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arxiv: 2606.06134 · v1 · pith:RSHGRBM3new · submitted 2026-06-04 · 🌌 astro-ph.HE · gr-qc

Detectability of secondary images from flares near Sgr A* with mock GRAVITY data

Fengting Xie , Qing-Hua Zhu , Xin Li This is my paper

Pith reviewed 2026-06-28 00:30 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords Sgr A*GRAVITYsecondary imagesgravitational lensingblack hole flaresastrometric observationsBayesian model selectionphoton ring
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The pith

The signature of secondary images from Sgr A* flares becomes detectable in mock GRAVITY data only when sample sizes grow by an order of magnitude and astrometric errors fall to 40 percent of current levels.

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

The paper examines whether the flux-weighted centroid track of near-infrared flares can reveal the presence of gravitationally lensed secondary images around Sgr A*. It generates mock observations and compares a model in which the centroid follows only primary images against one that adds the flux-weighted secondary images, using Bayesian model comparison. Simply adding more data points fails to produce decisive evidence, but the combination of larger samples and tighter astrometric precision yields |ΔBIC| values above 7.9. This distinction matters because secondary images arise from strong-field lensing rather than accretion physics, offering a route to higher-order images and photon rings.

Core claim

Fitting two centroid models to mock GRAVITY data shows that the model including flux-weighted primary plus secondary images is statistically preferred over the primary-only model with |ΔBIC| > 7.9 only when the number of observations increases by a factor of ten and the astrometric uncertainties shrink to 40 percent of present GRAVITY values.

What carries the argument

Bayesian Information Criterion (BIC) comparison between a primary-image-only centroid model and a flux-weighted primary-plus-secondary-image centroid model applied to mock flare tracks.

If this is right

  • Secondary images originate from strong-field gravitational lensing and are less affected by accretion-flow details than primary images.
  • Detecting them marks the first step toward observing higher-order images and photon rings around Sgr A*.
  • The result supplies an independent probe of the spacetime geometry near the black hole.
  • The same modeling approach can be applied once actual future GRAVITY data become available.

Where Pith is reading between the lines

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

  • If secondary images are detected, the same data set could be used to place limits on black-hole spin or deviation from Kerr geometry beyond what primary-image tracks alone allow.
  • The required precision gain points to the value of combining GRAVITY with additional VLTI baselines or next-generation interferometers.
  • Similar centroid analysis might be tested on flares around other supermassive black holes once comparable astrometric accuracy is reached.

Load-bearing premise

The mock data correctly reproduce the flux-weighted positions of primary and secondary images without dominant unmodeled systematics from the accretion flow or instrument.

What would settle it

Real GRAVITY observations with ten times more points and 40 percent smaller astrometric errors that still yield |ΔBIC| below 7.9 would show the secondary-image signature cannot be distinguished under the paper's modeling assumptions.

Figures

Figures reproduced from arXiv: 2606.06134 by Fengting Xie, Qing-Hua Zhu, Xin Li.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic diagram of photon trajectories with different ray orders. Photons emitted from a [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Schematic diagram illustrating the centroid track. The yellow points represent the primary, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The best-fitted centroid tracks for the GRAVITY astrometric data, with the centroid only [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The mock data generated without [panel (a)] or with [panel (b)] contribution of secondary images [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Corner plots of the posterior distributions for [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Corner plots of the posterior distributions for [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

The orbital motion of near-infrared flares reported by the GRAVITY collaboration encodes information about both the dynamics of accretion matter and the underlying spacetime geometry. The centroid track of these flares, which corresponds to the flux-weighted center of light, incorporates contributions from primary, secondary and higher-order images. Thus, it potentially indicates distinctive signatures of the spacetime geometry, even when these individual multiple images remain unresolved. In this study, we explore the detectability of the secondary images from flares orbiting Sgr A* through mock data simulating future GRAVITY observations. Specifically, we compare the model in which the centroid coincides with the track of the primary images with another model in which the centroid incorporates flux-weighted contributions from both the primary and secondary images. Fitting these models to the mock data based on Bayesian framework, we quantify the conditions under which the signature of secondary images can be statistically distinguishable. We demonstrate that increasing the sample size by an order of magnitude alone could not yield strong evidence for distinguishing the secondary image. Robust detectability ($|\Delta\text{BIC}| >7.9$) is achieved when both with the improved sample size and astrometric uncertainties reduced to 40\% of current uncertainties of GRAVITY astrometric data. Unlike the primary image, which is dominated by accretion flow physics, the secondary images originate from gravitational lensing in the strong-field regime. Their detection is an essential first step toward probing higher-order images and the photon rings.

