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Characterizing the Properties and Constitution of Compact Objects in Gravitational-Wave Binaries

T0 review · 3 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

Pith's one-line read Tidal heating could reveal whether black holes really have horizons

desk verdict Solid measurability and waveform modeling, but the late-inspiral horizon test is an unvalidated, self-admittedly ad hoc model. read the letter →

arxiv 2411.19481 v1 pith:HZJ7A3OF submitted 2024-11-29 gr-qc

classification gr-qc
keywords tidalheatingblackholehorizonsexoticcompactobjectsgravitationalwavesinspiral-merger-ringdownwaveformhorizonparametersnumericalrelativitypost-Newtoniantheory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This thesis argues that tidal heating—the absorption of orbital energy by a black hole's horizon—leaves a measurable imprint on gravitational waves from merging compact binaries. If the compact objects are horizonless exotic alternatives to black holes, that imprint is weaker, so measuring it offers a way to tell black holes apart from their mimickers. The author derives two effective horizon parameters, Heff5 and Heff8, shows they could be tightly constrained with future detectors, and builds a phenomenological inspiral-merger-ringdown waveform model that includes tidal-heating corrections, improving agreement with numerical-relativity data.

What carries the argument

The central mechanism is tidal heating: the horizon of a black hole absorbs energy and angular momentum from the companion's tidal field, altering the inspiral rate and thus the gravitational-wave phase and amplitude. The horizon parameters Heff5 and Heff8, which enter the phase at 2.5PN and 4PN order, quantify the fraction of that absorption; they are defined as mass- and spin-weighted combinations of the individual horizon parameters, and their measured values distinguish black holes from horizonless compact objects.

What would settle it

Compute the total mass change dM/dt from high-resolution numerical-relativity simulations of nonspinning binaries at frequencies between Mf = 0.01 and merger, and check whether the linear ramp of Eq. (5.22) reproduces the simulated data within errors. If the ramp fails to connect the PN and NR regimes, the late-inspiral dephasing model would be invalidated.

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Extended reading notes

Core claim

Tidal heating imprints a phase and amplitude correction on gravitational-wave signals from binary black holes, characterized by two effective horizon parameters Heff5 and Heff8, which take known values for BHs and smaller values for horizonless exotic compact objects. The thesis claims that these parameters are measurable, especially in future third-generation detectors like Einstein Telescope and Cosmic Explorer, with projected 1-sigma errors as small as about 8% for Heff5 and 2% for Heff8 for a fiducial binary. It further constructs a frequency-domain waveform model, IMRPhenomD Horizon, that adds these corrections to the inspiral phase and amplitude, and shows it improves mismatch against numerical-relativity waveforms by about 4%, making tidal heating a practical discriminant for black holes.

Load-bearing premise

That the late-inspiral horizon-flux model, fitted to a narrow frequency band of numerical-relativity data, can be spliced to the low-frequency post-Newtonian result through a linear ramp—the thesis itself states this complete dephasing model is an ad hoc construction that behaves poorly at lower frequencies.

