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arxiv: 2606.22446 · v1 · pith:PSBMGLG5new · submitted 2026-06-21 · 🌌 astro-ph.HE · gr-qc

Unified Mass-Scaled QPO Signatures of Kerr Sen Black Holes from Stellar Mass to Supermassive Sources

Orhan Donmez , G. Mustafa This is my paper

Pith reviewed 2026-06-26 10:00 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords Kerr-Sen black holesquasi-periodic oscillationsBondi-Hoyle-Lyttleton accretionshock-cone oscillationsblack hole timingmass accretion rateinverse mass scaling
0
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The pith

Kerr-Sen black hole shock-cone oscillations produce QPO frequencies that scale inversely with mass to match observations from stellar-mass to supermassive black holes.

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

This paper numerically solves relativistic Bondi-Hoyle-Lyttleton accretion in the equatorial plane of Kerr-Sen black holes at two spin values. It computes the mass accretion rate time series, derives the power spectral density, and fits Lorentzian components to extract dominant QPO-like modes. These modes exhibit shifted frequencies and near-resonant structures due to the spacetime deformation. When the frequencies are scaled inversely with black hole mass, they align reasonably with observed QPOs in seven listed sources spanning stellar, intermediate, and supermassive regimes. A sympathetic reader would care because the work proposes a single hydrodynamical mechanism that could unify timing data across mass scales and help bound deviations from the Kerr geometry.

Core claim

The central claim is that the charge-related deformation of the Kerr-Sen spacetime alters shock-cone morphology and the resulting mass accretion rate variability, shifting characteristic frequencies and generating near-resonant harmonic structures close to 3:2 and 2:1 ratios; after inverse-mass scaling, these numerically obtained frequencies show reasonable agreement with observed QPOs in GRS 1915+105, IGR J17091-3624, M82 X-1, NGC 5408 X-1, RE J1034+396, 1H 0707-495, and ESO 113-G010, supporting the possibility of a unified framework for interpreting timing features across black hole mass ranges.

What carries the argument

The mass accretion rate time series extracted from numerical simulations of equatorial relativistic BHL flow around Kerr-Sen black holes, whose power spectral density is decomposed into multi-component Lorentzian profiles to isolate dominant QPO-like modes.

If this is right

  • Kerr-Sen shock-cone oscillations can serve as a unified framework for timing features over a broad range of black hole masses.
  • The approach may help constrain mass and spin parameters for sources whose properties remain observationally uncertain.
  • Combined hydrodynamical and timing diagnostics can test the extent of empirical deviations from Kerr spacetime.
  • Near-resonant harmonic structures produced in the simulations offer specific frequency ratios for observational comparison.

Where Pith is reading between the lines

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

  • If the scaling holds, the same simulation pipeline could be rerun for other non-Kerr metrics to generate testable frequency templates.
  • High-cadence monitoring of additional intermediate-mass black hole candidates could tighten bounds on the charge parameter.
  • Incorporating radiative transfer post-processing would allow direct comparison with energy-dependent QPO data rather than accretion-rate proxies alone.

Load-bearing premise

The simulated mass accretion rate oscillations correspond directly to observed QPOs through simple inverse-mass scaling without further modeling of radiative transfer or disk emission.

What would settle it

Detection of QPO frequencies in any of the compared sources that deviate substantially from the mass-scaled values predicted by the Kerr-Sen shock-cone simulations, after accounting for the quoted spin values.

Figures

Figures reproduced from arXiv: 2606.22446 by G. Mustafa, Orhan Donmez.

Figure 1
Figure 1. Figure 1: FIG. 1. The inner and outer horizons of the Kerr–Sen black hol [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Azimuthal variation of the rest-mass density around [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time evolution of the mass-accretion rate at [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. PSD analyses and Lorentzian fits for the rapidly rotat [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. It is same as Fig [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

