Supplement: The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914

TL;DR

This paper details the methodology and analysis used to estimate the rate of binary black hole mergers from Advanced LIGO data around GW150914, providing a comprehensive account of their search pipeline, likelihood derivation, and sensitivity estimation.

Contribution

It introduces a detailed methodology for inferring BBH merger rates from LIGO data, including likelihood formulation, search pipeline, and calibration uncertainty modeling.

Findings

Estimated BBH merger rate range: 2–600 Gpc^{-3} yr^{-1}

Developed a calibrated analytic method for detector sensitivity estimation

Provided detailed computational and methodological framework for rate inference

Abstract

Supplemental information for a Letter reporting the rate of binary black hole (BBH) coalescences inferred from 16 days of coincident Advanced LIGO observations surrounding the transient gravitational wave signal GW150914. In that work we reported various rate estimates whose 90\% credible intervals fell in the range $2$--$600 \, \mathrm{Gpc}^{-3} \mathrm{yr}^{-1}$. Here we give details of our method and computations, including information about our search pipelines, a derivation of our likelihood function for the analysis, a description of the astrophysical search trigger distribution expected from merging BBHs, details on our computational methods, a description of the effects and our model for calibration uncertainty, and an analytic method of estimating our detector sensitivity that is calibrated to our measurements.