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REVIEW 4 major objections 3 minor 68 references

Is the Spin of the Black Hole in GX 339-4 Negative?

T0 review · 4 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The measured spin of GX 339–4 swings from −1 to +0.8 depending on the disk model used, so the spin is not a settled number.

desk verdict The paper convincingly shows continuum-fitting spin in GX 339-4 is model dependent at the ~0.3 level, but the specific negative-vs-positive family dichotomy is weakened by one-sided model grids. read the letter →

arxiv 2412.15705 v2 pith:MMEZCIP5 submitted 2024-12-20 astro-ph.HE

Andrzej A. Zdziarski , Srimanta Banerjee , Michal Szanecki , Ranjeev Misra , Gulab Dewangan This is my paper · ORCID
classification astro-ph.HE
keywords GX339-4blackholespinaccretiondiskmodelscontinuumfittinglow-massX-raybinarysoftstatespectraretrogradewarmcorona
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

The paper asks whether the black hole in the X-ray binary GX 339–4 spins backwards, and its answer is that the measured spin is not a fixed property of the source but a consequence of the disk model chosen. Fitting two very clean, disk-dominated soft-state spectra from NICER and NuSTAR, the authors obtain spins ranging from strongly negative (retrograde) under the commonly used color-correction models kerrbb and kerrbb2, to a* ≈ 0.7 under a slim disk with full atmospheric radiative-transfer spectra, to a spin consistent with zero when an optically thick warm corona is added above the disk. The inclination is the only parameter that comes out nearly the same in every model, at roughly 30–34 degrees. The result matters because published black-hole spins are usually quoted from a single disk model; this paper shows that the model choice alone can shift the spin by about 0.3 or more, so a one-model answer is not to be trusted as the true spin.

What carries the argument

The argument is carried by comparing spectral fits of the same two data sets across a suite of relativistic disk models that differ in how they treat the disk's vertical structure and emergent spectrum: the color-correction models kerrbb and kerrbb2, the thin-disk and slim-disk models with fully computed atmospheric spectra (bhspec and slimbh, the latter including finite disk thickness), and a slim disk covered by a warm Comptonizing layer. All of these models assume the disk's inner radius sits at the ISCO, the innermost stable circular orbit, whose radius encodes the spin through the Bardeen–Press–Teukolsky relation; the fitted spin is the one that makes the model's ISCO radius match the data. A self-consistent Comptonization and relativistically broadened reflection treatment (comppsc with xilconv and relconv) is what allows the fits to separate mass, distance, inclination and spin, and the stability of the diskbb normalization across the two epochs is used as an indirect argument that the inner radius is indeed at the ISCO.

What would settle it

An independent dynamical mass and geometric distance measurement would separate the model families: the negative-spin fits cluster at M1 ≈ 4–7 M☉ with D ≈ 10.6–10.8 kpc, whereas the positive-spin atmospheric fits cluster at M1 ≈ 10–13 M☉ with D ≈ 11.4–11.6 kpc. A measurement matching one cluster would select that family's spin; a value between the clusters would strain both.

Watch

Extended reading notes

Core claim

Jointly fitting two simultaneous NICER/NuSTAR spectra of GX 339–4 in very soft states, the authors find that the black-hole spin inferred from the spectra strongly depends on how the accretion disk's local emission is modeled. With the widely used kerrbb and kerrbb2 models, which treat departures from local blackbody emission through a color-correction factor fcol, the best fits give strongly negative spins (a* = −0.53 and −1.0 in the joint fits, respectively) and low masses near 4–7 M☉. With the slim-disk model slimbh and the thin-disk model bhspec, which use radiative-transfer calculations of the disk atmosphere, the spins are moderately positive (a* = 0.71 and 0.40) with masses of 10–13 M☉ and distances of 11–12 kpc. Adding an optically thick warm corona above the disk leaves the spin weakly constrained and consistent with zero. The fit quality is best for the atmospheric slim-disk model, and only that model or the warm-corona model agrees with the binary mass function when the fitted inclination equals the binary inclination; the negative-spin solutions put the mass near 4–7 M☉, below the range the mass function allows. The authors' stated conclusion is that the spin of GX 339–4 is strongly model-dependent, with the spread reaching about 0.3 even when the mass, distance and inclination are fixed.

Load-bearing premise

Every spin value in the paper rests on the assumption that the disk's inner edge sits exactly at the innermost stable circular orbit; if the disk is truncated, warped or covered by a scattering layer instead, the continuum-fitting spin constraints no longer apply, and the paper's support for that assumption is indirect (a stable diskbb normalization) rather than a direct measurement.

