⚛️ general relativity

Improving constraints on the Yukawa correction at the Galactic Center with multiple stellar orbits

By analyzing astrometric and spectroscopic data from multiple stars (S2, S55, S29, S38, and S301) orbiting the Galactic Center's supermassive black hole, this study significantly improves constraints on a Yukawa-like correction to Newtonian gravity, achieving a five-fold tighter bound on the coupling strength compared to previous single-star analyses and establishing the most stringent limits to date at both short and large distance scales.

Original authors: GRAVITY+ Collaboration, :, A. Foschi, K. Abd El Dayem, N. Aimar, A. Berdeu, J. -P. Berger, G. Bourdarot, W. Brandner, Y. Cao, C. Correia, S. Cueves Cardona, R. Davies, D. Defrère, F. Delplancke-Ströb

Published 2026-09-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: GRAVITY+ Collaboration, :, A. Foschi, K. Abd El Dayem, N. Aimar, A. Berdeu, J. -P. Berger, G. Bourdarot, W. Brandner, Y. Cao, C. Correia, S. Cueves Cardona, R. Davies, D. Defrère, F. Delplancke-Ströbele, A. Drescher, F. Eisenhauer, L. Esteras~Otal, M. Fabricius, H. Feuchtgruber, S. Flesch, N. M. Förster Schreiber, Q. Fournier, P. Garcia, R. Garcia Lopez, R. Genzel, S. Gillessen, F. Gonté, X. Haubois, S. F. Hönig, M. Houllé, S. Joharle, J. Kammerer, A. Kaufer, P. Kervella, L. Kreidberg, L. Labadie, S. Lacour, O. Lai, R. Laugier, J. -B. Le Bouquin, J. Leftley, R. Li, B. Lopez, D. Lutz, F. Mang, A. Mérand, F. Millour, M. Montargès, N. Morujão, H. Nowacki, M. Nowak, J. Osorno, T. Ott, S. Pappert, C. Paladini, T. Paumard, K. Perraut, G. Perrin, R. Petrov, N. Pourré, S. Rabien, D. C. Ribeiro, S. Robbe-Dubois, M. Sadun Bordoni, J. Sanchez-Bermudez, J. Sauter, J. Scigliuto, J. Shangguan, T. T. Shimizu, F. Soulez, S. Spezzano, C. Straubmeier, E. Sturm, M. Subroweit, C. Sykes, L. J. Tacconi, P. Thévenet, I. Urso, F. H. Vincent, J. Woillez, G. Zins

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Gravity is the force that holds our world together, the invisible hand that keeps planets in their paths and apples falling from trees. For over a century, our best description of this force has been Albert Einstein's theory of General Relativity, a framework that has passed every test we have thrown at it, from the bending of starlight to the ripples of spacetime caused by colliding black holes. Yet, despite its success, the theory leaves some cosmic mysteries unsolved, such as the nature of dark matter and the strange acceleration of the universe's expansion. Because of these gaps, scientists have long wondered if gravity behaves slightly differently in extreme environments or at very specific distances. One popular idea suggests that gravity might have a tiny, extra "push" or "pull" that fades away quickly over distance, a concept known as a Yukawa correction. If such a force exists, it would be a fifth force of nature, distinct from the four we already know, and finding it would rewrite the laws of physics.

To hunt for this elusive force, astronomers have turned their most powerful eyes toward the center of our own Milky Way galaxy. There, hidden behind clouds of dust, lies a supermassive black hole, a monster of gravity so dense that not even light can escape it. Orbiting this black hole are several stars, moving at incredible speeds on paths that bring them dangerously close to the event horizon. By watching how these stars move, scientists can measure the strength of gravity in a regime far more intense than anything found in our solar system. If the extra "fifth force" exists, it would nudge these stars off their expected paths, leaving a subtle fingerprint in their motion that our current theories cannot explain.