In this study, we numerically investigate Bondi-Hoyle-Lyttleton (BHL) accretion around Kerr-Sen black holes and examine how the charge-related deformation of the spacetime affects the shock-cone morphology, the variation of the mass accretion rate, and the quasi-periodic oscillation (QPO)-like temporal behavior. The relativistic BHL flow is solved numerically in the equatorial plane for two different black hole spin parameters, a = 0.9 M and a = 0.5 M. From the numerically computed mass accretion rate signal, we calculate the power spectral density (PSD) and perform multi-component Lorentzian fits to identify the dominant QPO-like modes excited around the black hole. The results show that the Kerr-Sen deformation shifts the characteristic frequencies, changes the coherence properties of the oscillation modes, and produces near-resonant harmonic structures close to 3:2 and 2:1. By using inverse mass scaling, the numerically computed frequencies are compared with observed QPOs from stellar-mass, intermediate-mass, and supermassive black hole systems. In particular, reasonable agreement between the numerical simulation results and observations is found for the sources GRS 1915+105, IGR J17091-3624, M82 X-1, NGC 5408 X-1, RE J1034+396, 1H 0707-495, and ESO 113-G010. This comparative analysis indicates that Kerr-Sen black hole shock-cone oscillations may provide a unified framework for interpreting timing features over a broad range of black hole masses and may additionally contribute to constraining the mass and spin parameters of sources whose properties are not yet fully established observationally. These findings further imply that combined hydrodynamical and timing diagnostics constitute a promising approach for assessing the extent to which deviations associated with the Kerr-Sen geometry can be empirically distinguished from those of the Kerr spacetime.

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 numerically simulates equatorial Bondi-Hoyle-Lyttleton accretion onto Kerr-Sen black holes at spins a=0.9M and a=0.5M, extracts QPO-like modes from the PSD of the mass-accretion-rate time series via multi-Lorentzian fits, notes shifts and near-resonant 3:2/2:1 structures due to the charge deformation, and applies inverse-mass scaling to report reasonable agreement with observed QPOs in GRS 1915+105, IGR J17091-3624, M82 X-1, NGC 5408 X-1, RE J1034+396, 1H 0707-495, and ESO 113-G010, proposing that shock-cone oscillations supply a unified framework across stellar to supermassive scales.

Significance. If the frequency mapping survives radiative post-processing, the work would supply a concrete hydrodynamical mechanism for QPO generation in non-Kerr spacetimes and a potential route to joint mass-spin constraints; the numerical extraction of modes from BHL flows and the explicit inverse-mass scaling constitute reproducible steps that could be tested further.

major comments (2)
  1. [Numerical setup and comparison with observations] The unified-framework claim (abstract) rests on the premise that dominant frequencies identified in the Ṁ(t) PSD map directly to observed X-ray QPO frequencies. The simulations solve only the relativistic hydro equations; no radiative transfer, Comptonization, or disk-emission modeling is performed, leaving untested whether the reported 3:2 and 2:1 structures would survive in the emergent light curve.
  2. [Abstract and results] The statement of 'reasonable agreement' after inverse-mass scaling is presented without quantitative metrics, χ^{2} values, or resolution tests; the matches are described qualitatively, which weakens the cross-mass-scale claim.
minor comments (2)
  1. [Methods] The multi-Lorentzian fitting procedure and the precise definition of the charge deformation parameter's effect on the shock-cone frequencies could be stated more explicitly.
  2. [Results] Figure captions or tables listing the fitted frequencies, widths, and scaled values for each source would improve traceability of the comparisons.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and indicate the revisions we will incorporate in the next version.

read point-by-point responses

  1. Referee: [Numerical setup and comparison with observations] The unified-framework claim (abstract) rests on the premise that dominant frequencies identified in the Ṁ(t) PSD map directly to observed X-ray QPO frequencies. The simulations solve only the relativistic hydro equations; no radiative transfer, Comptonization, or disk-emission modeling is performed, leaving untested whether the reported 3:2 and 2:1 structures would survive in the emergent light curve.

    Authors: We agree that our simulations are purely hydrodynamical and do not include radiative transfer or emission modeling. This is an inherent limitation of the current study, and the direct mapping to X-ray light curves remains an assumption. Similar hydro-only analyses have been employed in prior QPO literature to identify dynamical mechanisms. We have revised the abstract, introduction, and discussion sections to explicitly frame the results as a hydrodynamical mechanism for QPO generation and to note that survival of the frequency structures in the emergent radiation requires future radiative post-processing. This clarification strengthens rather than weakens the unified-framework proposal by defining its current scope. revision: partial

  2. Referee: [Abstract and results] The statement of 'reasonable agreement' after inverse-mass scaling is presented without quantitative metrics, χ² values, or resolution tests; the matches are described qualitatively, which weakens the cross-mass-scale claim.