Editorial extensions

If this is right

  • If the horizon parameters can be measured, gravitational-wave observations could directly test for the presence of horizons in stellar-mass binaries.
  • In third-generation detectors, Heff5 and Heff8 could be constrained tightly enough to distinguish black holes from exotic compact objects for binaries out to a gigaparsec.
  • Adding tidal-heating corrections to phenomenological waveforms reduces systematic errors, improving parameter estimation and tests of general relativity in strong-field regimes.
  • The late-inspiral horizon-flux model could be attached to IMRPhenomD Horizon to search for deviations from the black-hole prediction in heavier binaries.
  • Current and future detectors could use these methods to probe the nature of compact objects across the entire detectable mass range.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The two effective parameters may serve as a model-independent diagnostic: measuring both simultaneously could distinguish a single-parameter deviation from general relativity from a genuine two-parameter horizon modification.
  • Extending the horizon-flux modeling to spinning binaries would likely boost the signal, since higher spins strengthen the phase correction and widen the measurable parameter space.
  • A practical next step would be to reanalyze existing gravitational-wave events with the new waveform model, searching for statistically significant deviations of Heff5 and Heff8 from the black-hole prediction.
  • If tidal-heating corrections are as significant as modeled, this approach could complement other black-hole tests such as quasinormal-mode ringdown and tidal Love numbers, covering binaries too heavy for inspiral-only analyses and too light for ringdown-only tests.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This manuscript, posted as a PhD thesis, develops tidal heating (TH) as a gravitational-wave discriminant for black-hole horizons. Chapter 3 forecasts the measurability of two effective horizon parameters, H_eff5 and H_eff8, using Fisher and Bayesian analyses of a TaylorF2+TH inspiral model in LIGO-Virgo, Einstein Telescope, and Cosmic Explorer, reporting projected 1-sigma constraints of about 8% (H_eff5) and 2% (H_eff8) at 1 Gpc in a fiducial fixed-spin configuration. Chapter 4 builds 'IMRPhenomD Horizon,' a frequency-domain phenomenological inspiral-merger-ringdown model that adds TH phase and amplitude corrections to IMRPhenomD, calibrates it on 20 SEOBNRv2+NR hybrids, validates it on 40 hybrids, and reports a median mismatch improvement over IMRPhenomD of about 4% (aLIGO ZDHP) and 2% (flat noise) against 219 SXS NR waveforms. Chapter 5 models the total horizon flux of nonspinning binaries from SXS apparent-horizon data using a four-parameter ansatz fitted over Mf in [0.03, 0.04], derives the corresponding frequency-domain dephasing, and proposes a linear ramp to splice this to the 4PN low-frequency expression, as a route to testing horizonless exotic compact objects in the late inspiral.

Significance. The Ch. 3 forecasts are useful, internally consistent benchmarks for 3G detectors, and the Bayesian cross-checks (Sec. 3.5) support the Fisher results. Ch. 4 delivers a concrete, self-contained IMR waveform with TH included and benchmarked against external SXS NR data; the full coefficient tables (Appendix C, Eq. 5.11) and the use of public toolkits (GWBENCH, Bilby, the SXS catalog) make the quantitative claims reproducible in principle. The thesis is also commendably transparent: it discloses that the headline errors rise by about an order of magnitude when spins are included (Fig. 3.6), that the amplitude correction is subdominant (Sec. 4.7), and that the Ch. 5 flux model deviates from the PN limit by orders of magnitude outside its fitted band (Sec. 5.3.2). If the Ch. 5 splicing were validated, the framework would be a genuine step toward late-inspiral horizon tests; as it stands, the Ch. 5 demonstration is a proposal with an unquantified error budget, and the abstract's horizon-test claim rests on that unvalidated ground.