A new study led by the GRAVITY+ Collaboration has taken this search to a new level of precision. Instead of relying on the motion of a single star, as previous studies had done, the team combined data from five different stars orbiting the central black hole. They used a massive collection of observations gathered over more than three decades, from 1992 to 2025, recorded by several advanced instruments on the Very Large Telescope in Chile. This dataset includes the well-known star S2, which has been tracked for years, but crucially, it also incorporates data on four other stars, including a newly discovered one named S301. This new star is particularly valuable because it dives much closer to the black hole than S2 does, allowing the team to test gravity at distances that were previously impossible to probe.

The researchers built a complex computer model to simulate the orbits of these five stars, accounting for the known laws of gravity as well as the potential extra force. They then compared their simulations against the actual observations to see if the stars moved exactly as predicted or if they showed signs of being tugged by something else. The results were a triumph of precision. The team found no evidence for this extra force. In fact, by combining the data from all five stars, they were able to rule out the existence of this fifth force with much greater certainty than ever before. They determined that if such a force does exist, its strength must be incredibly weak, far below the threshold that would affect the stars' orbits in any noticeable way.

The power of this study lies in the variety of the stars used. While the data from the star S2 alone provided a very tight limit on the force at a specific distance, adding the other stars allowed the scientists to test a much wider range of distances. The star S29, which travels on a much wider orbit, helped set strict limits on how the force might behave at large distances. Conversely, the newly discovered S301, with its tight, close-in path, allowed the team to test the force at very short ranges, a region where previous studies could not look. The team found that at a distance of roughly 100 astronomical units from the black hole, the strength of any such extra force must be less than six ten-thousandths of the strength of normal gravity. At even closer distances, the limits became even stricter.

This work represents the most stringent test of gravity ever conducted around a supermassive black hole. By tightening the constraints on this potential fifth force, the study effectively closes the door on a wide class of theories that predict such a force would be strong enough to be detected in the galactic center. While the search for deviations from Einstein's theory continues, this new analysis confirms that, at least in the violent neighborhood of the Milky Way's central black hole, gravity behaves exactly as General Relativity predicts. The stars dance to the tune of the known laws, and for now, the music remains unchanged.

Technical Summary: Improving constraints on the Yukawa correction at the Galactic Center with multiple stellar orbits

Problem and Motivation
While General Relativity (GR) remains the validated theory of gravity at Solar System scales and via gravitational wave observations, theoretical shortcomings such as the cosmological constant problem, dark matter, and the lack of a quantum completion motivate the search for deviations. A specific class of deviations involves a Yukawa-like correction to the Newtonian potential, characterized by an interaction strength $\alpha$ and a scale length $\lambda$ . This correction arises generically in the weak-field limit of Extended Theories of Gravity (ETGs) and in dark matter models with light mediators.

While Solar System tests provide tight constraints on $\alpha$ , many theories invoke screening mechanisms that suppress these effects in low-curvature environments like the Solar System. Consequently, the Galactic Center (GC), dominated by the supermassive black hole (SMBH) SgrA*, offers a distinct high-curvature environment to probe these corrections. Previous work (Paper I) established constraints using the orbit of the star S2 alone, but the sensitivity of a star to the Yukawa term is limited by its orbital radii: if $\lambda$ is much smaller than the pericenter, the force is exponentially suppressed; if $\lambda$ is much larger than the apocenter, the effect becomes degenerate with a rescaling of the central mass.

Methodology
The authors present a multi-star analysis combining astrometric and spectroscopic data from five stars: S2, S55, S29, S38, and the newly discovered S301. The dataset spans from 1992 to 2025 and utilizes observations from VLT instruments including NACO, SINFONI, GRAVITY, ERIS, and the upgraded GRAVITY+.

