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

We combine a large database of population synthesis calculations, models for the star formation history of the universe, and a simple selection model for bursts to predict short GRB detection rates, redshift distributions, and host galaxy distributions. We compare our space of possible models with observations of short GRBs (rates and redshifts) and, when assuming short GRBs are produced from NS-NS binaries, the current estimates for NS-NS merger rates from close binary pulsars in the Milky Way. Whether short GRBs are assumed to arise from BH-NS or NS-NS mergers, we conclude that a fraction of models are in agreement with available short GRB and binary pulsar observations. We do not need to introduce artificial models with long delay times. Most commonly, models produce mergers preferentially in spiral galaxies if short GRBs arise from NS-NS mergers alone. On the other hand, typically BH-NS mergers can also occur in elliptical galaxies, in agreement with existing observations. We expect 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 strong selection bias toward successful follow-up of low-redshift short GRBs. Finally, if we add plausible additional assumptions about what BH-NS mergers could produce short GRBs based on the work of Belczynski and coworkers, then we expect only a small fraction of BH-NS models could be consistent with all current available data.