PPN motion of the S-stars around Sgr A*

Abstract

Parametrized Post-Newtonian (PPN) equations of motion for several S-stars nearest to the Galactic Center compact relativistic object SgrA* are considered. The effect of the orbital periods difference between Newtonian and Post-Newtonian cases is taken into account. The best fit PN orbit of S2 has a period which is 16 days longer than Newtonian one. The PPN parameters ${\beta }_{\text{PPN}}$ and ${\gamma }_{\text{PPN}}$ are measured. Bayesian sampling is used to fit the trajectories of the PPN laws of motion. Posterior estimates of ${\beta }_{\text{PPN}}$ and ${\gamma }_{\text{PPN}}$ are $0.97_{-0.65}^{+0.42}$ and $0.81_{-0.60}^{+0.46}$ respectively. The result confirms General Relativity prediction for the Post-Newtonian equations of motion in the conditions of orbital motions in vicinity of the SgrA*.

arXiv commentPrepared for submission to 'Astrophysics' journal

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