Short Gamma-Ray Bursts and Binary Mergers in Spiral and Elliptical Galaxies: Redshift Distribution and Hosts

To test whether the short GRB rates, redshift distribution and host galaxies are consistent with current theoretical predictions, we use avery large database of population synthesis calculations to examine BH-NS and NS-NS merger rates in the universe, factoring in (i) the star formation history of the universe, (ii) a heterogeneous population of star-forming galaxies, including spirals and ellipticals, and (iii) a simple flux-limited selection model for short GRB detection. When we require our models reproduce the known short GRB rates and redshift measurements (and, for NS-NS, the merger rates extrapolated from binary pulsars in the Galaxy), a small fraction of models reproduce all observations, both when we assume a NS-NS and a BH-NS origin for bursts. Most commonly models produce mergers preferentially in spiral galaxies if short GRBs arise from NS-NS mergers alone. Model universes where present-day binary mergers occur preferentially in elliptical galaxies necessarily include a significant fraction of binaries with long delay times between birth and merger (often $O(10{rm Gyr})$). Though long delays occur, almost all of our models predict that a higher proportion of short GRBs should occur at moderate to high redshift (e.g., $z>1$) than has presently been observed, in agreement with recent observations which suggest a selection bias towards successful follow-up of low-redshift short GRBs. Finally, if only a fraction of BH-NS mergers have the right combination of masses and spins to make GRBs, then at best only a small fraction of BH-NS models could be consistent with all {em current} available data. (Abridged)