Editorial extensions

If this is right

  • A one-model spin quoted for GX 339–4, whether positive or negative, is not a settled measurement; the same data support values from a* ≈ −1 to +0.8 depending on the disk treatment.
  • If the atmospheric slim-disk model is right, the source has a relatively high spin (a* ≈ 0.71), a mass of about 12.5 M☉ and a distance of about 11.5 kpc.
  • If a warm corona covers the disk, the spin is consistent with zero, which matches the low natal spins inferred from gravitational-wave mergers.
  • The negative-spin solutions from the color-correction models are statistically disfavored and conflict with the binary mass function, but they cannot be excluded without better mass and distance measurements.
  • Past claims of retrograde accretion in low-mass X-ray binaries are, in the authors' review, none fully convincing, leaving negative spin in such systems without a confirmed example.

Reading between the lines

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

  • A natural next test is to apply the same model suite to other soft-state LMXBs; if similar spreads appear, published continuum-fitting spins across the population carry a hidden systematic uncertainty of at least this size.
  • If the warm-corona interpretation is combined with the gravitational-wave prior of low natal spins, the poorly constrained zero-spin solution becomes the physically preferred one, despite being statistically less decisive.
  • The negative-spin fits occupy a distinct corner of parameter space (M1 ≈ 4–7 M☉, D ≈ 10.6–10.8 kpc); an independent astrometric distance or dynamical mass would separate that family from the atmospheric fits without any spectral-model dispute.
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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

4 major / 3 minor

Summary. The paper presents joint NICER/NuSTAR spectral fits of two very soft state observations of the Galactic black-hole LMXB GX 339-4. Using a suite of relativistic disk models (diskbb, kerrbb, kerrbb2, bhspec, slimbh, and a slimbh-based warm-corona variant) coupled to self-consistent Comptonization and reflection, the authors find that the fitted black-hole spin depends strongly on the disk model: color-correction models yield negative spins and low masses, atmosphere-based models yield positive spins and high masses, and the warm-corona model leaves the spin weakly constrained and consistent with zero. The inclination is stable at roughly 30-34 degrees across all models. The paper's principal conclusion is a confirmation of strong model dependence of continuum-fitting black-hole spin measurements, with a preferred model being slimbh with atmospheric spectra giving a*=0.71+0.05-0.04.

Significance. If the model-dependence conclusion stands, the paper is a valuable cautionary result for the continuum-fitting method applied to LMXBs, where mass and distance are often free parameters. The data are of high quality, the treatment of Comptonization and reflection is more self-consistent than in much prior work, and the comparison across disk models directly quantifies systematic uncertainty. The robust low inclination and the mass-function consistency argument are useful. However, the more specific family-level claims (color-correction models give negative spins; atmosphere models give positive spins) are weakened by the asymmetric parameter ranges of the model grids, and the preference for model 3 is in tension with the disk-instability caveat the authors themselves state. The central model-dependence conclusion is defensible, but the interpretation of the sign dichotomy and the preferred-model designation require further work.

