The Redshift Distribution of Short Gamma-Ray Bursts from Dynamically Formed Neutron Star Binaries

Short-hard gamma-ray bursts (SHBs) may arise from gravitational wave (GW)driven mergers of double neutron star (DNS) systems. DNSs may be "primordial"or can form dynamically by binary exchange interactions in globular clustersduring core-collapse. For primordial binaries, the time delay between formationand merger is expected to be short, tau~0.1 Gyr, implying that the redshiftdistribution of merger events should follow that of star-formation. We pointout here that for dynamically formed DNSs, the time delay betweenstar-formation and merger is dominated by the cluster core-collapse time,rather than by the GW inspiral time, yielding delays comparable to the Hubbletime. We derive the redshift distribution of merger events of dynamicallyformed DNSs, and find it to differ significantly from that typically expectedfor primordial binaries. The observed redshift distribution of SHBs favorsdynamical formation, although a primordial origin cannot be ruled out due topossible detection biases. Future red-shift observations of SHBs may allow todetermine whether they are dominated by primordial or dynamically formed DNSs.Comment: Accepted to ApJL; Minor revision