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

Abstract

The recently discovered S301 star, with an orbital period of 8.7 years and eccentricity $e=0.982$, reaches a pericenter of just $140R_{\mathrm{s}}$ --- 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 $46.1\mathrm{km}{\mathrm{s}}^{-1}$, 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 $\varphi /c^2\sim 10^{-4}$ 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.

13 pages (two columns), 4 tables, 4 figures