major comments (3)
  1. [Sec. 5.3; Eqs. (5.9), (5.15)-(5.22)] The late-inspiral horizon-flux model that underpins the paper's horizon-test proposal is not validated at either end of its frequency range. The four-parameter ansatz (5.9) is calibrated to apparent-horizon data from only six SXS simulations over the narrow band Mf in [0.03, 0.04], and Sec. 5.3.2 states that outside this band the model 'behaves extremely poorly at lower frequencies,' with orders of magnitude of deviation from the 4PN term. The complete dephasing is then assembled by the linear ramp (5.22) on {a_i} between Mf = 0.022 and 0.032. No test is presented that the spliced dM/dt (and hence delta_PSI_TH in Eqs. (5.15)-(5.21)) reproduces either the NR horizon data at Mf approximately 0.032 or the 4PN expression at Mf approximately 0.022, and no held-out SXS simulation is used to check the fit. The concern is compounded by the fact that the low-frequency anchor itself is applied at v approximately 0.41, where truncated 4PN is not expected to be accurate. Because delta_PSI_TH is constructed directly from this flux model, the claim that the late inspiral can be leveraged to test for horizonless compact objects inherits an unquantified error budget. I recommend: (i) validating the spliced model against one or two nonspinning SXS binaries not in Table 5.1; (ii) checking continuity of dM/dt and delta_PSI_TH at both interfaces; and (iii) propagating the 1-sigma fit errors of Fig. 5.1 into the dephasing, together with a report on the conditioning of the four-parameter fit over such a short band.
  2. [Secs. 3.4.2, 3.7, and 6] The headline measurability numbers, Delta_H_eff5 approximately 0.05 (8.3%) and Delta_H_eff8 approximately 0.2 (2%) for M = 30 M_sun, q = 1.5, DL = 1 Gpc, are obtained in the reduced five-parameter space {Mc, eta, DL, Heff5, Heff8} with the spins held fixed at chi1 = chi2 = 0.8. The paper's own Sec. 3.4.2 reports that adding the spins together with tc and phi_c (Fig. 3.6) raises the errors by roughly an order of magnitude relative to the seven-parameter Fig. 3.5, and describes Fig. 3.6 as the more realistic estimate. This disclosure is commendable, but Sec. 3.7 and Ch. 6 restate the five-parameter numbers without that qualification, and the abstract's general claim of tight constraints inherits the same framing. The summary should present the spin-marginalized errors as the primary benchmark, or clearly label the 8% and 2% values as fixed-spin, idealized projections.
  3. [Sec. 4.7; Eq. (4.37), Figs. 4.7-4.8] The central accuracy claim of Ch. 4, a roughly 4% (ZDHP) and 2% (flat noise) improvement in median mismatch against 219 SXS waveforms, is reported without a significance statement, and the comparison set includes the 20 hybrids used to calibrate the model (Table 4.1). The two histograms in Figs. 4.7 and 4.8 overlap substantially, so the shift in medians could be within sampling error or driven by the calibration subset; the single outlier noted in Sec. 4.6 (q = 4, chi1 = 0, chi2 = 0.8; 1.21% at 70 M_sun) shows that the model is not uniformly better. Please report the median improvement computed on the 199 non-calibration waveforms only, add an uncertainty on the median shift (e.g., a bootstrap over the SXS set), and state the fraction of the 219 waveforms for which PhenomD Horizon is the better template.
minor comments (7)
  1. [Various] There are several typos and notation slips that should be cleaned up: 'fequencies' (Sec. 3.4.2, first paragraph), 'covarinaces' (Sec. 3.6), 'IMRPheonmD' (Sec. 5.4), and 'post-Newtonain' (Sec. 4.4).
  2. [Fig. 3.7 caption] The instruction that '14.65 is to be added to the tick labels of Mc' is confusing; the chirp-mass axis should simply be relabeled with the correct values.
  3. [Sec. 4.4, Eqs. (4.18)-(4.20)] For reproducibility, please state the actual values of the Planck-taper window parameters (x1, x2, x3, x4) used in the hybridization, rather than only the functional form.
  4. [Sec. 5.3] The restriction to nonspinning binaries and the simplifying assumption H1 = H2 = H should be stated at the beginning of Sec. 5.3, where the modeling strategy is set, rather than appearing in the middle of the paragraph describing the mass-flux data.
  5. [Eq. (5.11)] The entries of the beta_ij matrix are quoted to inconsistent precision (four entries to two or three significant figures, the rest to six or more), and no uncertainties are given for the coefficients despite the 1-sigma error bars displayed on the individual a_i fits in Fig. 5.1.
  6. [Table 4.1] The column labeled 'chi_PN' should be defined in the caption as the effective spin parameter of Eq. (4.25), since the table otherwise appears to list only component spins.
  7. [Secs. 3.2 and 4.3.1] The manuscript should state explicitly at first use that the TH phase expressions, Eqs. (3.4), (3.7), and (4.10)-(4.12), are taken from the authors' own Ref. [114], so that the reader can distinguish restated published material from new derivations in this thesis.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measurability forecasts and waveform model rest on a previously published, parameter-free tidal-heating phase and are benchmarked against external SXS NR waveforms, not against the paper's own fitting targets.

