Identifying Host Galaxies of Binary Black Hole Mergers with Next-Generation Gravitational Wave Detector Networks

TL;DR

This work evaluates the feasibility of identifying host galaxies for BBH mergers with next-generation GW detector networks by injecting BBH signals into nearby M_* galaxies and quantifying 3D localization volumes. Using Fisher-information-based parameter estimation via BILBY and two injection grids, the authors compare realized localization volumes against theoretical comoving-volume thresholds derived from the galaxy stellar mass function, including metallicity- and dynamical-weighted variants. They find that networks including ET, CE, and LIGO-India can localize many events to volumes smaller than these thresholds, enabling unique host identifications out to ~1000 Mpc at rates approaching ~100 per year, with even better performance for higher-mass BBHs and favorable sky positions. The framework also supports population-level constraints on BBH formation channels and can be extended to account for galaxy catalog completeness and additional channels such as AGN-disk formation or lensing, offering a path to meaningful BBH environment studies and cosmological measurements such as the Hubble constant $H_0$.

Abstract

Identifying the host galaxy of a binary black hole (BBH) merger detected via gravitational waves (GWs) remains a challenge due to the absence of electromagnetic counterparts and the large localization volumes produced by current-generation detectors. A confident host association would provide stellar population properties to constrain BBH formation channels and enable measurements of cosmological parameters such as the Hubble constant, H0. We simulate BBH mergers in nearby (z<0.25) host galaxies to evaluate the feasibility of host identification with future GW detector networks, including configurations with the planned LIGO-India detector and third-generation detectors such as the Einstein Telescope (ET) and Cosmic Explorer (CE). We construct two injection grids to explore variations in BBH mass, distance, and directional sensitivity, and infer localization volumes using the Fisher Information Matrix (FIM)-based parameter estimation implemented through BILBY. To assess the prospects for unique host identification, we introduce a set of diagnostics: theoretical comoving volume thresholds for galaxies of a given stellar mass, derived from galaxy stellar mass functions, a metallicity-based volume threshold motivated by progenitor environment models, stellar mass fractions to quantify candidate host prominence, and the probability of chance alignment (p_c). These metrics provide ways to evaluate host associations and constrain BBH formation channels. We find that future networks that include ET and CE localize BBH mergers to volumes smaller than those theoretical thresholds, implying potentially unique host identification, out to ~1000 Mpc at a rate of ~100 yr^{-1}. While associations for individual events may remain uncertain, our framework is well-suited to population-level analyses, enabling constraints on BBH formation scenarios in the era of next-generation GW detector networks.

Figures (12)

• Figure 1: Heatmap of the network optimal SNRs for the injected BBH mergers across masses and distances. Black vertical lines separate Grids I and II (maximum and minimum sensitivity), and the white vertical lines separate the GW detector networks. Each triplet of columns within a network corresponds to distances of 500, 750, and 1000 Mpc (left to right), and rows correspond to mass configurations from 50+50 $\mathrm{M}_\odot$(top) to 5+5 $\mathrm{M}_\odot$(bottom). The colourbar indicates the logarithm of the network optimal SNR, with lighter shades corresponding to higher SNR values. The network optimal SNR is calculated as $\rho_{\rm network} = \sqrt{\sum_j \rho_j^2}$, where $\rho_j$ is the optimal matched-filter SNR in detector $j$.
• Figure 2: Antennae pattern maps for the three GW detector networks considered in this study: (A) HLVKIEC, (B) HLV, and (C) EC. Each panel shows the combined network antenna amplitude response, defined as $\sqrt{\sum_j F_{+,j}^2 + F_{\times,j}^2}$finn20012011schutz, as a function of sky position in equatorial coordinates at time t. The red, green, and blue crosses mark the locations of the three injected $\mathrm{M}_*$ galaxies at 1000 Mpc, 750 Mpc, and 500 Mpc (Table \ref{['tab:injected_hosts']}), respectively, used in Grid I. The lime green and white circles denote the “bright” (maximum sensitivity) and “dark” (minimum sensitivity) sky locations in panels (A) and (C) (Table \ref{['tab:bright_dark_points']}), respectively, selected based on the network antenna pattern and used in Grid II.
• Figure 3: Weighted and unweighted GSMFs at $z = 0.2$; The black curve shows the original GSMF $\Phi(M)$ (Equation \ref{['schechter']}), modeled using a redshift-interpolated double Schechter function. The blue curve, $\Phi^{\rm iso}(M)$ (Equation \ref{['phi_iso']}), represents the mass function weighted by a BBH merger efficiency model for the isolated formation channel, normalized over stellar mass. The red curve, $\Phi^{\rm dyn}(M)$ (Equation \ref{['phi_dyn']}), is weighted by a globular cluster (GC) scaling relation to represent dynamical BBH formation.
• Figure 4: Minimum comoving volumes $V_{\min}$ required to contain, on average, one galaxy of mass $M$ as a function of galaxy stellar mass and redshift. Each panel corresponds to a different injected host at distances of 500 Mpc, 750 Mpc, and 1000 Mpc. Coloured curves show $V_{\min}(M)$ (Equation \ref{['vmin_eqn']}) scaled by different values of $\lambda$. The black dashed line denotes the fiducial case of $\lambda = 1$. The vertical blue dashed line marks the mass of the injected $\mathrm{M}_*$ galaxy (Grid I, Table \ref{['tab:injected_hosts']}), while the horizontal blue dashed line indicates the corresponding $V_{\min}$ value at that mass. All three curves assume the redshift-dependent GSMF $\Phi (M, z)$ (Equation \ref{['schechter']}).
• Figure 5: Localization volumes for simulated BBH mergers in Grid I, at luminosity distances of 500, 750, and 1000 Mpc (Panels a–c). For each mass configuration and network: HLVKIEC (red), HLV (blue), EC (green), we plot $V_{50}$(hollow marker) and $V_{90}$(filled marker), with a vertical line connecting the two. Horizontal shaded bands indicate the minimum comoving volume required to contain, on average, one galaxy of mass $\mathrm{M}_*$ or higher under three different BBH formation channel assumptions: $V_{\min}$ (gray, Equation \ref{['vmin_eqn']}), $V_{\min}^{\mathrm{iso}}$ (blue), and $V_{\min}^{\mathrm{dyn}}$ (red). These threshold comoving volumes were computed within a redshift range of $z = 0.12$ and $z = 0.23$, corresponding to the injected $\mathrm{M}_*$ hosts (Table \ref{['tab:vmin_channels']}). The dashed purple horizontal line corresponds to the metallicity-dependent minimum comoving volume, $V^Z_{\min}$ = 370.70 $\rm Mpc^3$, as calculated in Section \ref{['metallicity']}.