⚛️ general relativity

One Year and One Night to 1% in $\mathbf{H_0}$ : Efficient Spectroscopic Strategy for Dark Siren Cosmology

This paper proposes an efficient spectroscopic strategy requiring just one to five nights of follow-up observations to achieve a 1% precision measurement of the Hubble constant ( $H_0$ ) using dark siren events from the LIGO-India network at A# sensitivity.

Original authors: Yixuan Dang, Ariel J. Amsellem, Ignacio Magaña Hernandez, Antonella Palmese, B. S. Sathyaprakash

Published 2026-07-21

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CC BY 4.0

Original authors: Yixuan Dang, Ariel J. Amsellem, Ignacio Magaña Hernandez, Antonella Palmese, B. S. Sathyaprakash

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

Imagine the universe as a giant, expanding balloon. For decades, scientists have been trying to measure exactly how fast this balloon is inflating right now. This speed is called the Hubble constant, and knowing it is crucial because it tells us the universe's age, its size, and its ultimate fate. But here's the twist: when scientists measure this speed using the "baby pictures" of the universe (the cosmic microwave background), they get one number. When they measure it using "adult" stars and supernovae nearby, they get a different, slightly faster number. This disagreement is a massive headache in physics, a tension that suggests our current understanding of the universe might be missing a piece of the puzzle.

To solve this, scientists are turning to a new kind of cosmic ruler: gravitational waves. These are ripples in space-time caused by massive objects crashing together, like two black holes merging. When these waves hit Earth, they tell us exactly how far away the crash happened (the distance). But to calculate the expansion speed, we also need to know how fast the crash is moving away from us (the redshift). Usually, we find this by looking at the light from the galaxy where the crash happened. However, black hole mergers are "dark"—they don't emit light. So, scientists have to play a cosmic game of "Where in the galaxy did this happen?" by looking at a map of all the galaxies in that direction and guessing which one is the host. This is the "dark siren" method. The problem is, if the map of galaxies is incomplete or fuzzy, the guess is bad, and the answer to the expansion rate is wrong.

This paper is about making that map sharper and the game faster. The authors, a team of physicists, asked a simple but tricky question: How deep do we need to look into the universe to get a perfect answer? Do we need to find every tiny, faint galaxy in the sky, or is it enough to just find the bright, easy-to-see ones? They ran massive computer simulations to test this, acting like a cosmic detective agency planning a one-year mission.

Their main finding is surprisingly efficient: you don't need to dig as deep as you thought. They discovered that to measure the universe's expansion rate with incredible precision (about 1% accuracy), you only need to build a catalog of galaxies that are brighter than a specific limit (an apparent magnitude of $r \sim 19$ ). You don't need to hunt for the faintest, most distant galaxies (which would require looking down to $r \sim 24$ ). Going that deep would cost a fortune in telescope time and money, but their simulations show it wouldn't actually improve the answer much.

The paper argues that if you focus your telescope time on just the ten best-localized black hole mergers that happen in a single year, and you only map the galaxies down to that $r \sim 19$ limit, you can get an unbiased, high-precision measurement. In fact, they found that using a catalog this "shallow" (relatively speaking) is just as good as using a super-deep one for these specific, well-localized events. If you try to use a catalog that is even shallower than $r \sim 19$ , you start to miss galaxies entirely, and your answer becomes unreliable. But once you hit $r \sim 19$ , you've reached the sweet spot.

The authors also calculated the "cost" of this strategy in terms of time. They found that with the next generation of gravitational wave detectors (specifically the LIGO Hanford, Livingston, and LIGO-India network), a team could gather all the necessary data in as little as one night of telescope observations, or perhaps five nights if they want to be super cautious. This makes the project feasible for real-world telescopes like DESI or Subaru, which can scan the sky quickly.

However, the paper is careful to note that these results come from simulations, not a finished experiment. They simulated millions of galaxies and thousands of black hole collisions to predict what would happen. They also found that if you ignore the mass of the galaxies (treating a tiny dwarf galaxy the same as a giant one), your results get slightly fuzzier, so you do need to be careful about which galaxies you count. They also spotted a tiny, unexplained wobble in their numbers where the answer was slightly off-center, but they suspect it's just a small glitch in how they simulated the distances, not a fundamental flaw in the method.

In short, this paper suggests that we don't need to spend years mapping the entire universe to solve the Hubble tension. Instead, we can be smart and efficient: grab the ten best black hole crash sites of the year, point our telescopes at the bright galaxies around them for just a few nights, and we might finally get the precise answer we've been chasing for decades. It's a strategy that trades brute force for clever targeting, promising to turn the "dark siren" method into a powerful tool for understanding our expanding universe.

Technical Summary: One Year and One Night to 1% in H0

Problem Statement
The Hubble constant ( $H_0$ ) remains a subject of significant tension in cosmology, with measurements from the Cosmic Microwave Background (CMB) and the local distance ladder differing by $\sim 5\sigma$ . Gravitational-wave (GW) standard sirens offer an independent route to resolve this tension. While "bright sirens" (events with electromagnetic counterparts) provide direct constraints, the majority of compact binary coalescences (CBCs), particularly binary black hole (BBH) mergers, lack detectable electromagnetic counterparts. These "dark sirens" require statistical association with galaxies in a redshift catalog within the GW localization volume.