full rationale

The thesis's three analysis chapters are each self-contained in the sense required here. Chapter 3 injects TaylorF2 waveforms augmented with the tidal-heating phase of Eq. (3.7) and uses Fisher/Bayesian parameter estimation to forecast errors on Heff5 and Heff8; the phase is taken from the authors' earlier Ref. [114], but that reference is a published derivation from horizon-flux expressions and is parameter-free with respect to the measurability question, so citing it is evidence, not circularity. Chapter 4 constructs hybrids by stitching SEOBNRv2 plus TH corrections to SXS NR waveforms, recalibrates the PhenomD-style pseudo-PN coefficients against those hybrids, and then validates the model against an independent set of test hybrids and 219 SXS NR waveforms; the claimed ~4% median mismatch improvement is an externally measured comparison, not an identity imposed by construction. Chapter 5 explicitly fits the phenomenological flux ansatz Eq. (5.9) to NR horizon data over Mf in [0.03,0.04] and derives the dephasing Eqs. (5.15)-(5.21) from that fit; this is model calibration, not a disguised prediction. The paper's own admission that the NR-fitted flux model 'behaves extremely poorly at lower frequencies' and the linear ramp Eq. (5.22) are ad hoc, but that is a correctness and robustness limitation, not a circular step: the fitted parameters are not renamed as a prediction of the target claim. No equation in the paper reduces to its output by definition, and no load-bearing conclusion is justified solely by a self-citation chain. The appropriate verdict is therefore no circularity, with the Chapter 5 splice flagged as a validation concern outside the circularity category.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a small number of calibration fits: the pseudo-PN phase parameters sigma_i (Ch. 4), the horizon-flux parameters a_i (Ch. 5), and the linear splicing of the latter to the PN regime. No new fundamental entities are introduced; the effective parameters H_eff5/H_eff8 are recombinations of existing quantities.

free parameters (2)
  • sigma_0..sigma_4 (pseudo-PN inspiral phase parameters) = Coefficients lambda in Table C.1, fit to 20 hybrids
    Introduced in Eq. (4.21) to absorb higher-order PN terms; fitted to hybrid waveforms built from SEOBNRv2 plus TH corrections. They are calibration parameters, not derived from first principles.
  • a_1..a_4 (phenomenological horizon-flux parameters) = beta matrix in Eq. (5.11), fit to 6 SXS simulations
    Define the ansatz for dM/dt in Eq. (5.9); fit over Mf in [0.03, 0.04]. The dephasing coefficients psi_8..psi_12 in Eqs. (5.16)-(5.21) are derived from this fitted ansatz, so they inherit the fit.
assumptions (4)
  • domain assumption The total gravitational-wave phase separates as point-particle plus tidal deformability plus tidal heating, with the tidal-heating phase given by Eq. (3.7) computed from the flux Eq. (3.2) with horizon parameters H1, H2 scaling the BBH flux linearly.
    Taken from the authors' prior paper Ref. [114]; not re-derived in the thesis, and it is the basis of all measurability forecasts.
  • domain assumption SEOBNRv2 can serve as the point-particle baseline, and tidal-heating corrections can be added in the frequency domain without double-counting the NR calibrations present in SEOBNRv2.
    Used in Ch. 4 to build hybrids; the thesis argues the stitching frequency is low enough that little NR information from the inspiral approximant is present, but the baseline is the calibrated model.
  • ad hoc to paper The ansatz Eq. (5.9) with parameters a1..a4 describes the total horizon flux, and the piecewise splicing Eq. (5.22) connects it to the PN result.
    Central modeling choice of Ch. 5; acknowledged low-frequency failure and ad hoc linear ramp.
  • standard math Fisher matrix error forecasts are valid for the high-SNR, Gaussian-noise regime.
    Standard approximation used in Ch. 3; the thesis also provides Bayesian checks for a few points.

