolution is highly non-conservative (rotation-dependent), the formation of DNS systems involves a double helium star binary phase, the common envelope (CE) evolution initiates before the first NS formation. During the CE evolution the binary orbital energy is obviously larger when using a helium star rather than a NS to expel the donor envelope, this can help explain the formation of DNS systems with long periods. SN kicks at NS birth can lead to eccentric orbits and even the disruption of binary systems, the low eccentricities require that the DNSs receive a small natal kick at the second collapse. Compared with the overall distribution of orbital parameters for observed DNS binaries, we propose that the second born NSs in most DNS systems are subject to small natal kicks with the Maxwellian dispersion velocity of less than $ 80 \,\rm km\,s^{-1} $, which can provide some constraints on the SN explosion processes. The mass distribution of DNS binaries is also briefly discussed. We suggest that the rotation-dependent mass transfer mode and our results about SN kicks should be applied to massive binary evolution and population synthesis studies.