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arxiv: 2604.08439 · v2 · submitted 2026-04-09 · 🌌 astro-ph.HE · gr-qc

Recognition: unknown

Optical images of Kerr-Sen black hole illuminated by thick accretion disks

Yu-Kang Wang , Chen-Yu Yang , Xiao-Xiong Zeng
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:31 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords Kerr-Sen black holeaccretion diskblack hole shadowphoton ringpolarizationframe draggingRIAFBAAF
0
0 comments X

The pith

Increasing charge in a Kerr-Sen black hole shrinks its photon rings and central shadow while spin produces growing brightness asymmetry.

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

The paper calculates shadow and polarization images of a Kerr-Sen black hole lit by two thick, optically thin accretion disk models, one phenomenological and one analytical. It shows that raising the charge parameter Q makes both the bright photon rings and the dark central region smaller in both models, while the black hole's spin creates a left-right brightness difference that grows stronger at higher spin values and steeper viewing angles. Polarization maps reveal that lensing and frame dragging set the direction of the polarization vectors, with charge mainly affecting the brightness near the rings and the visibility of higher-order images. These results matter because they give concrete predictions for how charge and spin would appear in high-resolution images from future telescopes.

Core claim

Both the RIAF and BAAF accretion models produce images in which photon rings and central dark regions shrink together as the black hole charge Q rises. Frame dragging from the spin parameter a creates a clear brightness asymmetry across the image that strengthens with larger a and larger observer inclination θ. In the BAAF model the conical approximation makes higher-order images narrower and more distinctly separated from the direct image than in the RIAF case. Polarization vectors are arranged mainly by gravitational lensing and dragging, while charge Q controls the intensity scale near the photon ring and the size of higher-order features.

What carries the argument

Radiative transfer through geometrically thick, optically thin RIAF and BAAF accretion flows in the Kerr-Sen spacetime metric, which encodes both spin a and charge Q.

If this is right

  • Observed black hole shadows would appear smaller for higher-charge objects than for charge-free ones at the same mass and spin.
  • Rapidly spinning black holes viewed nearly edge-on would display stronger left-right brightness differences than slowly spinning or face-on ones.
  • Higher-order images would be brighter in the polar regions under anisotropic emission than under isotropic emission.
  • Polarization patterns near the ring would remain similar across different charge values, but overall ring brightness would drop with rising charge.

Where Pith is reading between the lines

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

  • Future Event Horizon Telescope upgrades could use the predicted ring-size versus charge relation to place upper limits on black hole charge.
  • The distinct separation of higher-order images in the BAAF model suggests that very long baseline observations might resolve model-dependent features.
  • The same radiative-transfer approach could be applied to other charged rotating metrics to compare image signatures across alternative gravity theories.

Load-bearing premise

The two chosen accretion disk models correctly describe the actual flow geometry and optical properties near the black hole.

What would settle it

High-resolution images of a supermassive black hole that show photon ring size increasing, rather than decreasing, with independent estimates of charge would contradict the predicted shrinkage.

Figures

Figures reproduced from arXiv: 2604.08439 by Chen-Yu Yang, Xiao-Xiong Zeng, Yu-Kang Wang.

Figure 1
Figure 1. Figure 1: Black hole shadow images of the RIAF model under isotropic radiation, with [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Blurred images obtained using a Gaussian filter with a standard deviation of 1 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The blurred images are obtained via Gaussian smoothing, with the Gaussian standard [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: Black hole shadow images of the RIAF model under isotropic radiation, with [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Blurred images obtained using a Gaussian filter with a standard deviation of 1 [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Black hole shadow images of the RIAF model under anisotropic radiation, with [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Blurred images obtained using a Gaussian filter with a standard deviation of 1 [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Black hole shadow images of the RIAF model under anisotropic radiation, with [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Blurred images obtained using a Gaussian filter with a standard deviation of 1 [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Black hole shadow images of the BAAF model, with [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Blurred images obtained using a Gaussian filter with a standard deviation of 1 [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Black hole shadow images of the BAAF model, with [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Blurred images obtained using a Gaussian filter with a standard deviation of 1 [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The resulting Stokes parameters I, Q, U, and V for the RAAF model. The accretion flow follows the conical solution, with parameters fixed at a = 0.5, Q2 = 1.0, θ = 85◦ , and an observation frequency of 230 GHz. 26 [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Polarized black hole shadow images for the RAAF disk model. The accretion flow follows [PITH_FULL_IMAGE:figures/full_fig_p028_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Polarized black hole shadow images for the BAAF model. The accretion flow follows the [PITH_FULL_IMAGE:figures/full_fig_p029_15.png] view at source ↗
read the original abstract

This paper investigates the shadow and polarization images of a Kerr-Sen black hole illuminated by geometrically thick and optically thin accretion disks. We adopt two classes of accretion models, namely the phenomenological radiatively inefficient accretion flow (RIAF) model and the analytical ballistic approximation accretion flow (BAAF) model. Based on radiative transfer theory, we examine the effects of the spin parameter $a$, black hole charge $Q$, and observer inclination angle $\theta$ on the shadow images. Both models show that, as the charge $Q$ increases, the photon rings and the central dark regions shrink simultaneously. Meanwhile, frame dragging gives rise to a pronounced brightness asymmetry, which becomes more significant with increasing $a$ and $\theta$. The main difference between isotropic and anisotropic radiation is that, in the latter case, the higher order images are brighter in the upper and lower polar regions. For the BAAF model, because the conical approximation renders certain regions geometrically thinner, the spatial extent of the higher order images is narrower than that in the RIAF model, and the separation between the direct image and the higher order images is more distinct. In the polarization images, the spatial distribution of the polarization vector directions is mainly determined by gravitational lensing and frame dragging, whereas the intensity near the photon ring and the scale of the higher order images are significantly influenced by $Q$.

