arxiv: 2604.11871 · v1 · submitted 2026-04-13 · 🌀 gr-qc · astro-ph.HE· astro-ph.IM

Recognition: unknown

Not too close! Evaluating the impact of the baseline on the localization of binary black holes by next-generation gravitational-wave detectors

Alessandra Corsi, B. S. Sathyaprakash, Digvijay Wadekar, Emanuele Berti, Francesco Iacovelli, Luca Reali

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:22 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEastro-ph.IM

keywords gravitational wavesbinary black holessky localizationnext-generation detectorsCosmic Explorertiming triangulationnetwork baselinesEinstein Telescope

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The pith

Baselines of 2300-3300 km give mostly usable sky localizations for binary black holes in next-generation detector networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests how the separation between next-generation gravitational-wave detectors changes the accuracy of sky positions recovered for binary black hole mergers. Because most of these signals last only minutes in the detectors' sensitive band, position is recovered mainly from the small arrival-time difference between sites. Simulations of both fixed events and a realistic population drawn from current observations show that light-travel times of 8-11 ms produce predominantly single-peaked or double-peaked sky maps. These maps remain useful for electromagnetic follow-up and for linking events to host galaxies. Shorter baselines produce many ambiguous, multimodal maps, especially for loud signals, while adding a third detector largely removes the ambiguity.

Core claim

In a two-detector Cosmic Explorer network, baselines corresponding to light travel times of 8-11 ms (~2300-3300 km) offer a reasonable compromise for localizing binary black holes with detector-frame total masses up to ~100 solar masses, yielding predominantly unimodal or bimodal sky maps suitable for follow-up observations. Shorter baselines degrade performance, especially at high signal-to-noise ratio. Networks including a third detector, such as LIGO-India or the Einstein Telescope, substantially reduce multimodality.

What carries the argument

Timing triangulation across the light-travel-time baseline between detectors, which converts measured arrival-time differences into sky-position constraints for signals that remain in band for only a few minutes.

If this is right

Shorter baselines significantly degrade localization, particularly for high signal-to-noise events.
A network of two Cosmic Explorers plus LIGO-India yields unimodal posteriors for a good fraction of events.
Two Cosmic Explorers plus the Einstein Telescope yields unimodal posteriors for essentially all events.
Baselines of 8-11 ms support both electromagnetic follow-up and statistical host-galaxy cross-correlation studies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Network planners may need to accept some logistical cost to achieve separations near 3000 km rather than clustering facilities more closely.
Statistical host-galaxy studies could still proceed if the fraction of events with usable (unimodal or bimodal) maps remains high.
The large improvement from adding a third distant detector suggests prioritizing global distribution over concentrating multiple next-generation instruments in one region.

Load-bearing premise

Localization of most binary black hole signals will continue to rely primarily on timing triangulation because the signals spend at most a few minutes in the sensitivity band.

What would settle it

A high signal-to-noise binary black hole event recorded on a short-baseline two-detector network that still shows persistent multimodal sky localization after full parameter estimation.

Figures

Figures reproduced from arXiv: 2604.11871 by Alessandra Corsi, B. S. Sathyaprakash, Digvijay Wadekar, Emanuele Berti, Francesco Iacovelli, Luca Reali.

**Figure 2.** Figure 2: FIG. 2. SNR distribution of 100 realizations of a 1 yr BBH [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Mollweide projections of the absolute value of the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Upper panels: Fraction of the points in the sky exhibiting a sky localization posterior with at most two distinct modes [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Same as in the top and bottom rows of Fig. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Fraction of the points in the sky exhibiting a uni [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Fraction of points in the sky exhibiting a unimodal sky localization posterior as a function of detector-frame mass for [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Scatter plots of the sky localization and relative statistical uncertainty attainable on the luminosity distance at 90% [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Fraction of events with a given number of modes in the sky localization posterior for combinations of two CE [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Fraction of the points in the sky exhibiting a unimodal sky localization posterior as a function of the detector frame [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. Scatter plot of the relative difference in localization [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗

read the original abstract

Next-generation (XG) gravitational-wave detectors, such as Cosmic Explorer (CE) and the Einstein Telescope (ET), will observe compact binary coalescences at unprecedented rates and signal-to-noise ratios (SNRs). Accurate sky localization of these sources is crucial for several aspects of the science case of CE and ET. The localization of most binary black hole (BBH) signals, which will spend at most a few minutes within the XG detector's effective sensitivity band, will continue to rely primarily on timing triangulation across a network of detectors. A key design choice for triangulation is the baseline between instruments. We investigate how the baseline affects the localization capabilities of a two-detector CE network, analyzing both fixed-parameter injections and a realistic BBH population consistent with the latest GWTC-4 results. For detector-frame total masses up to $\sim\!100\,{\rm M}_\odot$, we find that baselines corresponding to light travel times of $8-11$ ms ($\sim\!2300-3300$ km) offer a reasonable compromise, producing predominantly unimodal or bimodal sky localizations suitable for electromagnetic follow-up and statistical host galaxy identification and galaxy cross-correlation studies. Shorter baselines significantly degrade localization, particularly for high SNR events. Crucially, we find that adding a third detector to the network eliminates localization multimodality for a substantial fraction of sources. A network with two CEs and LIGO-India provides unimodal posteriors for a good fraction of events, whereas two CEs plus ET would provide unimodal posteriors for essentially all of them. These considerations should be useful to inform the development of the XG detector network.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Baselines of 8-11 ms give a workable compromise for two Cosmic Explorer detectors, and a third detector removes most multimodality.