Current dark siren analyses rely on photometric catalogs (e.g., GLADE+, DES) which suffer from incompleteness in depth or sky coverage and large photometric redshift uncertainties ( $\sigma_z \sim 10^{-2}$ ). While spectroscopic redshifts ( $\sigma_z \sim 10^{-3}–10^{-4}$ ) offer superior precision, the optimal depth for a volume-limited galaxy catalog and the observational cost of achieving complete spectroscopic coverage for well-localized events have not been systematically quantified. Specifically, it is unclear if shallow catalogs (e.g., $r \sim 19$ ) introduce bias or underestimate uncertainty compared to deeper catalogs ( $r \sim 24$ ), and whether a feasible spectroscopic campaign exists to achieve sub-2% precision on $H_0$ .

Methodology
The authors employ a Bayesian statistical framework to infer $H_0$ from a collection of $N_{GW}$ GW events using a galaxy catalog (CAT). The posterior probability is constructed from the joint likelihood of GW strain data and the probability of host galaxy identification within the catalog.

Simulations and Injections:
- A simulated galaxy catalog was constructed using the Uchuu- $\nu^2$ GC dark matter N-body simulation, assigning galaxy properties via semi-analytic models.
- The simulation generated a lightcone extending to redshift $z=0.5$ , including galaxies with $i$ -band magnitude up to 24.1.
- $245,760$ galaxies were drawn and weighted by stellar mass to preferentially select massive galaxies as potential BBH hosts.
- BBH merger properties (mass, spin) were assigned using Broken Power Law + 2 Peaks and Gaussian Component Spin models. The merger rate followed the Madau-Dickinson star formation history.
- GW parameters were estimated using Fisher matrices (GWBENCH) and refined via Bayesian inference (Bilby) with the IMRPhenomXPHM waveform family.
Networks and Event Selection:
- Two detector network configurations were analyzed:
  - HLI#: LIGO Hanford, LIGO Livingston, and LIGO-India at A# sensitivity.
  - HLV+: LIGO Hanford, LIGO Livingston, and Virgo at A+ sensitivity.
- From 10 years of simulated observations, the best-localized events (defined by sky area $\Delta\Omega_{90}$ ) were selected. The study focuses on the top 10 best-localized events observed in a single year.
Catalog Depth Analysis:
- The authors varied the apparent magnitude limit ( $r_{app}$ ) of the volume-limited catalog from $r=17.5$ to $r=24$ .
- They assessed the fractional uncertainty ( $\sigma_{H_0}/H_0$ ) and the statistical bias (offset of the posterior median from the injected value) for different numbers of events (3, 5, 10, 15).
Observational Cost Estimation:
- The paper evaluates the telescope time required to obtain spectroscopic redshifts for the 10 best-localized events.
- Multiple facilities were modeled: DESI, Subaru/PFS, HET/VIRUS, AAT/2dF, 4MOST, and Magellan/IMACS.
- Exposure times and overheads were calculated based on instrument specifications, target densities, and fiber/slit capacities.

Key Contributions and Results

Optimal Catalog Depth:
- The study demonstrates that for well-localized events, a shallow volume-limited catalog with an apparent magnitude limit of $r \ge 19$ does not underestimate the uncertainty in $H_0$ compared to a much deeper catalog ( $r \sim 24$ ).
- For the top 10 best-localized events, the median precision improves only marginally from $0.92\%$ at $r=17.5$ to $1.0\%$ at $r=24$ .
- However, catalogs shallower than $r=19$ show significant statistical instability and potential bias, as some events may match zero galaxies, leading to uninformative posteriors. Thus, $r=19$ is identified as the optimal trade-off between depth and stability.
Precision and Bias:
- A# Network (HLI#): Combining the 10 best-localized events from one year yields an unbiased measurement of $H_0$ with a median precision of $0.98^{+0.56}_{-0.32}\%$ . The 84th percentile of the precision distribution is $1.54\%$ , safely below the 2% target. The measurement is statistically unbiased, with the median offset from the injected value being consistent with zero ( $-0.03^{+0.15}_{-0.45}\%$ ).
- A+ Network (HLV+): Using the same 10-event strategy with the HLV+ network yields a median precision of $2.63^{+1.87}_{-1.53}\%$ . Only 32% of realizations reach the 2% goal, though 88% reach 5% or less.
Observational Feasibility:
- A dedicated spectroscopic follow-up campaign for the 10 best-localized events requires a minimum of one night of telescope time under optimal conditions.
- Under conservative assumptions (accounting for scheduling, overheads, and varying target densities), the campaign requires approximately five nights (totaling $\sim 20.5$ hours).
- Instruments like DESI, Subaru/PFS, and Magellan/IMACS are capable of completing this survey in a single night, while HET/VIRUS is slower but uniquely suited for regions lacking pre-existing photometric catalogs.

Significance and Claims
The paper claims to identify a highly efficient, feasible strategy for achieving a sub-1% measurement of the Hubble constant using dark sirens. The primary significance lies in demonstrating that:

Cost-Effectiveness: Achieving high-precision cosmology does not require deep, all-sky spectroscopic surveys. A targeted, shallow ( $r \sim 19$ ) spectroscopic follow-up of only the 10 best-localized events per year is sufficient.
Feasibility: The required observational time (1–5 nights) is well within standard telescope allocation limits, making this strategy immediately actionable for the upcoming A# and A+ observing runs.
Robustness: The results are robust against the depth of the catalog (provided $r \ge 19$ ) and the specific weighting of host galaxy stellar mass, offering a practical path to resolving the Hubble tension without waiting for future generations of GW detectors or massive spectroscopic surveys.

The authors note that peculiar velocities introduce a small additional redshift uncertainty and that roughly 20% of well-localized events fall within the zone of avoidance, which would extend the required observation period proportionally. However, the core conclusion remains that a "one year, one night" (optimistically) or "one year, five nights" (conservatively) campaign can deliver a precise, unbiased $H_0$ measurement.

Technical Summary: One Year and One Night to 1% in H0

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