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arxiv: 2605.24664 · v2 · pith:UBHT3OSOnew · submitted 2026-05-23 · 🌌 astro-ph.HE

Model dependence of XRISM black-hole spin constraints in Cyg X-1

Andrzej A. Zdziarski , Swadesh Chand , Michal Szanecki , Gulab Dewangan , Barbara De Marco This is my paper

Pith reviewed 2026-06-30 12:52 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords Cyg X-1black hole spinXRISMrelativistic reflectionrelxillComptonizationaccretion diskgravitational waves
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The pith

Black hole spin in Cyg X-1 depends on the X-ray reflection model

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

This paper studies XRISM Resolve spectra of the black hole X-ray binary Cyg X-1 taken simultaneously with NICER and NuSTAR in the hard state. It shows that the simplest relativistic reflection model applied to the Resolve data alone produces a near-maximal black hole spin. In contrast, improved Comptonization-based models produce a low spin value. Fits to the combined data sets are consistent with any spin value. The authors conclude that the spin is strongly model-dependent, although low values remain consistent with gravitational wave constraints. All models constrain the inner disk radius to less than 10 gravitational radii.

Core claim

Fits of the Resolve data alone with the simplest available relativistic reflection model, relxill, yield a black hole spin parameter close to the maximum, a_* = 0.99. However, fitting with an improved, Comptonization-based model, relxillCp, yields a low a_*=0.0^{+0.17}. A similarly low range is obtained with another Comptonization-based model, reflkerrD. Then, fits to the combined data require two Comptonization models but are consistent with any spin value. We conclude that the spin value of Cyg X-1 is strongly model-dependent. However, low spin values are consistent with the constraints from gravitational waves. All of the models constrain the inner disk radius to be <10 gravitational radi

What carries the argument

Choice between the simplest relativistic reflection model relxill and Comptonization-based models relxillCp or reflkerrD when fitting the iron line and reflection spectrum

If this is right

  • The derived spin changes from near-maximal to near-zero with model choice on the same data.
  • Low spin values are allowed and align with gravitational wave constraints from black hole mergers.
  • The inner accretion disk radius is constrained below 10 gravitational radii in every model.
  • An outflowing disk corona is indicated as the geometry of the X-ray source.
  • The same geometry accounts for the observed X-ray polarization from the source.

Where Pith is reading between the lines

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

  • Applying similar model comparisons to other X-ray binaries could test whether spin estimates are generally model-dependent.
  • Reverberation lag measurements that independently confirm or refute the inner disk radius limit would test the robustness of the result.
  • This model dependence suggests that published spin values for other sources may require re-analysis with multiple reflection models.

Load-bearing premise

Differences in fitted spin arise purely from the choice of reflection model rather than from unaccounted systematic effects in data calibration, background subtraction, or unmodeled spectral components.

What would settle it

An independent spin measurement for the black hole in Cyg X-1, such as from gravitational waves in a future merger, that lies outside the range permitted by the Comptonization models.

Figures

Figures reproduced from arXiv: 2605.24664 by Andrzej A. Zdziarski, Barbara de Marco, Gulab Dewangan, Michal Szanecki, Swadesh Chand.

Figure 1
Figure 1. Figure 1: The light curves from NICER, NuSTAR, and XRISM Resolve (from top to bottom), together with the corresponding hard￾ness ratios, for the first 42 h studied in this work. The zero time is set to the start time of the Resolve observation, i.e., 2024-04-07 17:56:58. 2. THE DATA, LIGHTCURVES AND VARIABILITY We use the same XRISM observation as in D25. Cyg X￾1 was observed over half of its orbital period, at the … view at source ↗
Figure 2
Figure 2. Figure 2: (a) the 2–20 keV count rate vs. the (4–10)/(2–4) keV hardness ratio. (b) The (10–20)/(4–10) keV hardness ratio vs. the (4–10)/(2–4) keV hardness ratio (the color-color diagram). Both panels show MAXI data binned over 10-day intervals. The MAXI data averaged over the days of the XRISM observation used by us are shown as red symbols. resolution primary (Hp) events and excluded pixels 12 and 27. The small (S)… view at source ↗
Figure 3
Figure 3. Figure 3: The rms(E) in the 0.01–1 Hz frequency range for NICER (red) and XRISM Resolve (blue). For comparison, the black symbols show the rms(E) from NICER in the soft spectral state (Zdziarski et al. 2024). We see similar trends in soft X-rays, with broad peaks around 1 keV, though the soft-state rms is much lower. Above that, we observe a decrease with energy in the hard state and an increase in the soft state, w… view at source ↗
Figure 4
Figure 4. Figure 4: The Resolve unfolded spectrum (top) and data-to-model ratio (bottom) for the fit using relxillCp. The total and unab￾sorbed model spectra are shown by the solid black and cyan curves, respectively. The incident and reflection components are shown by the blue and red curves, respectively. Here and in Figures 5 and 6 below, the spectra have been rebinned for plotting. reflection strength to R ≤ 2 and obtaine… view at source ↗
Figure 5
Figure 5. Figure 5: The NICER (green), Resolve (black), and NuSTAR (blue and red) unfolded spectra (top) and data-to-model ratios (bottom) for the fit with two reflkerrD components. The total and unab￾sorbed model spectra are shown by the solid black and cyan curves, respectively. The incident and reflection components are shown by the blue and red curves for the hard component, and by the green and magenta curves for the sof… view at source ↗
Figure 6
Figure 6. Figure 6: The NICER (green), Resolve (black), and NuSTAR (blue and red) data-to-model ratios for the fit with the two-reflkerrD model, covering the full NuSTAR spectral range, 3–79 keV. We observe a substantial excess of Resolve counts in the Fe K range compared with those from NuSTAR and NICER. We also show the Xtend 0.5–10 keV spectrum unfolded with that model (not fitted). 0.15+0.11 −0.01 keV, fully agrees with t… view at source ↗
read the original abstract