    Authors: We accept that the original presentation relies on qualitative description. In the revised manuscript we add a dedicated table that lists the inverse-mass-scaled numerical frequencies against the observed QPO values for each cited source, together with the relative percentage differences. We also include a short subsection reporting resolution tests (three grid resolutions) that demonstrate convergence of the dominant Lorentzian-fitted modes to within a few percent. These additions provide the requested quantitative support while preserving the original conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's chain consists of independent numerical solution of relativistic BHL hydrodynamics in Kerr-Sen spacetime for fixed spins a=0.9M and a=0.5M, extraction of dominant frequencies via multi-Lorentzian fits to the PSD of the simulated Ṁ(t) time series, and subsequent application of standard inverse-mass scaling (f ∝ 1/M) for external comparison against observed QPO frequencies in listed sources. No step reduces by construction to its own inputs: the simulated frequencies are generated from the hydro equations without reference to the observational data, the Lorentzian fitting is performed on the numerical PSD alone, and the scaling is a physical expectation independent of the specific sources chosen for illustration. The text contains no self-citations, uniqueness theorems, or ansatzes that load-bear the central claim. The reported 'reasonable agreement' is a post-simulation comparison, not a fitted prediction or self-definitional equivalence.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the numerical hydrodynamics accurately capturing shock-cone oscillations and on those oscillations being the physical origin of the observed QPOs; no independent evidence for either link is provided.

free parameters (2)
  • Black hole spin parameter a = 0.9M, 0.5M
    Fixed at 0.9M and 0.5M for the two simulation runs; chosen rather than derived.
  • Kerr-Sen charge deformation parameter
    Varied implicitly to produce the reported frequency shifts; exact values not stated.
axioms (2)
  • domain assumption The spacetime geometry is exactly the Kerr-Sen metric
    Invoked as the background for all simulations.
  • domain assumption BHL accretion can be accurately modeled in the equatorial plane with the chosen numerical scheme
    Core modeling choice stated in the abstract.

pith-pipeline@v0.9.1-grok · 5889 in / 1415 out tokens · 26638 ms · 2026-06-26T10:00:25.123838+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

92 extracted references

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    Thus, the inter- action between the black hole spin and the Kerr–Sen defor- mation parameters defines both the shock-cone morphology and the temporal behavior of the accretion rate. These resul ts show that the variation in the mass-accretion rate appears a s an important condition for observationally distinguishin g the 8 5000 10000 15000 20000 25000 3000...

  2. [2]

    The dominant Lorentzian components occur approximately at 10 . 15, 17 . 48, 27 . 11, 49 . 40, and 82 . 91 Hz. The low-frequency components at 10 . 15 and 17 . 48 Hz show that the oscillations of the shock cone excite more than one mode in the inner accretion flow. The component around

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    11 Hz is particularly important because the ratio of these frequencies, 27 . 11/ 17. 48 ≃ 1. 55, gives an approximate 3:2 ratio. These types of resonance conditions are frequently discussed in the context of black-hole QPO phenomenology [ 34, 59, 60]. Such a near-commensurable structure may be the result of nonlinear couplings between the modes trapped in...

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    61, and 91 . 84 Hz. When compared with the KS1 and KS2 models, the frequency distribution is more irregular, show - ing that the stronger deformation changes the oscillatory r e- sponse of the accretion flow. The low-frequency component at

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    On the other hand, the components at 19

    35 Hz may be a result of the global modulation of the shock cone. On the other hand, the components at 19 . 09, 34 . 12, and 47 . 61 Hz may have formed as a result of the excitation of the modes trapped inside the shock cone in the post-shock region. An approximately 2:1 ratio is observed between 91 . 84 and 47 . 61 Hz, since 91 . 84/ 47. 61 ≃1. 93. In ge...

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    67, and 52

    69, 42 . 67, and 52 . 75 Hz. This model appears as one of the models that produces the clearest near-resonant struct ure among the models considered so far. For example, the ratio

  7. [7]

    73/ 10. 46 ≃ 1. 50 gives a value very close to the 3:2 re- lation. The ratio 52 . 75/ 26. 69 ≃ 1. 98 produces a resonance state very close to 2:1. Thus, the KS4 model, which describes a strongly deformed case, supports the formation of multipl e coupled oscillation modes. This behavior is consistent wit h the strong temporal variations previously observed...

  8. [8]

    90, and 68 . 72 Hz. The low-frequency component at

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    74 Hz has a very large quality factor, Q = 79. 04. This im- plies that this peak is highly coherent. This peak may have emerged as a result of the slow variation of the global mod- ulation of the shock structure. The component at 16 . 74 Hz has a very small quality factor. This shows that this peak is very broad and has very low coherence. This means that...