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Pith. "Pith review of Characterizing the Properties and Constitution of Compact Objects in Gravitational-Wave Binaries." pith.science (2026). https://pith.science/paper/HZJ7A3OF

@misc{pith2026241119481,
  author       = {Pith},
  title        = {Pith review of: Characterizing the Properties and Constitution of Compact Objects in Gravitational-Wave Binaries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HZJ7A3OF}},
  note         = {Machine review of arXiv:2411.19481}
}
read the original abstract

Astrophysical observations point toward strong evidence for the existence of black holes (BHs). Nevertheless, it is yet to be established or ruled out with confidence whether some exotic compact objects (ECOs), capable of mimicking black holes from an observational point of view, are indeed doing so. In classical General Relativity (GR), a horizon is the defining feature of a black hole, which prevents any event inside from causally affecting the outside Universe. The quest for distinguishing black holes from horizonless compact objects using gravitational wave (GW) signals from compact binary coalescences (CBCs) can be helped by utilizing the phenomenon of tidal heating (TH), which leaves its imprint on the binary waveforms through the horizon parameters. First, we study the measurabilities of these parameters within the inspiral regime. Then, to extend our investigation for heavier binaries, we construct an inspiral-merger-ringdown waveform by using post-Newtonian calculations for the inspiral and numerical relativity data for the merger-ringdown part that incorporates the effects of tidal heating of black holes in the phase and the amplitude. The new model shows improvements in waveform accuracy when compared to numerical relativity data. In the late inspiral phase when the compact objects are closer to each other, the effects of tidal heating are stronger, opening up the possibility of identifying the objects more precisely. We demonstrate, from numerical relativity data of binary black holes, how one can model tidal heating in the late inspiral regime and leverage this knowledge to test for horizonless compact objects mimicking black holes. These studies bear significance in determining the nature of compact objects having masses in the entire range that LIGO and future ground-based gravitational-wave detectors can detect.

Figures

Figures reproduced from arXiv: 2411.19481 by the authors.

