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Exploring the presence of a fifth force at the Galactic Center

The GRAVITY Collaboration, K. Abd El Dayem, R. Abuter, N. Aimar, P. Amaro Seoane, A. Amorim, J. P. Berger, H. Bonnet, G. Bourdarot, W. Brandner, V. Cardoso, Y. Clénet, R. Davies, P. T. de Zeeuw, A. Drescher, A. Eckart, F. Eisenhauer, H. Feuchtgruber, G. Finger, N. M. Förster Schreiber, A. Foschi, P. Garcia, E. Gendron, R. Genzel, S. Gillessen, M. Hartl, X. Haubois, F. Haussmann, T. Henning, S. Hippler, M. Horrobin, L. Jochum, L. Jocou, A. Kaufer, P. Kervella, S. Lacour, V. Lapeyrère, J. -B. Le Bouquin, P. Léna, D. Lutz, F. Mang, N. More, J. Osorno, T. Ott, T. Paumard, K. Perraut, G. Perrin, S. Rabien, D. C. Ribeiro, M. Sadun Bordoni, S. Scheithauer, J. Shangguan, T. Shimizu, J. Stadler, O. Straub, C. Straubmeier, E. Sturm, L. J. Tacconi, I. Urso, F. Vincent, S. D. von Fellenberg, E. Wieprecht, J. Woillez

Abstract

Aims: The presence of a Yukawa-like correction to Newtonian gravity is investigated at the Galactic Center, leading to a new upper limit for the intensity of such a correction. Methods: We perform a Markov Chain Monte Carlo analysis using the astrometric and spectroscopic data of star S$2$ collected at the Very Large Telescope by GRAVITY, NACO and SINFONI instruments, covering the period from $1992$ to $2022$. Results: The precision of the GRAVITY instrument allows us to derive the most stringent upper limit at the Galactic Center for the intensity of the Yukawa contribution ($\propto \, αe^{- λr}$) to be $|α| < 0.003$ for a scale length $λ= 3 \cdot 10^{13}\, \rm m\, (\sim 200 \, \rm AU)$. This improves by roughly one order of magnitude all estimates obtained in previous works.

Exploring the presence of a fifth force at the Galactic Center

Abstract

Aims: The presence of a Yukawa-like correction to Newtonian gravity is investigated at the Galactic Center, leading to a new upper limit for the intensity of such a correction. Methods: We perform a Markov Chain Monte Carlo analysis using the astrometric and spectroscopic data of star S collected at the Very Large Telescope by GRAVITY, NACO and SINFONI instruments, covering the period from to . Results: The precision of the GRAVITY instrument allows us to derive the most stringent upper limit at the Galactic Center for the intensity of the Yukawa contribution () to be for a scale length . This improves by roughly one order of magnitude all estimates obtained in previous works.

Paper Structure

This paper contains 12 sections, 15 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Observations
  3. Yukawa correction to Newtonian force
  4. Model
  5. Method
  6. Results
  7. Comparison with theoretical estimates
  8. Conclusions
  9. Details of the numerical integration
  10. Coordinates transformations and inclusion of relativistic effects.
  11. Coordinate transformation
  12. Relativistic effects and Rømer's delay

Figures (3)

  • Figure 1: Comparison of the posterior distributions $P(|\alpha||D)$ between the Keplerian model (black curve) and the $1$PN model (red curve).
  • Figure 2: $95\%$ confidence level on $|\alpha|$ obtained in this work (red dots), compared with previous estimates by Hees:2017aal (blue dots). The dotted vertical line represents the minimum of the curve, in correspondence to $\lambda \sim 3 \cdot 10^{13} \, \text{m} \sim 200\, \text{AU}$
  • Figure 3: Posterior probability density of $|\alpha|$ using the $1$PN expression in Eq. \ref{['1pn']} (black curve) versus the $1$PN expansion for $f(R)$ gravity derived in Tan:2024wuk (red curve), when $\lambda = 3 \cdot 10^{13}$ m.