VLBA Astrometry of the Galactic Double Neutron Stars PSR J0509+3801 and PSR J1930-1852: A Preliminary Transverse Velocity Distribution of Double Neutron Stars and Its Implications

The mergers of double neutron stars (DNSs) systems are believed to drive themajority of short γ-ray bursts (SGRBs), while also serving as productionsites of heavy r-process elements. Despite being key to i) confirming thenature of the extragalactic SGRBs, ii) addressing the poorly-understoodr-process enrichment in the ultra-faint dwarf galaxies (UFDGs), and iii)probing the formation process of DNS systems, the space velocity distributionof DNSs is still poorly constrained due to the small number of DNSs withwell-determined astrometry. In this work, we determine new proper motions andparallaxes of two Galactic DNSs – PSR J0509+3801 and PSR J1930-1852, using theVery Long Baseline Array, and estimate the transverse velocities v_⊥ ofall the 11 isolated Galactic DNSs having proper motion measurements in aconsistent manner. Our correlation analysis reveals that the DNS v_⊥ istentatively correlated with three parameters: spin period, orbitaleccentricity, and companion mass. With the preliminary v_⊥ distribution,we obtain the following findings. Firstly, the refined v_⊥ distributionis confirmed to agree with the observed displacements of the localized SGRBsfrom their host galaxy birth sites. Secondly, we estimate that around 112515km s^-1 and 25km s^-1, respectively. Hence, theretained DNSs might indeed be responsible for the r-process enrichmentconfirmed so far in a few UFDGs. Finally, we discuss how a future ensemble ofastrometrically determined DNSs may probe the multimodality of the v_⊥distribution.