Data Composition:
- S2: 129 NACO and 82 GRAVITY astrometric points; 92 SINFONI and 2 ERIS radial velocity (RV) points (1992–2022).
- S29, S38, S55: Combined NACO and GRAVITY astrometry with SINFONI/ERIS/GNIRS RV data (2002–2022).
- S301: 19 real GRAVITY+ astrometric points (2023.3–2025.4). To constrain the orbit fully, particularly the periastron passage, the authors generated a mock dataset of 32 additional points (covering 2017.4–2023.3 and 2025.9–2030) with uncertainties averaging $\sigma \approx 50$ mas. No RV measurements for S301 were available.
Model: The gravitational potential is modeled as $U = -GM/r (1 + |\alpha|e^{-r/\lambda})$ . The analysis incorporates the Yukawa correction alongside the first-order Post-Newtonian (1PN) Schwarzschild precession. The equations of motion are integrated using the OOGRE (Osculating Orbits in General Relativistic Environments) code, which accounts for Rømer delay, relativistic Doppler shift, gravitational redshift, and Solar System motion.
Analysis: A Markov Chain Monte Carlo (MCMC) analysis is performed using the emcee package. The Yukawa scale length $\lambda$ is held fixed across the range $10^{11} \le \lambda \le 10^{16}$ m, while the intensity $|\alpha|$ and orbital parameters for each star (along with shared parameters $M_\bullet$ , $R_0$ , and dataset offsets) are solved for. The 95% confidence upper limits on $|\alpha|$ are derived from the posterior distributions.

Key Contributions and Results
The primary contribution is the extension of Yukawa constraints to scale lengths previously inaccessible to single-star analyses by leveraging the diverse orbital parameters of the S-star cluster.

Improved Constraints at S2 Scales: The inclusion of S55, S29, and S38 reduces the statistical uncertainty on $|\alpha|$ in the range probed by S2 ( $\lambda \sim 10^{13} - 10^{14}$ m). The tightest bound is found at $\lambda = 3 \cdot 10^{13}$ m ( $\sim 200$ AU), where $|\alpha| < 6 \cdot 10^{-4}$ . This represents an improvement of roughly a factor of five compared to the S2-only analysis in Paper I.
Short-Range Constraints via S301: The inclusion of S301, which has a pericenter roughly ten times smaller than S2's, allows for constraints in the short-range regime ( $\lambda \sim 10^{11} - 10^{12}$ m). The analysis yields $|\alpha| < 0.004$ at $\lambda = 10^{12}$ m and $|\alpha| < 0.006$ at $\lambda = 5 \cdot 10^{11}$ m. These are the tightest limits obtained to date around an SMBH at these scale lengths, improving previous estimates by several orders of magnitude.
Long-Range Constraints via S29: The larger apoapsis of S29 (roughly 8 times that of S2) enables constraints at larger scales ( $\lambda \gtrsim 10^{15}$ m) where the Yukawa term was previously degenerate with the central mass. The study finds $|\alpha| < 0.1$ at $\lambda \sim 2 \cdot 10^{15}$ m.
Limits of Sensitivity: For $\lambda \lesssim 10^{11}$ m, the exponential suppression of the Yukawa term prevents meaningful constraints. For $\lambda \gg 10^{15}$ m, the term is absorbed into a rescaling of $M_\bullet$ , causing constraints to degrade.

Significance
The paper claims that while Solar System tests remain more stringent at comparable scale lengths (e.g., $|\alpha| \lesssim 10^{-10}$ at $\lambda \sim 10^{11}$ m), the Galactic Center provides a unique testing ground. It probes an environment where screening mechanisms invoked by various theories may behave differently and which is inaccessible to Solar System experiments by definition. The results represent the tightest bounds on Yukawa corrections around a supermassive black hole to date, demonstrating the necessity of multi-star fitting to break degeneracies and extend the probed parameter space. The authors emphasize that the inclusion of S301 is critical for accessing the short-range regime, while S29 is essential for the long-range regime, highlighting the complementary nature of the S-star population.

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