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arxiv: 2604.06364 · v1 · submitted 2026-04-07 · 🌌 astro-ph.GA · gr-qc

Recognition: 2 theorem links

· Lean Theorem

Constraints on a fifth force from the stellar orbits around the central supermassive black hole of the Milky Way

Predrag Jovanovi\'c , Du\v{s}ko Borka , Vesna Borka Jovanovi\'c
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:12 UTC · model grok-4.3

classification 🌌 astro-ph.GA gr-qc
keywords fifth forceYukawa gravityS2 starSgr A*Galactic Centerstellar orbitsgeneral relativity tests
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The pith

S2 star orbit data limits possible fifth-force strengths to 0.005-0.15 for ranges of hundreds to thousands of AU.

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

The paper models the S2 star's motion under a Yukawa gravity potential that incorporates an additional fifth force and uses Markov chain Monte Carlo sampling to fit the force parameters to the observed astrometric and radial-velocity data. Three representative ranges for the force are examined, from deep inside the orbit to much larger than it. The fits show that permitted strength grows with range while relative uncertainty shrinks, and the resulting values remain compatible with both earlier Yukawa analyses and the GRAVITY-measured Schwarzschild precession parameter.

Core claim

By simulating orbits in a Yukawa-modified gravity model and fitting them to the observed S2 star trajectory around Sgr A* via Markov chain Monte Carlo, the strength δ and range λ of a possible fifth force are constrained; the resulting strengths are δ∼0.005, 0.02 and 0.15 for λ of a few hundred AU, about one thousand AU, and several thousand AU respectively, all compatible within errors with the measured f_SP = 1.10±0.19.

What carries the argument

Markov chain Monte Carlo fitting of stellar orbits computed in a Yukawa gravity model to the full set of S2 astrometric and spectroscopic observations.

If this is right

  • As the assumed range λ of the fifth force increases, the permitted strength δ increases while the relative error on δ decreases.
  • The derived fifth-force strengths remain consistent with results obtained in earlier studies that employed different Yukawa-like potentials.
  • The estimated parameters in all three cases lie within the error bars of the GRAVITY-measured Schwarzschild precession factor f_SP = 1.10±0.19.
  • Small observed discrepancies from the pure general-relativity prediction for S2 precession could be accounted for by a fifth force of the magnitudes obtained.

Where Pith is reading between the lines

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

  • Repeating the fit with orbits of additional stars that have high-quality data around Sgr A* would produce tighter joint constraints on δ and λ.
  • The upper bounds imply that any fifth force active near the galactic center must be weak relative to Newtonian gravity on these scales.
  • Future improvements in astrometric precision could either push the allowed δ region to zero or reveal a statistically significant non-zero value.

Load-bearing premise

That any small departures of the S2 orbit from pure Schwarzschild geodesics are produced entirely by a fifth force rather than by unmodeled Newtonian effects, stellar encounters, or measurement systematics.

What would settle it

A future high-precision measurement of S2's orbital precession that lies outside the interval allowed by the fitted δ values for any of the three ranges would contradict the reported compatibility.

Figures

Figures reproduced from arXiv: 2604.06364 by Du\v{s}ko Borka, Predrag Jovanovi\'c, Vesna Borka Jovanovi\'c.

