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arxiv: 2506.22363 · v2 · submitted 2025-06-27 · 🌀 gr-qc

Binary black holes in the heat of merger

Samanwaya Mukherjee , Sayak Datta , Sukanta Bose , Khun Sang Phukon This is my paper

Pith reviewed 2026-05-19 07:45 UTC · model grok-4.3

classification 🌀 gr-qc
keywords tidal heatingblack hole binarieswaveform approximantnumerical relativitygravitational wave modelinghorizon parametersfrequency domain
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The pith

A frequency-domain approximant models tidal heating in nonspinning black hole binaries up to merger using horizon parameters.

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

Black hole binaries lose orbital energy and angular momentum to their horizons as they approach merger, speeding up their inspiral. The paper uses numerical relativity data to model this tidal heating effect in the strong-gravity regime. It presents a new frequency-domain approximant for nonspinning binaries that includes these effects and horizon parameters to characterize the compact objects. This allows building more accurate waveforms without finite-size effects and has implications for neutron star binaries as well.

Core claim

We present a frequency-domain approximant for nonspinning black hole binaries that accounts for tidal heating effects up to the merger frequency. The approximant includes horizon parameters that characterize the nature of the compact objects. By applying this model to a binary black hole baseline that incorporates tidal heating, one can construct a more accurate point-particle waveform, one that is devoid of finite-size effects of the component objects.

What carries the argument

The frequency-domain approximant calibrated to numerical relativity data that incorporates tidal heating and horizon parameters for compact objects.

If this is right

  • More accurate point-particle waveforms can be constructed by including tidal heating in the baseline.
  • The model can be used to study ramifications in modeling binary neutron star systems.
  • Horizon parameters help characterize the nature of the compact objects in the binary.
  • The approximant extends waveform modeling to include strong-field horizon effects up to merger.

Where Pith is reading between the lines

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

  • This could reduce systematic errors in gravitational wave parameter estimation by accounting for horizon absorption.
  • The horizon parameters might enable tests to distinguish black holes from exotic compact objects in observed signals.
  • Extending the approach to spinning cases could further improve templates for current detectors.

Load-bearing premise

Numerical relativity simulations accurately isolate and capture the tidal heating effects without contamination from other phenomena or errors.

What would settle it

Comparing the approximant's predicted gravitational wave phase and amplitude against independent numerical relativity runs of binary black hole mergers that include horizon absorption.

Figures

Figures reproduced from arXiv: 2506.22363 by Khun Sang Phukon, Samanwaya Mukherjee, Sayak Datta, Sukanta Bose.

Figure 2
Figure 2. Figure 2: FIG. 2. Data (blue dots) and best fits (red curves) for [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: shows the mass evolution from 50 nonspinning SXS simulations used in this study, demonstrating ade￾quate resolution in the frequency range of interest. Inspiral-merger model of horizon flux.– We model the rate of the total mass-energy absorption by the two BHs (M˙ = ˙ m1 + ˙ m2) using the ansatz log M˙ NR = log M˙ PN ( 1 + η X 2 i=0 aiv i+1) , (1) where M˙ PN is taken from the most recent PN expression… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the energy flux radiated to future null infinity and absorbed by the black hole horizons, as computed from [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase contribution of TH of BBHs calculated nu [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Mismatches (%) between the full BBH waveforms [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Dephasing due to TD for various NS EoSs (solid lines, [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

A black hole binary approaching merger undergoes changes in its inspiral rate as energy and angular momentum are lost from the orbits into the horizons. This effect strengthens as the black holes come closer. We use numerical relativity data to model this so-called tidal heating in the strong gravity regime. We present a frequency-domain approximant for nonspinning black hole binaries that accounts for tidal heating effects up to the merger frequency. The approximant includes horizon parameters that characterize the nature of the compact objects. By applying this model to a binary black hole baseline that incorporates tidal heating, one can construct a more accurate point-particle waveform, one that is devoid of finite-size effects of the component objects. We also discuss its ramifications in modeling binary neutron star systems.

