PPN--spin degeneracies in mock S62-like stellar-orbit inference

Abstract

We investigate the degeneracies between black hole (BH) spin effects and parametrized post-Newtonian (PPN) parameters in the relativistic orbital dynamics of S2-like and S62-like stars orbiting Sagittarius A$^{\ast}$. Using a 1PN+SO Hamiltonian framework and synthetic astrometric and radial velocity datasets, we perform Bayesian parameter inference. For current baseline observational precisions, the dominant relativistic observable--the Schwarzschild periapsis advance--allows the recovery of the effective precession parameter $\Upsilon$, while leaving the individual PPN parameters $\gamma$ and $\beta$ degenerate. Assuming microarcsecond-level astrometric precision, the spin-induced Lense-Thirring signal becomes partially detectable; fixing the PPN sector to General Relativity allows the BH spin magnitude to be constrained to an uncertainty of $\sim10^{-2}$. However, simultaneously varying PPN and spin parameters reveals a strong, approximately linear covariance between $\Upsilon$ and the dimensionless spin parameter $\chi$. To overcome this limitation, we demonstrate that joint multi-star inference can disentangle the degeneracy by combining a wider-orbit star, which constrains the dominant 1PN sector, with a compact relativistic orbit that is sensitive to Lense-Thirring frame dragging.