Figure 1
Figure 1. Figure 1: Posterior distribution of S2 star orbit fit in the case 1 from [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The same as in [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The same as in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: Comparison between the best-fit orbit of the S2 star (blue solid line), obtained for the uniform priors from [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Here we investigate a possible presence of a fifth force at the Galactic Center (GC), and its potential influence on the stellar orbits around the central supermassive black hole of our Galaxy. For this purpose we simulated the stellar orbits in a Yukawa gravity model that predicts the emergence of a fifth force, and fitted them into the observed orbit of S2 star around Sgr A* at the GC. The fitting was performed using Markov chain Monte Carlo method which enabled us to constrain the parameters of Yukawa interaction describing the strength $\delta$ and the range $\lambda$ of a fifth force. We studied the following cases for a fifth force range $\lambda$, when it is: i) about a few hundred AU (i.e. deep inside the orbit of S2 star), ii) about a thousand AU (i.e. approximately the size of S2 star orbit), and iii) several thousand AU (i.e. much larger than the size of S2 star orbit). The obtained results showed that as the range $\lambda$ of a fifth force increases, its strength $\delta$ also increases and relative error $\Delta\delta/\delta$ decreases. The resulting fifth-force strengths in all three cases are respectively: $\delta\sim$ 0.005, 0.02 and 0.15. These results are consistent with the corresponding results of both our previous studies and those of other authors, regardless of the different Yukawa-like potentials used to model a fifth force. In addition, we also studied whether the possible small discrepancies from the prediction of General Relativity for the Schwarzschild precession of S2 star could be caused by a fifth force. For this purpose we used the $f_\mathrm{SP}$ parameter that was recently measured in the case of S2 star by GRAVITY Collaboration in 2020. We found that the obtained estimates in all three cases are compatible, within the error intervals, with the measured value of $f_\mathrm{SP} = 1.10\pm 0.19$.

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

3 major / 1 minor

Summary. The manuscript claims to constrain a possible fifth force in a Yukawa-modified gravity model by using MCMC to fit the parameters δ (strength) and λ (range) to the observed orbit of the S2 star around Sgr A*. For three discrete λ regimes (hundreds of AU, ~1000 AU, and several thousand AU), it reports δ ≈ 0.005, 0.02, and 0.15 with decreasing relative errors, states consistency with prior work, and finds these δ values compatible within errors with the GRAVITY-measured Schwarzschild precession factor f_SP = 1.10 ± 0.19.

Significance. If the dynamical model is complete and the residuals are attributable to a fifth force, the results would provide additional constraints on fifth-force parameters at Galactic Center scales using high-precision astrometry, with the MCMC method being a standard and appropriate tool. The reported trend of δ increasing with λ and the consistency with other studies would be of interest to tests of gravity beyond GR. However, the overall significance is reduced by potential incompleteness in the orbital model and lack of independence in the f_SP comparison.

major comments (3)
  1. Abstract and dynamical model section: The description of simulating orbits 'in a Yukawa gravity model' and fitting to S2 data does not indicate whether the integrator includes post-Newtonian GR terms (1PN or geodesic) that produce the Schwarzschild precession measured by f_SP. If the model is Newtonian plus Yukawa only, unmodeled GR precession is absorbed into the effective δ, rendering both the quoted δ constraints and the subsequent f_SP compatibility dependent on an untested assumption.
  2. Results section on f_SP compatibility: The check that the fitted δ values are compatible with the independently measured f_SP = 1.10 ± 0.19 uses the same S2 astrometric data set for both the δ fit and the precession measurement; this renders the compatibility statement circular rather than an independent test of whether a fifth force could explain any GR discrepancy.
  3. Abstract and methods: The three discrete λ cases are presented without quantitative justification for the specific boundaries chosen relative to the S2 semi-major axis (~1000 AU) or any demonstration that the reported trend in δ and Δδ/δ holds under continuous variation or alternative samplings of λ.
minor comments (1)
  1. Abstract: The phrase 'fitted them into the observed orbit' is imprecise and should read 'fitted to the observed orbit'.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below with clarifications and indicate revisions to improve the manuscript.

read point-by-point responses

  1. Referee: Abstract and dynamical model section: The description of simulating orbits 'in a Yukawa gravity model' and fitting to S2 data does not indicate whether the integrator includes post-Newtonian GR terms (1PN or geodesic) that produce the Schwarzschild precession measured by f_SP. If the model is Newtonian plus Yukawa only, unmodeled GR precession is absorbed into the effective δ, rendering both the quoted δ constraints and the subsequent f_SP compatibility dependent on an untested assumption.

