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arxiv: 2510.08832 · v1 · submitted 2025-10-09 · 🌀 gr-qc · astro-ph.HE

Distinguishing between Black Holes and Neutron Stars within a Population of Weak Tidal Measurements

Michael M\"uller , Reed Essick This is my paper

Pith reviewed 2026-05-18 08:22 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavestidal deformabilityneutron starsblack holescompact binary populationspopulation inferencegravitational wave catalogs
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The pith

Gravitational-wave catalogs of over 100 events are needed to rule out that all low-mass objects are black holes using tidal data alone.

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

The paper examines whether tidal signatures in the gravitational-wave inspiral of compact binaries can separate neutron stars from black holes on a population level. Single events yield weak constraints because tidal effects are subtle at low masses. The authors generate mock catalogs that incorporate realistic measurement uncertainties and find that more than roughly 200 events are required to measure the neutron-star mass fraction precisely, while more than roughly 100 events are needed merely to exclude the hypothesis that every low-mass object is a black hole. These thresholds lie beyond the reach of current advanced detectors even at design sensitivity, but fall within the expected yield of next-generation instruments.

Core claim

Simulated catalogs with realistic tidal-deformability uncertainties show that the neutron-star fraction f_NS(m) as a function of mass cannot be measured accurately until O(200) events have been collected, and that the all-black-hole hypothesis for low-mass objects cannot be ruled out with gravitational-wave observations alone until O(100) events are in hand.

What carries the argument

The mass-dependent neutron-star fraction f_NS(m) inferred from a catalog of events whose tidal deformability measurements carry realistic uncertainties.

If this is right

  • Catalogs exceeding O(100) events can begin to exclude the possibility that every low-mass compact object is a black hole.
  • O(200) or more events are required before the neutron-star fraction f_NS(m) can be measured with useful precision.
  • Advanced detectors at design sensitivity will not reach the necessary catalog sizes.
  • Next-generation detectors such as Cosmic Explorer and Einstein Telescope could accumulate the required number of events.

Where Pith is reading between the lines

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

  • Electromagnetic counterparts will remain essential for identifying neutron stars until gravitational-wave catalogs grow substantially larger.
  • Improving the precision of tidal measurements in future detector designs would lower the required catalog size.
  • Joint analyses that combine gravitational-wave tidal data with electromagnetic observations could distinguish the populations earlier than gravitational waves alone.

Load-bearing premise

The simulated measurement uncertainties on tidal deformability accurately represent the constraints that will be obtained from real low-mass events.

What would settle it

A catalog of 100 low-mass events whose combined posterior on f_NS(m) remains consistent with zero at low masses would falsify the claim that such a catalog size suffices to exclude an all-black-hole population.

Figures

Figures reproduced from arXiv: 2510.08832 by Michael M\"uller, Reed Essick.

Figure 1
Figure 1. Figure 1: FIG. 1. Tidal deformability (Λ) as a function of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Measurement uncertainty for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Mass distribution assumed in our analysis. ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. ( [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Hyperposteriors and credible region sizes for the two-dimensional inference with [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows log10 B for different catalog real￾izations in grey and the mean over catalog real￾izations in black. In general, we find that even these simpler criteria are difficult to achieve with catalogs of fewer than 100 events. However, when f true NS = 1, we find B 0 1 < 0.1 on average for catalogs of Ndet ∼ O(75) events, meaning we would rule out a population of only BHs with confidence with GW data alone.… view at source ↗
read the original abstract

We study the ability of tidal signatures within the inspiral of compact binaries observed through gravitational waves (GWs) to distinguish between neutron stars (NSs) and black holes (BHs). After quantifying how hard this measurement is on a single-event basis, we investigate the ability of a large catalog of GW detections to constrain the fraction of NS in the population as a function of mass: $f_{\mathrm{NS}}(m)$. Using simulated catalogs with realistic measurement uncertainty, we find that $> O(200)$ events will be needed before we can precisely measure $f_{\mathrm{NS}}$, and catalogs of $> O(100)$ events will be needed before we can even rule out the possibility that all low-mass objects are BHs with GW data alone (i.e., without electromagnetic counterparts). Therefore, this is unlikely to occur with advanced detectors, even at design sensitivity. Nevertheless, it could be feasible with next-generation facilities like Cosmic Explorer and Einstein Telescope.

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.

