Echoes from the dark: Galaxy catalog incompleteness in standard siren cosmology

TL;DR

This work tackles how galaxy catalog incompleteness influences standard siren cosmology and $H_0$ measurements using gravitational waves from binary black holes. It develops a self-consistent hierarchical Bayesian framework that integrates population models, redshift priors from galaxy catalogs, and a formal treatment of incompleteness through a completeness function and homogeneous completion, all implemented in the CHIMERA pipeline. Forecasts for 100 O5-like BBH events show percent-level $H_0$ constraints with complete spectroscopic catalogs, with a sigmoid-like degradation as completeness decreases; notably, a 2% precision is achievable at about 50% average completeness, and 1% precision requires host probabilities to scale as $M_ullet^{2}$. These results underscore the importance of spectroscopic galaxy surveys for standard siren cosmology and provide a practical framework for optimizing future facilities and survey strategies, including possible extensions to higher redshift and photometric redshift handling.

Abstract

Gravitational wave observations can be combined with galaxy catalogs to constrain cosmology and test modified gravity theories using the standard siren method. However, galaxy catalogs are intrinsically incomplete due to observational limitations, potentially leaving host galaxies undetected, thereby weakening constraints and potentially introducing systematic errors. In this work, we present a self-consistent framework to study catalog incompleteness and host weighting effects, implemented in the publicly available CHIMERA pipeline. We obtain joint cosmological and astrophysical population constraints from 100 binary black hole (BBH) events in a LIGO-Virgo-KAGRA O5-like configuration using spectroscopic galaxy catalogs with varying completeness levels and stellar-mass host weighting schemes. We find percent-level constraints on $H_0$ with complete catalogs, reaching precisions of 1.6%, 1.3%, and 0.9% for constant, linear, and quadratic mass weighting, respectively. As completeness decreases, the precision degrades following a sigmoid trend, with a threshold and steepness that increase for stronger weightings. Simultaneously, the correlation between $H_0$ and the BBH population mass scale increases, making results more sensitive to assumptions about the astrophysical population. Remarkably, 2% precision remains achievable even when catalogs contain only 50% of the potential host galaxies within the gravitational wave detection horizon, while 1% precision requires host probabilities scaling with stellar mass squared. The results are robust against host weighting mismodeling, even at moderate completeness levels. This work further highlights the importance of spectroscopic galaxy surveys in standard siren cosmology and provides a pathway for developing the science case of future facilities.

Figures (9)

• Figure 1: Effects of galaxy catalog incompleteness within the CHIMERA framework. (a) Sky localization and pixelization (represented with the grid) for a GW event from a stellar mass-weighted MICECATv2 catalog (the underlying blue points). The marker shows the host true position and pixel, from which the distributions in the subsequent panel are computed. (b) Catalog redshift distribution for complete (light blue), $i<22$ cut (blue), and empty catalogs (dark blue flat line). The arrow shows the true host redshift. (c) Completion terms accounting for missing galaxies; dark blue shows the background distribution used in standard siren constraints. (d) Resulting galaxy distribution terms, individually normalized for better comparison.
• Figure 2: Stellar mass and redshift distribution of the parent galaxy catalog. Left panel: Stellar mass function in different redshift bins measured from the original MICECATv2 galaxy catalog. The points indicate the peak number density at each redshift bin. Central panel: Theoretical stellar mass function modeled as a double Schechter function evolving in redshift. Right panel: Redshift distribution of the parent galaxy catalog. The black line shows the theoretical distribution obtained from the product of the cosmological volume element dominating at low-$z$ (dotted orange line) and the integral of the Schechter damping the distribution at high-$z$ (dotted purple line). The bottom panel shows the percentage difference, highlighting the median (gray line) and the 16-84 percentile range (gray band).
• Figure 3: Host galaxy weighting schemes considered in this work: constant (gray), linear (blue), and quadratic (red) mass weighting. For comparison, we show the $z=0.1$ trend from Artale2020 (dotted blue line) and the cut used in previous work Borghi2024.
• Figure 4: Main properties of 100 O5-like BBH events with $\mathrm{S/N} > 25$ drawn from MICECATv2 with three host weighting schemes: unweighted (mock0, gray), weighted by stellar mass (mock1, blue), and weighted by stellar mass squared (mock2, red). Top panels: Distribution in the sky localization ($90\%$ C.L.) versus luminosity-distance uncertainty plane color-coded by the network $\mathrm{S/N}$. Bottom panels: Distributions of source redshift, number of galaxies within the localization volume ($N_{\mathrm{gal,vol}}$), host galaxy stellar mass, and $i$-band magnitude for the various samples; the arrows indicate the median values. The dot-dashed lines show the background redshift distribution of potential BBH host galaxies used to generate GW events. The vertical dashed line shows the mass and magnitude cuts that are applied in this work to study incompleteness effects.
• Figure 5: Effects of galaxy survey incompleteness on $H_0$ constraints for different stellar mass (left panel) and $i$-band magnitude (right panel) completeness cuts across three host weighting schemes: unweighted (mock0, gray), weighted by stellar mass (mock1, blue), and weighted by stellar mass squared (mock2, red). The values annotated below each panel indicate the number of host galaxies retained in the catalog after applying each cut.