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

To critically assess the binary compact object merger model for short gamma ray bursts (GRBs) – specifically, to test whether the short GRB rates, redshift distribution and host galaxies are consistent with current theoretical predictions – it is necessary to examine models that account for the high-redshift, heterogeneous universe (accounting for both spirals and ellipticals). We present an investigation of predictions produced from a very large database of first-principle population synthesis calculations for binary compact mergers with neutron stars (NS) and black holes (BH), that sample a seven-dimensional space for binaries and their evolution. We further link these predictions to (i) the star formation history of the universe, (ii) a heterogeneous population of star-forming galaxies, including spirals and ellipticals, and (iii) a simple selection model for bursts based on flux-limited detection. We impose a number of constraints on the model predictions at different quantitative levels: short GRB rates and redshift measurements, and, for NS-NS, the current empirical estimates of Galactic merger rates derived from the observed sample of close binary pulsars. Because of the relative weakness of these observational constraints (due to small samples and measurement uncertainties), we find a small, but still substantial, fraction of models are agreement with available short GRB and binary pulsar observations, both when we assume short GRB mergers are associated with NS-NS mergers and when we assume they are associated with BH-NS mergers. Notably, we do not need to introduce artificial models with exclusively long delay times. Most commonly models produce mergers preferentially in spiral galaxies, in fact predominantly so, if short GRBs arise from NS-NS mergers alone. On the other hand, typically BH-NS mergers can also occur in elliptical galaxies (for some models, even preferentially), in agreement with existing observations. As one would expect, model universes where present-day BH-NS binary mergers occur preferentially in elliptical galaxies necessarily include a significant fraction of binaries with long delay times between birth and merger (often O(10Gyr)); unlike previous attempts to fit observations, these long delay times arise naturally as properties of our model populations. Though long delays occur, almost all of our models (both a priori and constrained) 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 strong selection bias towards successful follow-up of low-redshift short GRBs. Finally, if we adopt plausible priors on the fraction of BH-NS mergers with appropriate combination of spins and masses to produce a short GRB event based on Belczynski et al. (2007), then at best only a small fraction of BH-NS models could be consistent with all current available data, whereas NS-NS models do so more naturally. Subject headings: Stars: Binaries: Close; Gamma-ray bursts