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    03, and 59 . 27 Hz. This model represents the case with the strongest Kerr–Sen deformation for the moderately rota t- ing black hole model with a = 0. 5M. The PSD structure formed in this case shows that more complex oscillation be- havior occurs. The low-frequency component at 11 . 63 Hz has a moderate quality factor. In contrast, the peak at 21 . 17 Hz ...

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    03/ 21. 17 ≃ 1. 99, which is very close to a 2:1 harmonic structure. In addition, 59 . 27 Hz gives 59 . 27/ 21. 17 ≃ 2. 80, indicating that higher-order harmonics or nonlinear coupl ings may exist. Thus, the KS6 model shows that, in the strongly de- formed case, a mixture of coherent peaks can form, together with broader oscillation components and near-ha...

    1915

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    91 Hz obtained in the KS1 model are rescaled according to the observed mass range of this source, the frequencies ar e found to be in the ranges 0. 75–3 . 53 Hz and 1. 26–5 . 92 Hz. The numerical QPO-like peaks calculated for this source are com - patible with the observed 3 . 32 and 5 . 07 Hz QPOs. Thus, the KS1 model can reproduce the observed QPO pair ...

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    In the KS5 model, the frequencies obtained for a black hole with M = 10M⊙ are 53

    5M also provides important comparison results for the source M82 X—1 as seen in Table III. In the KS5 model, the frequencies obtained for a black hole with M = 10M⊙ are 53. 90 and 68 . 72 Hz. When these frequencies are rescaled according to the observed mass range of M82 X–1, the QPO frequencies become 0 . 82–3 . 85 Hz and 1 . 04–4 . 91 Hz. These values f...

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    The corresponding observed black-hole masses vary in the range 1000–9000 M⊙

    020 Hz. The corresponding observed black-hole masses vary in the range 1000–9000 M⊙. When the numerically com- puted frequencies 10 . 15 and 17 . 48 Hz of the rapidly rotating black-hole model KS1 are rescaled using the observed masses, the numerical results for the source NGC 5408 X–1 are found to be in the ranges 0 . 011–0 . 102 Hz and 0 . 019–0 . 175 H...

    1915

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    74 Hz, computed for a black-hole mass of M = 10M⊙, are rescaled using the observed black-hole masses in the range 1000–9000 M⊙, the frequencies are found to occur in the ranges 0 . 005–0 . 047 Hz and 0 . 019–0 . 167 Hz. The sec- ond scaled frequency interval includes the observed 0 . 010–

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    Thus, the KS5 model can explain only part of the observed temporal behavior of this source

    020 Hz range, while the first interval extends below the ob- served band. Thus, the KS5 model can explain only part of the observed temporal behavior of this source. However, the KS5 model does not naturally reproduce the observed range completely, as in the KS1 model. This implies that the KS1 model may be a stronger model for explaining the source NGC 54...

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    When the Kerr–Sen model KS1, namely the model with spin parameter a = 0

    83) ×10−4 Hz, while the observed black-hole mass is re- ported to be in the range (1–4) ×106M⊙. When the Kerr–Sen model KS1, namely the model with spin parameter a = 0. 9M, is considered, the numerically computed frequencies for a black-hole mass of M = 10M⊙ are 49 . 40 and 82 . 91 Hz. If these frequencies are rescaled using the observed mass of th e sour...

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    These rescaled frequency intervals are com- patible with the observed QPO range

    87) ×10−4 Hz. These rescaled frequency intervals are com- patible with the observed QPO range. Thus, both the KS1 and KS5 models are capable of explaining the observed temporal behavior of the source RE J1034 +396. On the other hand, the spin of this source has not been fully calculated. There- fore, due to the agreement between the numerically computed Q...

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    This appears as the numerical QPO-like be- 15 TABLE III

    15) ×10−4 Hz. This appears as the numerical QPO-like be- 15 TABLE III. Comparison between observed intermediate-mass black-hole QPO candidates and the mass-scaled numerical Ke rr–Sen frequen- cies. The numerical frequencies are originally computed fo r M = 10M⊙and are rescaled using Eq. 11. Source Observed mass Observationally Observed QPOs Numeri cal mod...

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    1915

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    53 Hz and 1 . 26–5 . 92 Hz are obtained. This is seen to be compatible with the frequency range observed from the source M82 X–1. At the same time, the numerical frequencies ob- tained from the KS5 model for the moderately rotating black hole are also seen to be compatible with the observational re - sults of the same source. In particular, the agreement ...

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