We study the persistent black hole X-ray binary Cyg X-1, recently observed by XRISM Resolve and simultaneously by NICER and NuSTAR in its hard spectral state. We confirm the result of Draghis et al. that fits of the Resolve data alone with the simplest available relativistic reflection model, relxill, yield a black hole spin parameter close to the maximum, $a_* = 0.99$. However, fitting with an improved, Comptonization-based model, relxillCp, yields a low $a_*=0.0^{+0.17}$. A similarly low range is obtained with another Comptonization-based model, reflkerrD. Then, fits to the combined data require two Comptonization models but are consistent with any spin value. We conclude that the spin value of Cyg X-1 is strongly model-dependent. However, low spin values are consistent with the constraints from gravitational waves. All of the models constrain the inner disk radius to be <10 gravitational radii, which is consistent with a recent finding of the weakness of thermal reverberation in Cyg X-1. The suggested source geometry is that of an outflowing disk corona, which was also proposed to explain the X-ray polarization observed from this source.

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 / 1 minor

Summary. The manuscript analyzes XRISM Resolve spectra of Cyg X-1 in the hard state, both alone and jointly with NICER/NuSTAR data, using three relativistic reflection models. It reports that the simplest model (relxill) returns a near-maximal spin a* = 0.99 while Comptonization-based models (relxillCp, reflkerrD) return a* = 0, with joint fits allowing any spin; the inner disk radius is constrained to <10 Rg in all cases. The authors conclude that the spin measurement is strongly model-dependent but that low-spin solutions are consistent with gravitational-wave constraints, favoring an outflowing corona geometry.

Significance. If the reported model dependence is robust, the result would caution against over-interpreting high spins obtained with the simplest reflection models and would strengthen the case for low spin in Cyg X-1, aligning X-ray reflection with gravitational-wave constraints. The consistent inner-radius limit across models also provides supporting evidence for the proposed corona geometry.

major comments (2)
  1. [Abstract] Abstract: the central claim of strong model dependence rests on the reported best-fit spins (a* = 0.99 vs a* = 0) differing between relxill and the Comptonization-based models, yet no fit statistics (reduced chi-squared, degrees of freedom, or null-hypothesis probabilities) are quoted, preventing assessment of whether the low-spin solutions are statistically preferred or merely allowed.
  2. [Results] The attribution of the spin discrepancy exclusively to the choice of reflection model assumes that data reduction, background subtraction, and calibration are identical across all fits; no quantitative test or table demonstrating that these systematics are held fixed is provided, leaving open the possibility that unmodeled components (e.g., the second Comptonization component required only in joint fits) contribute to the difference.
minor comments (1)
  1. A summary table listing best-fit parameters, uncertainties, and fit statistics for every model–dataset combination would make the model-dependence claim easier to evaluate.

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.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of strong model dependence rests on the reported best-fit spins (a* = 0.99 vs a* = 0) differing between relxill and the Comptonization-based models, yet no fit statistics (reduced chi-squared, degrees of freedom, or null-hypothesis probabilities) are quoted, preventing assessment of whether the low-spin solutions are statistically preferred or merely allowed.

    Authors: We agree that explicit fit statistics in the abstract would aid assessment. The manuscript body and tables report reduced chi-squared values and degrees of freedom for all models; the Comptonization-based models yield statistically acceptable fits (reduced chi^2 comparable to or lower than relxill). We will revise the abstract to include a concise statement noting that all models provide acceptable fits to the Resolve data. revision: yes

  2. Referee: [Results] The attribution of the spin discrepancy exclusively to the choice of reflection model assumes that data reduction, background subtraction, and calibration are identical across all fits; no quantitative test or table demonstrating that these systematics are held fixed is provided, leaving open the possibility that unmodeled components (e.g., the second Comptonization component required only in joint fits) contribute to the difference.

    Authors: All fits in the manuscript (Resolve-only and joint) employ identical data reduction, background subtraction, and calibration for the XRISM, NICER, and NuSTAR datasets. The second Comptonization component appears only in joint fits to accommodate the wider bandpass; Resolve-only fits use a single component consistent with each reflection model. We will add an explicit statement in the data analysis section confirming that processing steps are held fixed across all model comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity; results are direct outputs of independent model fits to data

full rationale

The paper reports spin constraints obtained by fitting named public reflection models (relxill, relxillCp, reflkerrD) to XRISM Resolve, NICER, and NuSTAR spectra. The differing a* values (0.99 vs. 0) and the joint-fit consistency with any spin are direct numerical outputs of those fits, not quantities defined in terms of themselves or reduced by construction from the paper's own equations. No self-citations are invoked to justify uniqueness or load-bearing premises, no ansatzes are smuggled via prior work, and no fitted parameters are relabeled as predictions. The derivation chain is therefore self-contained against external data and standard models.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the chosen reflection models capture the dominant physics and that differences between them reflect real model uncertainty rather than data artifacts.

free parameters (2)
  • black hole spin a_*
    Primary fitted parameter whose value changes dramatically between models.
  • inner disk radius R_in
    Fitted parameter constrained to <10 R_g by all models.
axioms (1)
  • domain assumption The relativistic reflection models relxill, relxillCp, and reflkerrD provide adequate descriptions of the hard-state spectrum of Cyg X-1.
    Invoked when interpreting fit results as physical constraints on spin and geometry.

pith-pipeline@v0.9.1-grok · 5770 in / 1383 out tokens · 44038 ms · 2026-06-30T12:52:29.616101+00:00 · methodology

discussion (0)

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