Compact Binary Coalescence Sensitivity Estimates with Injection Campaigns during the LIGO-Virgo-KAGRA Collaborations' Fourth Observing Run

TL;DR

This paper presents a comprehensive framework and public data products for characterizing compact-binary coalescence sensitivity during LIGO-Virgo-KAGRA's fourth observing run (O4). It develops a hierarchical forward model linking astrophysical populations to detector data, and uses an extensive injection campaign to estimate detection probabilities via Monte Carlo importance sampling, enabling robust population inferences with large catalogs. The O4a campaign generated over $4.3\times 10^8$ injections and recovered more than $4.7\times 10^5$ detections across multiple searches, revealing both expected correlations from selection and subtler diurnal and sky-position effects; the authors provide detailed workflows, validation, and data products to support community use and future O4 campaigns. They also discuss injection design choices, effective sampling requirements, and practical considerations such as PSD variability, calibration, and potential truncation issues, with plans to extend to O4b and O4c and to deliver cumulative data products for broader scientific use.

Abstract

We describe the effort to characterize gravitational-wave searches and detector sensitivity to different types of compact binary coalescences during the LIGO-Virgo-KAGRA Collaborations' fourth observing run. We discuss the design requirements and example use cases for this data product, constructed from $> 4.33\times10^8$ injections during O4a alone. We also identify subtle effects with high confidence, like diurnal duty cycles within detectors. This paper accompanies a public data release of the curated injection set, and the appendixes give detailed examples of how to use the publicly available data.

Figures (13)

• Figure 1: Directed acyclic graph (DAG) showing the conditional (in)dependencies between variables involved in the construction of a catalog Essick:2023upv. Circles (nodes) represent individual variates, and arrows (directed edges) denote conditional dependencies. Shaded rectangles (plates) represent independently and identically distributed variables (i.e., $N_\mathrm{det}$ events and $N_\mathrm{ifo}\times N_\mathrm{det}$ data vectors, one in each IFO for each event). Red nodes and edges represent values that are recorded within the public data products GWTC-4-cumulative-injectionsGWTC-4-injections. Importantly, we record $p(\theta_e|\Lambda_\mathrm{inj})$ and $\theta_e$ for each event so that users can easily reweight samples to follow other populations within Monte Carlo sums; see Eq. \ref{['eq:Phat(D|Lambda)']} and Appendix \ref{['sec:using the data product']}.
• Figure 2: Reference power spectral densities (PSDs) used when constructing the O4 injection set and benchmarking the number of expected events. (left) Observed PSDs during O3 and (right) expected and observed PSDs during O4a. There is a separate trace for each LIGO's PSD during each month of O4a (May 2023 -- January 2024) as the injection sets were created on a monthly basis. See Appendix \ref{['sec:psd variability']} for more discussion about the impact of PSD variability.
• Figure 3: The distribution of the expected number of detections in O3 ($E_\mathrm{O3}$) given the observed number of detection in O3 ($N_\mathrm{O3}=63$ with FAR $<$ 1/year) and the distribution of the observed number of detections in 25 months of O4 ($N_\mathrm{O4}$) given $N_\mathrm{O3}$ based on semianalytic estimates for $P(\mathbb{D}|\Lambda)$Essick:2023toz. Annotations denote the maximum-likelihood and 90% highest-probability-density credible regions. We denote the distribution over $E_\mathrm{O3}$ with a line because it is continous, and we denote the distribution over $N_\mathrm{O4}$ with dots because it is discrete.
• Figure 4: Horizon (left axis) distance and (right axis) redshift as a function of detector-frame primary mass for equal-mass, maximally spinning/aligned-spin binaries using the expected LIGO PSD for O4 O4-projected-PSD with $\rho_\mathrm{opt,net} = 10$.
• Figure 5: Injected (blue) and recovered (orange) distributions for the O4a injection campaign for the (top left) source-frame primary mass, (bottom left) redshift, and primary spin (top right) magnitude and (bottom right) tilt or polar angle. An event is detected if at least one search reported FAR $< 1$/year. Shaded bands for $p(\cdot|\mathbb{D},\Lambda)$ represents 1-$\sigma$ uncertainty from the finite number of samples.