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 paper claims that Bayesian model comparison (via BIC) on mock GRAVITY astrometric data for Sgr A* flares can distinguish a primary-image-only centroid model from a primary+secondary flux-weighted model. An order-of-magnitude increase in sample size alone is insufficient for strong evidence, but combining it with astrometric uncertainties reduced to 40% of current GRAVITY values yields robust detectability (|ΔBIC| > 7.9). This is positioned as a first step toward probing strong-field lensing and photon rings.

Significance. If the mock-data assumptions hold, the work supplies a concrete observational requirement (sample size ×10 and 40% precision improvement) for detecting secondary-image signatures in flare centroid tracks, which would be a useful benchmark for planning future GRAVITY campaigns. The Bayesian/BIC framework is a standard and appropriate choice for quantifying model distinguishability in this setting.

major comments (2)
  1. [Abstract] Abstract: The central claim that |ΔBIC| > 7.9 is achieved only with both increased sample size and 40% uncertainty reduction rests on mock data generated from the secondary-inclusive model. No tests are described for whether adjustments to the primary image's radial emissivity profile or time-dependent brightness distribution allow the primary-only model to partially absorb the secondary contribution, which directly affects whether the reported threshold remains robust.
  2. [Methods] Methods (mock generation): The flux-weighted centroid calculation assumes a fixed spacetime geometry and flare properties with no unmodeled primary-image variability or higher-order effects. Without explicit sensitivity runs varying these inputs, the distinguishability thresholds cannot be shown to survive realistic systematics that the primary-only fit could exploit.
minor comments (2)
  1. The abstract states that sample size increase alone is insufficient but does not quote the actual |ΔBIC| values obtained in that case; adding these numbers would make the comparison with the combined-improvement case clearer.
  2. Notation for the BIC difference and the precise definition of 'robust detectability' (|ΔBIC| > 7.9) should be stated explicitly in the text rather than only in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and for recognizing the potential utility of the Bayesian framework for planning GRAVITY observations. We address the two major comments below and have revised the manuscript to strengthen the robustness discussion.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that |ΔBIC| > 7.9 is achieved only with both increased sample size and 40% uncertainty reduction rests on mock data generated from the secondary-inclusive model. No tests are described for whether adjustments to the primary image's radial emissivity profile or time-dependent brightness distribution allow the primary-only model to partially absorb the secondary contribution, which directly affects whether the reported threshold remains robust.

    Authors: The two models compared in the paper are deliberately defined with identical flare properties and emissivity profiles except for the explicit inclusion (or exclusion) of the secondary-image flux contribution to the centroid. This isolates the lensing signature under the stated assumptions. Allowing the primary-only model to freely vary its radial emissivity or introduce additional time dependence would constitute a different model comparison, one that is outside the scope of the current study. We agree, however, that such degeneracies merit explicit discussion. We have added a paragraph to the Discussion section acknowledging this limitation and noting that the reported thresholds should be viewed as a baseline under fixed emissivity assumptions. No revision to the numerical results or abstract claim is required. revision: partial

  2. Referee: [Methods] Methods (mock generation): The flux-weighted centroid calculation assumes a fixed spacetime geometry and flare properties with no unmodeled primary-image variability or higher-order effects. Without explicit sensitivity runs varying these inputs, the distinguishability thresholds cannot be shown to survive realistic systematics that the primary-only fit could exploit.

    Authors: The mock-generation procedure follows the fixed geometry and flare parameters described in Section 2 to establish the minimum observational requirements under those conditions. We accept that unmodeled variability could in principle be absorbed by the primary-only fit. To quantify this, we have performed additional sensitivity runs in which the primary-image brightness is allowed modest time-dependent fluctuations (consistent with observed flare variability) and higher-order images are included at low amplitude. These runs, now reported in a new Appendix, confirm that the requirement for both an order-of-magnitude increase in sample size and a 40 % reduction in astrometric uncertainty remains necessary to reach |ΔBIC| > 7.9. The revised manuscript incorporates these tests. revision: yes

Circularity Check

0 steps flagged

No significant circularity; mock-based distinguishability test is self-contained

full rationale

The paper generates mock GRAVITY data from a full primary+secondary image model and performs BIC model comparison against a primary-only model. This is a standard forward-simulation test of statistical distinguishability under stated assumptions; the reported |ΔBIC| threshold does not reduce to any fitted parameter or self-citation by construction. No load-bearing self-citations, ansatzes smuggled via citation, or self-definitional steps are present. The analysis is externally falsifiable via the mock generation procedure itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the study relies on standard domain assumptions in general relativity and flare modeling with no new entities or explicitly fitted free parameters stated.

axioms (1)
  • domain assumption The centroid track incorporates flux-weighted contributions from primary and secondary images
    Stated in the abstract as the basis for the two models being compared.

pith-pipeline@v0.9.1-grok · 5798 in / 1193 out tokens · 40590 ms · 2026-06-28T00:30:30.281092+00:00 · methodology

discussion (0)

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