Figure 1.1
Figure 1.1. Illustration of the structure of a KBH. The Ergosphere In the Schwarzschild case, the event horizon also represented the “infinite redshift” surface, i.e. photons emanating from a source reaching the horizon would be infinitely redshifted to an observer far away. This surface appears as the solution of gtt = 0, which, for an SBH, is also at r = 2M. For a KBH, however, the horizon and the infinite redshift surfaces a… view at source ↗
Figure 2.1
Figure 2.1. Illustration of the effective potential for a perturbed SBH (top panel) and a [PITH_FULL_IMAGE:figures/full_fig_p057_2_1.png] view at source ↗
Figure 3.1
Figure 3.1. Error values in the TH parameters Heff5 (top) and Heff8 (bottom) as a function of total mass, when measured by the three detector network of LIGO (Hanford, Livingston) and Virgo. mass-ratio (q) has been varied from 1.5 to 3 for getting different curves. We consider aligned spins here, so that Lˆ · Sˆ i = 1. Heff5 = 0.6, Heff8 = 12, DL = 200 Mpc, χ1 = χ2 = 0.8 have been taken. in the range M < 30M⊙, and we find that … view at source ↗
Figures from the paper (23 more)
Figure 3.2
Figure 3.2. Figure 3.2: Errors in Heff5 (top row) and Heff8 (bottom row) as a function of total mass M, when measured in ET (first column) and CE (second column). Injection parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p082_3_2.png]
Figure 3.3
Figure 3.3. Figure 3.3: Variation of SNR with the total mass M in LIGO-Virgo, ET and CE, as calculated from Eq. (3.12). We consider binaries at DL = 200 Mpc with mass-ratio q = 1.5 [PITH_FULL_IMAGE:figures/full_fig_p082_3_3.png]
Figure 3.4
Figure 3.4. Figure 3.4: Errors in Heff5 (top row) and Heff8 (bottom row) as a function of luminosity distance, when measured in ET (first column) and CE (second column). Along the X-axis, DL varies from 100 Mpc to 1 Gpc. Other parameters are fixed at Heff5 = 0.6, Heff8 = 12, M = 30M⊙, χ1 = …
Figure 3.5
Figure 3.5. Figure 3.5: Variation of errors in Heff5 (left column) and Heff8 (right column) in ET (solid lines), CE (dashed lines) with dimensionless spins. χ1, χ2 are varied from 0 to 1 along the X and Y -axes respectively. Total binary mass is M = 40M⊙, and mass-ratios are q = 1.1 (top pa…
Figure 3.6
Figure 3.6. Figure 3.6: Variation of errors in Heff5 (left column) and Heff8 (right column) in CE, with the parameter space Θ ≡ {Mc, η, DL, χ1, χ2, Heff5, Heff8, tc, ϕc}. χ1, χ2 are varied from 0 to 1 along the X and Y -axes respectively. Optimally oriented binaries are considered at DL = 2…
Figure 3.7
Figure 3.7. Figure 3.7: Posterior plots from Bayesian parameter estimation. Injection parameters [PITH_FULL_IMAGE:figures/full_fig_p088_3_7.png]
Figure 3.8
Figure 3.8. Figure 3.8: Bayesian posterior plot in LIGO-Virgo with M = 40M⊙, q = 3, DL = 50 Mpc, χ1 = χ2 = 0.8, Heff5 = 0.6, Heff8 = 12. 3.6 Principal Component Analysis So far we have considered the diagonal elements of the error covariance matrix C, which are the variances. In this sectio…
Figure 3.9
Figure 3.9. Figure 3.9: Fisher ellipses in LIGO-Virgo with normalized templates, implying SNR = [PITH_FULL_IMAGE:figures/full_fig_p091_3_9.png]
Figure 3.10
Figure 3.10. Figure 3.10: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p092_3_10.png]
Figure 3.11
Figure 3.11. Figure 3.11: Variation of the rotation angle of X − Y coordinate axes with respect to the Heff5 − Heff8 axes with M for q = 4, 6 in [PITH_FULL_IMAGE:figures/full_fig_p095_3_11.png]
Figure 3.12
Figure 3.12. Figure 3.12: Sections of the M = 0.99 ellipses with their principal axes in [PITH_FULL_IMAGE:figures/full_fig_p097_3_12.png]
Figure 4.1
Figure 4.1. Figure 4.1: Hybrid waveforms for four different configurations in the parameter space of [PITH_FULL_IMAGE:figures/full_fig_p114_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: Rescaled amplitude of the full IMR waveforms as functions of [PITH_FULL_IMAGE:figures/full_fig_p124_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Phase, phase derivative, and phase difference between the hybrids (same as [PITH_FULL_IMAGE:figures/full_fig_p125_4_3.png]
Figure 4.4
Figure 4.4. Figure 4.4: Fits of σi calculated by the NonLinearModelFit module of Mathematica. The surfaces correspond to the 2D fits with η and χPN as described in Eq. (4.27). where χeff = m1χ1 + m2χ2 M . (4.26) In this model, χPN is used as a single spin parameter to generate the phe￾nomen…
Figure 4.5
Figure 4.5. Figure 4.5: Mismatches (%) between IMRPhenomD Horizon and the hybrid waveforms ( [PITH_FULL_IMAGE:figures/full_fig_p130_4_5.png]
Figure 4.6
Figure 4.6. Figure 4.6: Mismatches (%) between PhenomD Horizon and PhenomD. (a) Mismatches with only the phase correction but no amplitude correction in PhenomD Horizon. (b) Mismatches with only the amplitude correction without any phase correction. (c) Mis￾matches with corrections in both …
Figure 4.7
Figure 4.7. Figure 4.7: Mismatches of 219 non-precessing noneccentric NR waveforms from SXS with [PITH_FULL_IMAGE:figures/full_fig_p136_4_7.png]
Figure 4.8
Figure 4.8. Figure 4.8: Same as in Fig [PITH_FULL_IMAGE:figures/full_fig_p137_4_8.png]
Figure 5.1
Figure 5.1. Figure 5.1: Fits for the phenomenological parameters defined in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p150_5_1.png]
Figure 5.2
Figure 5.2. Figure 5.2: Comparison of the accuracy of horizon data from various NR simulations of [PITH_FULL_IMAGE:figures/full_fig_p151_5_2.png]
Figure 5.3
Figure 5.3. Figure 5.3: This figure shows the total tidal heating fluxes experienced by the binary [PITH_FULL_IMAGE:figures/full_fig_p152_5_3.png]
Figure 5.4
Figure 5.4. Figure 5.4: The fitted models shown for each of the binaries in Fig. [PITH_FULL_IMAGE:figures/full_fig_p153_5_4.png]

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