A New Window for Testing the PPN in the Strong-Field Regime: Stellar Rotation of S301

RESUMO

The recently discovered S301 star, with an orbital period of 8.7 years and eccentricity $e = 0.982$, reaches a pericenter of just $140\,R_{\mathrm{s}}$ --- approximately nine times closer than S2's $\sim 1200R_{\mathrm{s}}$ --- offering an unprecedented laboratory for testing strong-field gravity. We demonstrate that S301's stellar spin precession provides a novel probe of the PPN parameter $\gamma$, scaling as $(2\gamma_{\mathrm{PPN}} + 1)/3$ relative to general relativity (GR). For maximum projected velocity shifts of $46.1~\mathrm{km\,s^{-1}}$, next-generation spectrographs could constrain $\gamma_{\mathrm{PPN}}$ to $\sim 10\%$ precision. When combined with S301's orbital precession --- a substantial $\sim 1.95^\circ$ pericenter advance per orbit (GR prediction), approximately an order of magnitude larger than S2's $\sim 0.2^\circ$, constraining $(2\beta_{\mathrm{PPN}} + 2\gamma_{\mathrm{PPN}} - 1)/3$ --- the spin measurement breaks the $\beta$-$\gamma$ degeneracy. A MCMC analysis of projected S2 and S301 observations yields $\sigma_\beta \approx 2.3 \times 10^{-4}$, with the $\gamma$ precision limited by the spin precession measurement to $\sigma_\gamma \approx 0.1$. While the spin precession provides an independent consistency check, its true significance lies in probing gravity at $\phi/c^2 \sim 10^{-4}$ and $v/c \sim 0.08$ --- four orders of magnitude stronger than Solar System tests and an order of magnitude stronger than current S-star constraints. This complementary approach opens a new window for testing the PPN framework in the strong-field regime and demonstrates the power of combining multiple stellar probes at the Galactic Center.