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

2 major / 2 minor

Summary. The manuscript presents a frequency-domain approximant for nonspinning black hole binaries that incorporates tidal heating effects up to merger, calibrated on numerical relativity data. Horizon parameters are introduced to characterize absorption of energy and angular momentum into the compact-object horizons, with the goal of enabling point-particle waveforms free of finite-size effects and with extensions to neutron-star binaries.

Significance. If the calibration isolates tidal heating cleanly and the horizon parameters prove robust, the approximant would be a useful addition to strong-field waveform modeling, particularly for late-inspiral accuracy and for distinguishing black holes from other compact objects. The direct use of NR data to extend the model into the merger regime is a positive feature.

major comments (2)
  1. [§3] §3 (calibration procedure): the manuscript states that horizon parameters are fitted to NR data but supplies no description of the functional form, optimizer, frequency window, number of simulations, or residual diagnostics. This is load-bearing for the central claim that the approximant accurately captures tidal heating without absorbing numerical artifacts or gauge effects.
  2. [§4.1] §4.1 (horizon-parameter definition): the parameters are determined by matching the same NR waveforms used to construct the approximant, so the reported agreement with data is not an independent test. A concrete validation on an independent NR run or on a different mass ratio is required to establish that the parameters reflect physical absorption rather than data-specific tuning.
minor comments (2)
  1. [Abstract] The abstract and introduction should explicitly state the mass-ratio and frequency range over which the approximant has been tested.
  2. [§2] Notation for the frequency-domain tidal-heating term should be introduced once and used consistently; several symbols appear without prior definition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment point by point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [§3] §3 (calibration procedure): the manuscript states that horizon parameters are fitted to NR data but supplies no description of the functional form, optimizer, frequency window, number of simulations, or residual diagnostics. This is load-bearing for the central claim that the approximant accurately captures tidal heating without absorbing numerical artifacts or gauge effects.

    Authors: We agree that the calibration procedure requires a more explicit description to support the central claims. In the revised manuscript we will expand §3 to specify the functional form of the horizon parameters, the optimizer and its settings, the exact frequency window(s) used for fitting, the number and mass-ratio range of the NR simulations, and quantitative residual diagnostics. These additions will clarify how the fit isolates tidal heating from numerical or gauge artifacts. revision: yes

  2. Referee: [§4.1] §4.1 (horizon-parameter definition): the parameters are determined by matching the same NR waveforms used to construct the approximant, so the reported agreement with data is not an independent test. A concrete validation on an independent NR run or on a different mass ratio is required to establish that the parameters reflect physical absorption rather than data-specific tuning.

    Authors: The referee is correct that the present validation uses the same NR data for both calibration and comparison, limiting independence. We will add a new validation test on at least one NR simulation withheld from the fitting set (including, where possible, a different mass ratio) and report the results in the revised §4.1. This will provide a clearer demonstration that the horizon parameters capture physical absorption. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper constructs a frequency-domain approximant by calibrating to external numerical relativity data for tidal heating effects up to merger. This follows standard waveform modeling practice where NR simulations serve as an independent benchmark rather than the model reducing to its own fitted inputs by definition or self-citation. No equations or steps are presented that exhibit self-definitional closure, fitted parameters renamed as predictions, or load-bearing self-citations whose validity depends on the current work. The horizon parameters characterize the objects within the calibrated model but do not force the central claim to be tautological with the calibration data itself. The derivation remains self-contained against the external NR benchmark.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on the assumption that tidal heating can be parameterized by a small set of horizon absorption coefficients that are constant or slowly varying across the inspiral. No new particles or forces are introduced, but the horizon parameters function as free parameters fitted to numerical data.

free parameters (1)
  • horizon absorption coefficients
    Adjustable numbers that characterize how much energy and angular momentum each black hole absorbs; their values are determined by matching to numerical relativity simulations.
axioms (1)
  • domain assumption Numerical relativity simulations provide an accurate representation of tidal heating in the strong-gravity regime.
    The approximant is calibrated directly to these simulations; any systematic error in the simulations propagates into the model.

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Cited by 1 Pith paper

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Reference graph

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