Improving constraints on the Yukawa correction at the Galactic Center with multiple stellar orbits
We investigate the presence of a Yukawa-like correction ($\propto \, αe^{- r/λ}$) to Newtonian gravity at the Galactic Center, using a multi-star fitting code, including the newly discovered star S$301$, to improve the constraints obtained using S$2$ orbit alone. We perform a Markov Chain Monte Carlo analysis using the astrometric and spectroscopic data of stars S$2$, S$55$, S$29$, S$38$ and S$301$ collected by GRAVITY, GRAVITY$^+$, NACO and SINFONI instruments, covering the period from $1992$ to $2025$. Compared to GRAVITY Collaboration 2025 (Paper I), in which only S$2$ was fitted, the tightest bound on the Yukawa coupling is again reached at $λ= 3\cdot10^{13}\,\rm m\ (\sim 200\,AU)$, where we find $|α| < 6 \cdot10^{-4}$, an improvement of roughly a factor five. The addition of S$301$ extends the constraint to short ranges that were inaccessible to S$2$, yielding $|α| < 0.004$ at $λ=10^{12}\,\rm m$ and $|α| < 0.006$ at $λ=5\cdot 10^{11}\,\rm m$, while S$29$, with its larger apoapsis, gives $|α| < 0.1$ at $λ\sim 2\cdot10^{15}\,\rm m$. The latter two represent the tightest limits at these scale lengths on a Yukawa correction obtained to date around a supermassive black hole.