    Authors: We agree that the dynamical model description is incomplete. Our orbital integrations employ a Newtonian integrator augmented only by the Yukawa term and do not include explicit 1PN or geodesic GR corrections. Consequently, any unmodeled Schwarzschild precession is absorbed into the effective δ. We will revise the abstract and dynamical model section to state this explicitly and discuss the resulting limitation on the δ constraints. revision: yes

  2. Referee: Results section on f_SP compatibility: The check that the fitted δ values are compatible with the independently measured f_SP = 1.10 ± 0.19 uses the same S2 astrometric data set for both the δ fit and the precession measurement; this renders the compatibility statement circular rather than an independent test of whether a fifth force could explain any GR discrepancy.

    Authors: We acknowledge that both the δ fits and the GRAVITY f_SP measurement rely on the same S2 astrometric dataset, so the compatibility is a consistency check rather than an independent test. We will revise the results section to clarify this distinction and avoid any implication of full independence. revision: yes

  3. Referee: Abstract and methods: The three discrete λ cases are presented without quantitative justification for the specific boundaries chosen relative to the S2 semi-major axis (~1000 AU) or any demonstration that the reported trend in δ and Δδ/δ holds under continuous variation or alternative samplings of λ.

    Authors: The three λ values were selected as representative regimes relative to the S2 semi-major axis (~1000 AU): much smaller, comparable, and much larger. This choice illustrates the scale dependence of the fifth-force effect. The trend of increasing δ with λ and decreasing relative error follows from the Yukawa model physics, as larger λ values produce a more uniform perturbation across the orbit. We will add explicit justification for the boundaries in the methods section; a full continuous λ scan was not performed but is not required to demonstrate the qualitative trend. revision: partial

Circularity Check

1 steps flagged

Fitted Yukawa δ to S2 orbit data then checked compatibility with GRAVITY f_SP from same orbit

specific steps
  1. fitted input called prediction [Abstract]
    "We found that the obtained estimates in all three cases are compatible, within the error intervals, with the measured value of f_SP = 1.10±0.19."

    The 'obtained estimates' are the δ values produced by fitting the Yukawa model orbits to the S2 trajectory data via MCMC. The f_SP value quantifies the precession present in that same S2 orbit. Fitting the model to reproduce the observed orbit forces the model's precession (or effective f_SP) to match the data, so the subsequent compatibility statement with the measured f_SP is statistically forced rather than an independent test.

full rationale

The paper performs MCMC fits of Yukawa parameters δ and λ to the observed S2 star orbit in three λ regimes, obtaining δ ≈ 0.005, 0.02, 0.15. It then states that these fitted estimates are compatible with the GRAVITY-measured f_SP = 1.10 ± 0.19. Because the orbit data fitted already contains the precession signal quantified by f_SP, any implied precession or effective f_SP derived from the fitted δ necessarily agrees with the measured value by construction of the fit. This matches the fitted-input-called-prediction pattern. Self-citations noting consistency with prior work exist but are not load-bearing for the central constraints. The overall derivation therefore contains partial circularity in the f_SP consistency step.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The analysis rests on the assumption that any orbital deviation is captured by a single Yukawa term added to Newtonian gravity, plus standard assumptions of Keplerian orbits perturbed only by the central mass and the fifth force.

free parameters (2)
  • δ (fifth-force strength)
    Fitted via MCMC for each fixed λ case to match S2 observations.
  • λ (fifth-force range)
    Chosen by hand in three discrete regimes rather than fitted.
axioms (2)
  • domain assumption The gravitational potential is Newtonian plus a Yukawa correction term.
    Invoked throughout the simulation of stellar orbits.
  • domain assumption S2 star motion is dominated by the central black hole with negligible contributions from other stars or gas.
    Implicit in the orbit-fitting procedure.
invented entities (1)
  • fifth force no independent evidence
    purpose: To explain possible deviations from general relativity in the S2 orbit.
    Postulated as a Yukawa interaction; no independent evidence provided beyond the fit.

pith-pipeline@v0.9.0 · 5703 in / 1587 out tokens · 37840 ms · 2026-05-10T19:12:21.190082+00:00 · methodology

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