Referee Report

1 major / 2 minor

Summary. The paper quantifies the difficulty of measuring tidal deformability Lambda in individual low-mass compact binary coalescences and then uses forward simulations of GW catalogs with assigned measurement uncertainties to determine the catalog sizes needed to constrain the neutron-star fraction f_NS(m) at low masses. It reports that >O(200) events are required to precisely measure f_NS while >O(100) events are required to rule out the hypothesis that all low-mass objects are black holes (f_NS=0) using GW data alone, concluding that this is unlikely with advanced detectors but potentially feasible with Cosmic Explorer or Einstein Telescope.

Significance. If the assigned Lambda uncertainties are representative, the work supplies a concrete, simulation-derived benchmark for when population-level statements about the nature of low-mass objects become possible without electromagnetic counterparts. The forward-simulation approach is a strength, as it directly links single-event measurement precision to population constraints and can be updated with improved waveforms or detector sensitivities. The result is useful for planning next-generation detector science cases.

major comments (1)
  1. [§3] §3 (catalog simulation pipeline): The central O(100) and O(200) thresholds are derived from the specific distribution of Lambda posterior widths assigned to the mock events. The manuscript describes these widths as 'realistic' but does not provide an explicit validation (e.g., comparison of the adopted Fisher-matrix or approximate-PE scaling against full Bayesian parameter estimation for systems with m<1.5 M_sun and SNR~10-20). Because the statistical power to exclude f_NS=0 scales directly with these widths, any systematic mismatch would rescale the required catalog size; the paper should either supply this validation or demonstrate that the thresholds remain stable under reasonable variations of the uncertainty model.
minor comments (2)
  1. [Figure 3] Figure 3: the legend and axis labels should explicitly state whether the plotted f_NS(m) curves are medians or means and whether the shaded bands are 68% or 90% credible intervals.
  2. [§2] The notation f_NS(m) is introduced without a precise definition of the mass binning or smoothing kernel used when reporting population constraints; a short clarifying sentence in §2 would remove ambiguity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the single major comment below and have incorporated additional analysis to strengthen the robustness of our results.

read point-by-point responses

  1. Referee: [§3] §3 (catalog simulation pipeline): The central O(100) and O(200) thresholds are derived from the specific distribution of Lambda posterior widths assigned to the mock events. The manuscript describes these widths as 'realistic' but does not provide an explicit validation (e.g., comparison of the adopted Fisher-matrix or approximate-PE scaling against full Bayesian parameter estimation for systems with m<1.5 M_sun and SNR~10-20). Because the statistical power to exclude f_NS=0 scales directly with these widths, any systematic mismatch would rescale the required catalog size; the paper should either supply this validation or demonstrate that the thresholds remain stable under reasonable variations of the uncertainty model.

    Authors: We agree that the assigned Lambda uncertainties are central to the reported thresholds and that explicit validation would strengthen the work. The uncertainties in the manuscript are based on Fisher-matrix scaling relations calibrated against existing literature results for tidal measurements at comparable masses and SNRs. To address the referee's concern directly, we have added a sensitivity study in which the Lambda posterior widths are rescaled by multiplicative factors of 0.5, 0.8, 1.2, and 1.5 while keeping all other aspects of the catalog simulation fixed. The resulting thresholds for ruling out f_NS=0 remain in the range O(70–160) events and those for a precise measurement of f_NS(m) remain in the range O(140–280) events, confirming that the order-of-magnitude conclusions are stable under reasonable variations of the uncertainty model. We will include this analysis, together with a new supplementary figure, in the revised §3. A comprehensive comparison against full Bayesian parameter estimation for the specific low-mass, moderate-SNR regime would be computationally demanding and is beyond the scope of the present study, but the variation test provides the requested demonstration of robustness. revision: partial

Circularity Check

0 steps flagged

Simulation-derived thresholds are self-contained outputs

full rationale

The paper generates mock catalogs under stated assumptions about measurement uncertainties on tidal deformability, then computes the catalog sizes needed to constrain f_NS(m) or rule out a pure-BH population. These thresholds are direct numerical outputs of the forward-simulation pipeline rather than quantities fitted to real data or redefined by construction. No equations reduce a claimed prediction to an input parameter, and no load-bearing self-citation chain is invoked to justify the central result. The derivation remains independent of the target claim once the uncertainty model is accepted as an input.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the realism of the injected measurement uncertainties and the assumed underlying population model for compact binaries. No new physical entities are introduced.

axioms (1)
  • domain assumption Tidal deformability measurements from GW inspirals can be modeled with realistic uncertainties that reflect future detector performance.
    Invoked when generating the mock catalogs used to derive the event-number thresholds.

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