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 investigates the shadow and polarization images of a Kerr-Sen black hole illuminated by geometrically thick and optically thin accretion disks. It adopts two accretion models (phenomenological RIAF and analytical BAAF) and uses radiative transfer to examine effects of spin a, charge Q, and inclination θ. Both models show that increasing Q shrinks the photon rings and central dark regions simultaneously, while frame dragging produces brightness asymmetry that grows with a and θ. Differences between isotropic and anisotropic radiation, between the two flow models (e.g., narrower higher-order images in BAAF), and polarization vector distributions influenced by lensing, dragging, and Q are also reported.

Significance. If the reported qualitative trends hold, this work contributes useful predictions for how charge in the Kerr-Sen metric modifies black-hole images relative to Kerr, which may help interpret future EHT-style observations of potential non-Kerr objects. The comparison of two distinct accretion models provides a useful robustness check on geometry-dependent features. Strengths include the direct link between reported trends and known metric properties (photon-sphere radius decreasing with Q) and the inclusion of polarization maps, which are less frequently computed in such studies.

major comments (2)
  1. [Methods / Radiative Transfer] The radiative transfer and ray-tracing implementation (methods section): lacks any description of the numerical integration scheme for geodesics and intensity, image grid resolution, or convergence/error analysis. Without these, the specific claims of simultaneous shrinkage of photon rings and central dark regions with increasing Q cannot be independently verified, even though the trends are qualitatively expected from the metric.
  2. [Accretion Models] Accretion flow modeling (RIAF and BAAF sections): the assumptions of geometric thickness and optical thinness are adopted without quantitative justification or comparison to MHD simulations. Since the images and higher-order features depend directly on the flow geometry and emissivity, this is load-bearing for the reported model differences and Q-dependent effects.
minor comments (2)
  1. [Abstract / Introduction] The abstract and introduction would benefit from explicit statement of the parameter ranges explored (specific values or intervals for a, Q, θ) to allow readers to assess the scope of the trends.
  2. Notation for the Kerr-Sen charge parameter Q and the distinction between isotropic versus anisotropic emission should be defined at first use with a brief equation reference for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments, which will help improve the clarity and reproducibility of the manuscript. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Methods / Radiative Transfer] The radiative transfer and ray-tracing implementation (methods section): lacks any description of the numerical integration scheme for geodesics and intensity, image grid resolution, or convergence/error analysis. Without these, the specific claims of simultaneous shrinkage of photon rings and central dark regions with increasing Q cannot be independently verified, even though the trends are qualitatively expected from the metric.

    Authors: We agree that additional numerical details are required for independent verification. Although the simultaneous shrinkage of photon rings and central shadows with increasing Q is a direct consequence of the Kerr-Sen metric (the photon-sphere radius decreases with Q), we will revise the Methods section to specify the geodesic integration scheme (fourth-order Runge-Kutta with adaptive step-size control), the radiative transfer integration along null geodesics, the image-plane grid resolution (800×800 pixels for the main results), and convergence tests showing that photon-ring positions and shadow boundaries stabilize to better than 1% under refinement. These additions will be included in the revised manuscript. revision: yes

  2. Referee: [Accretion Models] Accretion flow modeling (RIAF and BAAF sections): the assumptions of geometric thickness and optical thinness are adopted without quantitative justification or comparison to MHD simulations. Since the images and higher-order features depend directly on the flow geometry and emissivity, this is load-bearing for the reported model differences and Q-dependent effects.

    Authors: The RIAF and BAAF models are standard phenomenological and analytical approximations for geometrically thick, optically thin disks in the RIAF regime. Their defining assumptions of H/R ∼ 1 and τ ≪ 1 are taken from the literature on low-luminosity systems. While a direct comparison to GRMHD simulations in the Kerr-Sen metric would be desirable, such simulations are not yet available and lie outside the scope of the present work. In the revision we will add a paragraph in the accretion-model sections that (i) cites the original model references, (ii) summarizes typical disk heights and optical depths from existing Kerr GRMHD runs, and (iii) explains how the reported differences (e.g., narrower higher-order images in BAAF) arise from the distinct geometric prescriptions. This will better justify the load-bearing assumptions while preserving the model-comparison robustness check. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central results are obtained by numerical ray-tracing and radiative transfer through the Kerr-Sen metric using two independent phenomenological accretion models (RIAF and BAAF). The reported trends (photon-ring shrinkage with Q, frame-dragging asymmetry increasing with a and θ) follow directly from the metric's photon-sphere properties and standard light-propagation equations under the stated geometric-thickness and optical-thinness assumptions. No self-definitional quantities, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the claims to tautology are present. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Claims rest on the Kerr-Sen metric as background geometry and standard general-relativistic radiative transfer; accretion models introduce several free parameters whose values are chosen to represent the flows.

free parameters (2)
  • RIAF density and velocity profile parameters
    Parameters defining the radiatively inefficient accretion flow structure and emissivity.
  • BAAF conical geometry and velocity parameters
    Parameters for the ballistic approximation flow including opening angle and speed.
axioms (2)
  • domain assumption Spacetime is exactly the Kerr-Sen solution of Einstein-dilaton-Maxwell theory
    Invoked as the fixed background metric for all ray tracing.
  • standard math Radiative transfer and polarization transport follow the standard general-relativistic equations
    Used without derivation for light propagation and Stokes parameters.

pith-pipeline@v0.9.0 · 5547 in / 1330 out tokens · 52242 ms · 2026-05-10T17:31:16.692812+00:00 · methodology

discussion (0)

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