read the letter

This paper gives a clear recommendation on how far apart to place two Cosmic Explorer detectors: light-travel times of 8-11 milliseconds, or roughly 2300-3300 km, strike a reasonable balance for localizing binary black holes. They also show that throwing in a third detector removes most of the sky-map ambiguities. They do this by injecting signals with fixed parameters and then with a full population matched to GWTC-4. For masses up to about 100 solar masses, the shorter baselines make high-SNR events have messy bimodal or multimodal posteriors, while the 8-11 ms range keeps most of them unimodal or bimodal. That's useful because it ties directly to electromagnetic follow-up and host-galaxy studies. Adding LIGO-India improves things for a decent fraction, but ET basically solves it for nearly all events. The simulations are straightforward and the results line up with what you'd expect from timing triangulation. The soft spots are limited. The whole analysis assumes that timing across the network stays the dominant localization tool, which holds for these short in-band durations but might not for heavier systems or if other methods improve. They don't push into very high masses where the signal lingers longer, but they state the scope clearly. No obvious circularity or fitting issues. This is aimed at the people deciding where to site the next detectors and at analysts who need to plan for follow-up observations. It is solid enough to go to peer review; the quantitative outputs are the kind of thing network designers can actually use.

Referee Report

2 major / 3 minor

Summary. The manuscript examines the effect of baseline separation in a two-detector Cosmic Explorer network on sky localization of binary black hole mergers. Using fixed-parameter injections and a realistic BBH population drawn from GWTC-4, it concludes that light-travel times of 8-11 ms (~2300-3300 km) yield predominantly unimodal or bimodal posteriors suitable for electromagnetic follow-up and statistical host-galaxy studies for detector-frame total masses up to ~100 M_⊙. It further shows that adding a third detector (LIGO-India or ET) largely eliminates multimodality.

Significance. If the results hold, the work supplies concrete guidance for siting next-generation detectors to support multi-messenger and statistical cosmology applications. The dual use of targeted injections and a full population study, together with the explicit demonstration that a third detector resolves most degeneracies, constitutes a practical contribution to network design.

major comments (2)

[§3] §3 (Methods): The assumption that BBH signals remain in band for at most a few minutes (justifying pure timing triangulation) is scoped to M_det ≲ 100 M_⊙, but an explicit verification of in-band duration for the highest-mass events using the adopted CE noise curve would confirm the approximation holds across the simulated population.
[§4] §4 (Results): The central claim that 8-11 ms baselines produce 'predominantly' unimodal or bimodal localizations requires the exact fractions (or cumulative distributions) of localization types versus baseline for the GWTC-4 population; without these numbers the quantitative support for the compromise region is incomplete.

minor comments (3)

[Abstract] Abstract: the parenthetical distance conversion (~2300-3300 km) should state the precise value of c employed or the formula used.
[Figure captions] Figure captions (sky-posterior figures): include a brief statement of the quantitative criterion used to label a posterior as unimodal versus bimodal.
[§5] §5 (Discussion): the trade-off between localization performance and other siting constraints (cost, seismic environment) is mentioned only qualitatively; a short table or paragraph summarizing these factors would help readers weigh the recommendation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the helpful suggestions that will improve the clarity and quantitative support of our manuscript. We address each major comment below.

read point-by-point responses

Referee: [§3] §3 (Methods): The assumption that BBH signals remain in band for at most a few minutes (justifying pure timing triangulation) is scoped to M_det ≲ 100 M_⊙, but an explicit verification of in-band duration for the highest-mass events using the adopted CE noise curve would confirm the approximation holds across the simulated population.

Authors: We agree that an explicit verification strengthens the methods section. In the revised manuscript we will add a short paragraph (or footnote) in §3 that computes the in-band duration for the highest-mass events in our GWTC-4 population (detector-frame total mass up to 100 M_⊙) using the adopted CE noise curve, confirming that all such signals remain in band for at most a few minutes and thereby justifying the timing-triangulation approximation. revision: yes
Referee: [§4] §4 (Results): The central claim that 8-11 ms baselines produce 'predominantly' unimodal or bimodal localizations requires the exact fractions (or cumulative distributions) of localization types versus baseline for the GWTC-4 population; without these numbers the quantitative support for the compromise region is incomplete.

Authors: We accept that providing the exact fractions will make the quantitative support more complete. While the existing figures already demonstrate the trends, we will add a new table (or cumulative-distribution panel) in §4 that reports the precise fractions of unimodal, bimodal, and multimodal sky localizations as a function of baseline for the full GWTC-4 population. This addition will directly substantiate the 8–11 ms compromise region. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript derives its conclusions on optimal baselines (8-11 ms light-travel time) exclusively from numerical injections and Bayesian parameter estimation on simulated signals, using both fixed-mass cases and a population drawn from external GWTC-4 statistics. No equation or result is obtained by fitting a parameter to a subset of the same data and then relabeling the fit as a prediction; no self-citation supplies a uniqueness theorem or ansatz that is then treated as external; the triangulation assumption is scoped explicitly to the short in-band durations of the simulated events and is tested by adding a third detector. All load-bearing steps are therefore independent of the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard assumptions in gravitational wave astronomy about signal durations and localization methods. No new free parameters or invented entities are introduced.

axioms (2)

domain assumption BBH signals spend at most a few minutes within the XG detector's effective sensitivity band
Stated explicitly as the reason localization relies on timing triangulation.
domain assumption Localization of most BBH signals relies primarily on timing triangulation across a network
Key premise for the baseline study.

pith-pipeline@v0.9.0 · 5636 in / 1349 out tokens · 39711 ms · 2026-05-10T15:22:05.996088+00:00 · methodology

discussion (0)

Reference graph

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