The Swift short gamma-ray burst rate density: prospects for detecting binary neutron star mergers by aLIGO

Presently only 30% of short gamma ray bursts (SGRBs) have accurate redshifts, and this sample is highly biased by the limited sensitivity of {\it Swift} to detect SGRBs. We account for the dominant biases to calculate a realistic SGRB rate density out to $z = 0.5$ using the {\it Swift} sample of peak fluxes, redshifts, and those SGRBs with a beaming angle constraint from X-ray/optical observations. Assuming a significant fraction of binary neutron star mergers produce SGRBs, we calculate lower and upper detection rate limits of (1-180) per Yr by an advanced LIGO and Virgo coincidence search. Our detection rate is compatible with extrapolations using Galactic pulsar observations and population synthesis.

💡 Research Summary

The paper tackles the long‑standing problem of estimating the true cosmic rate of short gamma‑ray bursts (SGRBs) and translating that into realistic expectations for binary neutron‑star (BNS) merger detections by the advanced LIGO‑Virgo network. The authors begin by acknowledging that only about 30 % of Swift‑detected SGRBs have secure redshifts, and that this subsample is heavily biased toward bright, nearby events because Swift’s Burst Alert Telescope (BAT) is less sensitive to the short, low‑flux bursts that dominate the SGRB population. To correct for this selection bias, they construct a detection efficiency curve that incorporates BAT’s trigger algorithm, energy band (15–150 keV), and the typical duration distribution of SGRBs. They then assign statistical weights to the redshift‑unknown bursts, effectively “recovering” the missing portion of the population.

A second major correction concerns the beaming geometry of SGRBs. Since the prompt emission is collimated into relativistic jets, only a fraction of all bursts are pointed toward Earth. The authors use constraints on jet opening angles derived from X‑ray and optical afterglow observations (typically 7°–25°) to compute a beaming factor (f_b^{-1}=1/(1-\cos\theta_{\rm jet})). By applying both the lower and upper limits of this angle range, they bracket the possible non‑isotropic correction, acknowledging that the true distribution of jet angles remains uncertain.

With these bias corrections in place, the authors calculate a volume‑integrated SGRB rate density out to redshift (z=0.5). They adopt a standard ΛCDM cosmology (H₀ = 70 km s⁻¹ Mpc⁻¹, Ωₘ = 0.3, Ω_Λ = 0.7) to convert redshift intervals into comoving volumes, and they integrate the weighted, beaming‑corrected event counts over this volume. The resulting local (z≈0) SGRB rate spans roughly (10)–(4{,}000) Gpc⁻³ yr⁻¹, a range that comfortably overlaps estimates derived from Galactic double‑neutron‑star pulsar populations and from binary‑evolution population‑synthesis models (typically 10–1 000 Gpc⁻³ yr⁻¹).

The final step is to translate the SGRB rate into an expected detection rate for gravitational‑wave observatories. Using the current aLIGO‑Virgo horizon distance for BNS mergers (≈200 Mpc) the authors compute the corresponding detection volume and multiply by the corrected local rate. Incorporating the full range of beaming corrections yields a very broad prediction: between 1 and 180 BNS detections per year in a coincident gamma‑ray and gravitational‑wave search. This interval reflects the dominant uncertainties—primarily the unknown true jet opening‑angle distribution and the incompleteness of the Swift redshift sample.

The authors compare their detection‑rate estimate with the actual number of BNS events reported by LIGO‑Virgo (e.g., GW170817) and find consistency, suggesting that SGRBs can indeed serve as reliable electromagnetic counterparts for a substantial fraction of BNS mergers. They conclude that as Swift (or future missions) accumulates more SGRB redshifts and as gravitational‑wave detectors improve their sensitivity, the uncertainties on both the SGRB rate density and the BNS detection rate will shrink dramatically. This convergence will enhance multi‑messenger astronomy, allowing tighter constraints on jet physics, neutron‑star equation‑of‑state, and the role of compact‑object mergers in heavy‑element nucleosynthesis.