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 clusters during core collapse. For primordial binaries, the time delay between formation and merger is expected to be short, tau similar to 0.1 Gyr, implying that the redshift distribution of merger events should follow that of star formation. We point out here that for dynamically formed DNSs, the time delay between star formation and merger is dominated by the cluster core-collapse time, rather than by the GW inspiraling time, yielding delays comparable to the Hubble time. We derive the redshift distribution of merger events of dynamically formed DNSs and find it to differ significantly from that typically expected for primordial binaries. The observed redshift distribution of SHBs favors dynamical formation, although a primordial origin cannot be ruled out, because of possible detection biases. Future redshift observations of SHBs may allow us to determine whether they are dominated by primordial or dynamically formed DNSs.