major comments (4)
  1. [Section 4.3 and Table 2 note; Section 4.2] The family-level sign dichotomy is not a symmetric test because the atmospheric models are tabulated only for a* >= 0 (slimbh for 0 <= a* <= 0.999 and bhspec for 0 <= a* <= 0.8), while the negative-spin results come only from kerrbb/kerrbb2, which allow a* < 0. The grid boundary is demonstrably active: the free-color-correction slimbh fit pegs at a* = 0, and the paper concedes in Section 4.3 that a negative spin is 'possibly a true solution in this case.' The abstract's contrast between strongly negative spins from color-correction models and moderately positive spins from atmospheric models therefore conflates disk physics with parameter-space support. A two-sided atmospheric grid, as used by Middleton et al. (2014), should be fitted before the sign dichotomy is asserted. The residual spread in the fixed M, D, i fits (Table 3) still supports the broader model-dependence conclusion, but that conclusion should be stated separately from the sign claim.
  2. [Sections 4.2 and 4.3] The paper's own results show that 'atmosphere versus color correction' is not the clean axis separating the outcomes. kerrbb2, which implements color corrections fitted to the same Davis & Hubeny atmospheres, gives a* = -1 at the lower boundary of its valid range (M1 = 4.1 Msun, D = 10.8 kpc) when M1, D, and i are free, whereas bhspec and slimbh with atmospheric spectra give a* = 0.40 and 0.71. This apparent contradiction is noted in Section 4.2 as surprising, but it is not resolved, and Section 6 still summarizes the results as a dichotomy between color-correction and atmosphere-based models. The authors should either identify the specific model ingredient (e.g., zero-stress boundary correction, finite disk thickness, or the treatment of fcol in kerrbb2) that drives the difference, or soften the attribution in the conclusions.
  3. [Section 5.3] The preferred model, model 3, uses the standard Shakura-Sunyaev/Novikov-Thorne vertical structure, yet Section 5.3 states that this structure predicts strong viscous and thermal instability for L/L_E >= 0.02, far below the fitted values of L/L_E ~ 0.09-0.24, while the observed disk is extremely stable (rms < 0.5%). The paper acknowledges this tension but still designates model 3 as preferred by both chi^2 and Ockham's razor. Since the instability applies to the same standard disk model used in model 3, the preferred-model designation is not physically self-consistent as presented. A test or discussion of how magnetic pressure support or another modification restores stability is needed before model 3 can be presented as the physically preferred solution; otherwise the model-dependence claim should rest on the Table 3 comparison rather than on any single preferred model.
  4. [Section 3 and Section 5.1] The load-bearing premise for all continuum-fitting spin values is that the disk inner radius equals the ISCO, as stated in Section 3. The supporting argument in Section 5.1 based on the stability of the diskbb normalization is indirect and does not exclude disk truncation, warping, or the presence of a scattering layer. Because this premise is common to all models, it does not undermine the relative model-dependence conclusion, but it does mean that the absolute spin values quoted for each model inherit this unverified assumption. The paper should state this limitation explicitly in the conclusions and avoid presenting any single model's spin as a true measurement.
minor comments (3)
  1. [Abstract and Section 6] The abstract and conclusions state that different models yield spin values differing by 'up to ~0.3' for fixed mass, distance, and inclination, but Table 3 shows a spread from 0.20 to 0.70 in the fixed row, i.e., roughly 0.4-0.5, even before considering the free-fit results. Please correct this numerical summary.
  2. [Section 6] There is a typo in 'all of of the fits appearing reasonable' in the conclusions; please remove the duplicated 'of'.
  3. [Table 3] The error bars for the free-fit kerrbb2 spin, a* = -1 +0.05, and for diskbb in Table 2, a* = -1 +0.46, indicate that these fits are at or near the allowed boundary of -1; this should be stated in the table caption or text so readers do not interpret these as interior best fits with two-sided errors.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the spin measurements are derived by fitting distinct, independently constructed disk models to the data, and the model-dependence claim is a comparison of those fits rather than an imposed result.

full rationale

The paper's central claims are (i) that the fitted BH spin of GX 339-4 depends strongly on the chosen disk model, and (ii) that the specific family-level spin values differ (negative with color-correction models, positive with atmospheric models, weakly constrained with a warm corona). Both claims are obtained by fitting the same NICER/NuSTAR spectra with independent model families (kerrbb, kerrbb2, bhspec, slimbh, warm-corona-modified slimbh) and comparing the resulting best-fit parameters and chi-squared values. The spin is not defined in terms of the model-dependence conclusion, and no fitted parameter is renamed as a prediction: the paper explicitly reports the spin as a fitted quantity for each model, and the 'model dependence' is the spread of those fitted values, including a control case with fixed M1, D, i (Table 3). The paper also externally anchors the disk-radius interpretation using the independently measured mass function (Heida et al. 2017) and the diskbb normalization stability argument, so the ISCO assumption is at least partially supported by an external constraint rather than being identical to the spin output. Some methodological self-citations exist (use of comppsc from Zdziarski et al. 2024a and the warm-corona treatment from Zdziarski et al. 2024b), but the cited work is code and modeling practice, not a uniqueness theorem that forces the present spin values; in any case the spin values are data-driven fits, not imported from those citations. A caveat noted by the reader is that the atmospheric models (slimbh and bhspec) are tabulated only for a* >= 0, so the negative-spin solutions are only explored with kerrbb/kerrbb2; this is an asymmetry in parameter-space coverage and a correctness risk, but it is openly disclosed in the paper and does not make the derivation circular. The broad conclusion of model dependence survives the fixed-parameter fits in Table 3, where the spin spans roughly 0.2-0.7 even with M1, D, and i fixed. Therefore no step reduces by construction to its inputs, and the circularity score is 0.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The spin result rests on fitted parameters (mass, distance, inclination, color correction, warm corona) and on domain assumptions about disk geometry and atmosphere modeling. No new physical entities are introduced; the warm corona is a pre-existing model component. The assumption with the largest leverage is that the inner disk radius sits at the ISCO.

