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

This paper presents a self-consistent framework, implemented in the CHIMERA pipeline, to quantify how galaxy catalog incompleteness and host weighting schemes affect cosmological constraints from gravitational wave standard sirens, demonstrating that high-precision $H_0$ measurements remain achievable even with incomplete catalogs if appropriate stellar-mass weighting is applied.

Original authors: Nicola Borghi, Michele Moresco, Matteo Tagliazucchi, Giulia Cuomo

Published 2026-02-11

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CC BY 4.0

Original authors: Nicola Borghi, Michele Moresco, Matteo Tagliazucchi, Giulia Cuomo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Echo: Finding the Universe's Speedometer with "Ghost" Galaxies

Imagine you are standing in a massive, dark forest at night. Suddenly, you hear a loud thud in the distance. You know something heavy just hit the ground, but because it’s pitch black, you can’t see what caused it. However, you do have a flashlight, but it’s a bit weak—it only lights up a few trees at a time.

This is essentially the problem astronomers are facing when they listen to Gravitational Waves—ripples in the fabric of space-time caused by massive collisions, like two black holes smashing into each other.

The Goal: The Universe's Speedometer

Astronomers want to measure the Hubble Constant ( $H_0$ ). Think of this as the "Universal Speedometer." It tells us how fast the universe is expanding. If we know how fast things are moving away from us, we can figure out how old the universe is and how it will end.

To find this speed, we use "Standard Sirens." A gravitational wave is like a "siren" that tells us exactly how far away a collision happened. But there is a catch: the siren tells us the distance, but it doesn't tell us the speed (the redshift). To get the speed, we need to know which galaxy the collision happened in.

The Problem: The "Incomplete Catalog"

To find the host galaxy, astronomers use "Galaxy Catalogs"—essentially giant maps of where all the galaxies are. But these maps aren't perfect. They are like a blurry photo of the forest: you can see the big, bright trees, but the small, dim bushes are invisible.

In the paper, the researchers ask: "If our map is missing half the galaxies, can we still figure out the speed of the universe?"

The Discovery: The "Safety Net" Effect

You might think that if your map is missing half the galaxies, your calculations would be a total mess. But the researchers found something surprising using a supercomputer program they built called CHIMERA.

They discovered that even if the "map" is missing a lot of the smaller, dimmer galaxies, we can still get a very accurate reading of the universe's expansion. Here is why:

The Heavy Hitters Matter Most: Most black hole collisions likely happen in big, massive galaxies. Even if our map misses the "small bushes" (tiny galaxies), as long as we see the "big trees" (massive galaxies), we have enough information to get the job done.
The Mathematical Safety Net: The researchers found that even with a catalog that is only 50% complete, they could still reach a precision of 2%. That is like trying to guess the weight of a car while only being able to see half of it, and still being almost perfectly right.

The "Weighting" Trick

The paper also talks about "weighting." Imagine you are trying to guess the average height of people in a city, but you only have a list of basketball players. If you treat every person on that list as "average," your guess will be way too high.

In astronomy, if you assume a tiny galaxy is just as likely to host a black hole as a giant galaxy, your "speedometer" will be wrong. The researchers showed that if we "weight" our guesses—giving more importance to the big galaxies where black holes actually live—our results become incredibly robust and accurate.

Why This Matters

We are entering a golden age of astronomy. New telescopes (like Euclid and DESI) are currently mapping the sky. This paper gives scientists a "confidence boost." It tells them: "Don't worry if your maps aren't perfect. Even with some gaps and blurry spots, the gravitational waves will still lead us to the truth about how our universe is growing."

In short: Even if we can't see the whole forest, the loud thuds of colliding black holes are enough to tell us exactly how fast the woods are expanding.

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

1. Problem Statement

The "standard siren" method uses gravitational wave (GW) detections from compact binary coalescences (CBCs) to measure the Hubble constant ( $H_0$ ). Because GWs provide direct luminosity distance measurements but lack intrinsic redshift information, researchers use "dark siren" methods: statistically associating GW events with potential host galaxies in electromagnetic (EM) catalogs.

