The Local Rate and the Progenitor Lifetimes of Short-Hard Gamma-Ray Bursts: Synthesis and Predictions for LIGO

The recent discovery of the first four afterglows of short-hard gamma-ray bursts (SHBs), suggests that they typically result from long-lived progenitor systems. The most popular progenitor model invokes the merger of either double neutron star (DNS) binaries or neutron star-black hole (NS-BH) systems. Such events are strong sources of gravitational-waves (GWs) and might be detected by ground-based GW observatories. In this work we combine the census of SHB observations with refined theoretical analysis to perform a critical evaluation of the compact binary model. We then explore the implications for GW detection of these events. Beginning from the measured star-formation rate through cosmic time, we consider what intrinsic luminosity and lifetime distributions can reproduce the known SHB redshifts and luminosities as well as the peak flux distribution of the large BATSE SHB sample. We find that: (1) The typical progenitor lifetime is long. Assuming lognormal lifetime distribution the typical lifetime is >4[1] Gyr (2[3]\sigma c.l.). If the lifetime distribution is a power-law with index \eta then \eta>-0.5 [-1] (2[3] \sigma c.l.). This result is difficult to reconcile with the properties of the observed galactic DNS population, suggesting that if SHBs do result from DNS mergers then the observed galactic binaries do not represent the cosmic one. (2) We find that the local rate of SHBs is larger than 10Gpc^-3/yr and may be higher by several orders of magnitude, significantly above previous estimates. (3) Assuming that SHBs do result from compact binaries, our predictions for the LIGO and VIRGO event rates are encouraging: The chance for detection by current facilities is not negligible, while a coincident detection of GW and electromagnetic radiation from an SHB is guaranteed for next-generation observatories.