free parameters (9)
  • a* (dimensionless spin) = varies by model: -1.0 to +0.71 in Table 2
    Primary fitted quantity in all models; strongly model dependent.
  • M1 (black hole mass) = about 4 to 13 solar masses depending on model
    Fitted jointly with spin; affects the mass function comparison and ISCO radius.
  • D (distance) = 8 to 12 kpc, with prior 8 to 12 kpc
    Fitted; degenerate with spin and mass through the relativistic disk normalization.
  • i (inclination) = about 28 to 34 degrees
    Fitted; robust across models, but used in the mass function argument.
  • fcol (color correction) = 1.3 to 2.0
    Free in kerrbb and slimbh color-correction variants; shifts the inferred spin.
  • Warm corona parameters (tau_warm, kT_warm) = tau_warm 15 to 25, kT_warm 0.57 to 0.73 keV
    Added in model 4; the warm corona absorbs disk emission and makes the spin unconstrained.
  • ISM abundances (Z_O, Z_Fe) and disk Fe abundance = Z_O about 0.65-0.67, Z_Fe about 0.75-0.90, Z_Fe_disk up to 6
    Fitted absorption abundances affect the low-energy NICER spectrum and the disk model normalization.
  • Coronal Comptonization parameters (kTe, y, p, gamma_min, gamma_max, fcov) = vary between 2020 and 2021 datasets
    Fitted to the high-energy tail and reflection; their choice affects the reflection model and the inferred disk flux.
  • Reflection parameters (R, log xi, q) = R 0.5 to 2.0, log xi 2.7 to 4.3, q 2.2 to 6.0
    Fitted reflection fraction, ionization, and emissivity index; affect the spin constraint from the reflection component.
assumptions (6)
  • domain assumption The disk inner radius equals the ISCO in the soft state
    All relativistic disk models used here assume inner radius at ISCO; continuum-fitting spin depends on this. Stated in Section 3.
  • domain assumption The vertical structure and emission of the disk are described either by color corrections or by Davis-Hubeny atmospheric radiative transfer
    The choice between these treatments changes a* by ~0.3 to more than 1, so this is load-bearing. Sections 3 and 4.3.
  • domain assumption Prior ranges D = 8 to 12 kpc, M1 >= 4 solar masses, i <= 60 degrees
    These priors bound the fits and affect the mass function argument. Section 3.
  • domain assumption Standard Shakura-Sunyaev / Novikov-Thorne slim disk is dynamically stable at L/LE ~ 0.1
    The paper notes the standard disk is predicted to be viscously and thermally unstable while the observed rms is very low, an unresolved contradiction affecting the preferred model. Section 5.3.
  • domain assumption The mass function relation of Heida et al. (2017) is correct
    Equation (7), M1 sin^3 ib / (1 + M2/M1)^2 = 1.91 +/- 0.08 solar masses, is used to favor high-mass models 3 and 4.
  • standard math General relativistic ISCO radius relation (Bardeen et al. 1972)
    Foundation of continuum fitting; not in dispute.

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Cite this review

Pith. "Pith review of Is the Spin of the Black Hole in GX 339-4 Negative?." pith.science (2026). https://pith.science/paper/MMEZCIP5

@misc{pith2026241215705,
  author       = {Pith},
  title        = {Pith review of: Is the Spin of the Black Hole in GX 339-4 Negative?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MMEZCIP5}},
  note         = {Machine review of arXiv:2412.15705}
}
abstract

We have studied the accreting black hole binary GX 339--4 using two highly accurate broad-band X-ray data sets in very soft spectral states from simultaneous NICER and NuSTAR observations. Joint fitting of both data sets with relativistic models of the disk, its Comptonization and reflection allows us to relatively accurately determine the black-hole mass and spin, and the distance and inclination. However, we find the measured values strongly depend on the used disk model. With widely used Kerr disk models treating departures from local blackbody spectra using color corrections, we find relatively low black-hole masses and strongly negative spins (i.e., retrograde accretion). Then, models employing radiative transfer calculations of the disk atmosphere predict moderately positive spins and high masses. When adding a warm corona above the disk (as proposed before for both AGNs and accreting binaries), we find the spin is weakly constrained, but consistent with zero. In all cases, the fitted inclination is low, $\approx 30$--$34^\circ$. For the spin axis aligned with the binary axis, the mass function for this source implies large values of the mass, consistent only with those obtained with either disk-atmosphere models or the presence of a warm corona. We also test different disk models for an assumed set of mass, distance and inclination. We find that different models yield values of the spin parameter differing up to $\sim$0.3. Our results confirm previously found strong model dependencies of the measured black-hole spin, now by comparing different disk models and for a low-mass X-ray binary.

Figures

Figures reproduced from arXiv: 2412.15705 by the authors.

Figure 1
Figure 1. The NICER (black) and NuSTAR (blue and red) unfolded spectra (top panels) and data-to-model ratios (bottom panels) for the joint fit with model 3 (see [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Correlations between the main parameters calculated by MCMC for model 3. The median values and the 90% uncertainties are shown by the middle and surrounding dashed lines, respectively. The corresponding numerical values are given by the posterior dis￾tributions, which agree well with those in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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