However, two major systematic challenges exist:

Catalog Incompleteness: Galaxy surveys are inherently limited by observational selection effects (e.g., magnitude or stellar mass limits), meaning many potential host galaxies are missing from the catalogs.
Host Weighting: BBH mergers are not distributed uniformly across all galaxies; they likely preferentially reside in galaxies with specific properties (e.g., higher stellar mass). If the relationship between BBH mergers and host properties is mismodeled or if the catalog is incomplete, it can introduce significant biases in cosmological parameters.

2. Methodology

The authors developed a self-consistent statistical framework to account for these effects, implemented in the updated CHIMERA (v2.1) pipeline.

Statistical Framework: They utilize a hierarchical Bayesian formalism that jointly constrains cosmological parameters ( $\lambda_c$ ) and astrophysical population parameters ( $\lambda_m, \lambda_z$ ).
Redshift Prior Construction: The core innovation is a redshift prior that incorporates both a catalog term (the observed galaxies) and a completeness term (the missing galaxies). They adopt a "homogeneous completion" approach, where missing galaxies are assumed to be distributed according to a theoretical background density derived from a redshift-evolving double Schechter stellar mass function.
Mock Data Generation:
- Galaxy Catalog: Derived from the MICE Grand Challenge (MICECATv2) simulation.
- GW Events: 100 BBH mergers are simulated for an LVK O5-like configuration (including a LIGO detector in India) with a signal-to-noise ratio (S/N) $> 25$ .
- Weighting Schemes: They test three stellar-mass weighting models: constant ( $\alpha_M=0$ ), linear ( $\alpha_M=1$ ), and quadratic ( $\alpha_M=2$ ).
- Incompleteness Simulation: They apply various stellar mass and $i$ -band magnitude cuts to simulate realistic survey limitations.

3. Key Contributions

CHIMERA v2.1: A publicly available, JAX-based, GPU-accelerated pipeline capable of handling massive galaxy catalogs and complex completeness functions.
Unified Modeling: A framework that bridges the gap between "complete" catalogs and "spectral sirens" (where no catalog is used), allowing for a continuous study of how precision degrades as completeness drops.
Quantification of Systematic Risks: A rigorous assessment of how mismodeling the host galaxy mass-weighting affects $H_0$ estimation.

4. Results

Precision with Complete Catalogs: With a perfect spectroscopic catalog, $H_0$ precision reaches 1.6%, 1.3%, and 0.9% for the constant, linear, and quadratic weighting schemes, respectively.
Robustness to Incompleteness:
- The precision degrades following a sigmoid trend as completeness decreases.
- Remarkably, 2% precision is still achievable even when the catalog contains only 50% of the potential hosts within the GW horizon.
- For quadratic weighting, 1% precision is maintainable even with significant incompleteness.
Parameter Correlations: At low completeness ( $<10\%$ ), a strong anti-correlation ( $\rho \approx -0.7$ ) emerges between $H_0$ and the BBH mass scale ( $\mu_g$ ). This correlation breaks once completeness exceeds $\sim 50\%$ , signaling the transition from the spectral siren regime to the dark siren regime.
Mismodeling Biases:
- In complete catalogs, incorrect weighting causes negligible bias.
- At moderate completeness ( $\sim 20\%$ ), assuming a weight that is too weak (e.g., constant weighting when the truth is linear) introduces significant biases ( $\sim 10 \text{ km s}^{-1} \text{ Mpc}^{-1}$ ).

5. Significance

This work provides a roadmap for future GW cosmology. It demonstrates that spectroscopic galaxy surveys (like DESI and Euclid) are highly effective for standard siren science, even if they are not perfectly complete. The findings suggest that the "dark siren" method is more resilient to catalog incompleteness than previously feared, provided that the weighting of massive galaxies is correctly prioritized. This provides a strong science case for upcoming facilities like the Wide-Field Spectroscopic Telescope (WST) and third-generation GW detectors.