Predictions for the Rates of Compact Binary Coalescences Observable by Ground-based Gravitational-wave Detectors

TL;DR

This paper assembles an up-to-date, comprehensive catalog of predicted rates for compact-binary coalescences observable by ground-based detectors, covering NS-NS, NS-BH, BH-BH, IMRI, and IMBH-IMBH sources. It standardizes how merger rates (per MWEG, per $L_{10}$, or per Mpc$^3$) are converted into detection rates for Initial and Advanced LIGO-Virgo using horizon-distance volumes and a fixed SNR threshold, without presenting new rate calculations. The work emphasizes substantial uncertainties—driven by small pulsar samples and diverse population-synthesis models—and provides guidance on reporting plausible ranges (low, realistic, high) and their implications for detector planning and astrophysical inference. Overall, the document serves as a reference for rate predictions, their conversion to detectability, and the relative robustness of different formation channels, informing both instrumentation choices and the interpretation of potential detections.

Abstract

We present an up-to-date, comprehensive summary of the rates for all types of compact binary coalescence sources detectable by the Initial and Advanced versions of the ground-based gravitational-wave detectors LIGO and Virgo. Astrophysical estimates for compact-binary coalescence rates depend on a number of assumptions and unknown model parameters, and are still uncertain. The most confident among these estimates are the rate predictions for coalescing binary neutron stars which are based on extrapolations from observed binary pulsars in our Galaxy. These yield a likely coalescence rate of 100 per Myr per Milky Way Equivalent Galaxy (MWEG), although the rate could plausibly range from 1 per Myr per MWEG to 1000 per Myr per MWEG. We convert coalescence rates into detection rates based on data from the LIGO S5 and Virgo VSR2 science runs and projected sensitivities for our Advanced detectors. Using the detector sensitivities derived from these data, we find a likely detection rate of 0.02 per year for Initial LIGO-Virgo interferometers, with a plausible range between 0.0002 and 0.2 per year. The likely binary neutron-star detection rate for the Advanced LIGO-Virgo network increases to 40 events per year, with a range between 0.4 and 400 per year.

Figures (2)

• Figure 1: The total blue-light luminosity within a sphere of a given radius (top curve) and the accessible blue-light luminosity for a given horizon distance $D_{\rm horizon}$, taking location and orientation averaging into account (bottom curve). Gray shaded lines are cubic extrapolations. The inset shows the ratio between the top and bottom curves, which asymptotes to $2.26^3$, as discussed in the text. Reproduced from LIGOS3S4Galaxies by permission of the AAS.
• Figure 2: Noise amplitude spectral densities (ASDs) as a function of frequency. The Initial LIGO noise ASD (solid red curve) corresponds to the typical detector sensitivity as measured from data taken during the S5 run PSD:S5. The Advanced LIGO noise ASD (dashed magenta) represents a possible Advanced LIGO configuration with high laser power and zero detuning PSD:AL. The Initial Virgo noise ASD (dotted blue) was measured during Virgo's VSR2 run PSD:VSR2. The Advanced Virgo noise ASD (dash-dotted green) is based on the Advanced Virgo Baseline Design PSD:AV.