Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of $|\alpha |<0.016$ at a length scale of $\lambda =150$ astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of $|{\dot{\omega }}_{\text{S0-2}}|<1.6\times {10}^{-3}\mathrm{rad}/\mathrm{yr}$, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.

Figure 1

The gravitational potential probed by different tests of gravitation against the mass of the central body that generates gravity in these tests. Short-period stars, such as S0-2, around our Galactic center explore a new region in this parameter space. The figure is inspired by Ref. [12].

Figure 2

95% confidence upper limits on $|\alpha |$ as a function of $\lambda$. The shaded regions are excluded by various experiments. Our analysis is represented by the red shaded area (GC), while the other curves are from Fig. 31 of Ref. [34]. The dashed curve is a reasonable extrapolation based on Solar System results from Ref. [34]. (Left panel) The horizontal axis is the fifth force length scale $\lambda$ in meters or in A.U. (Right panel) the horizontal axis is the length scale $\lambda$ expressed in term of the gravitational radius of the central mass that generates gravitation in the different experiments.

Figure 3

Statistical uncertainty on the fifth force strength ${\sigma }_{\alpha }$ expected for various observational scenarios: the dashed green (light) line corresponds to the data used in this analysis, the continuous orange (light) line corresponds to data that will be available by the end of 2018. The two red (dark) lines include 16 additional years of observations with two astrometric observations and one spectroscopic observation per year with the following astrometric (spectroscopic) accuracy for an S0-2-like star: current Keck accuracy, 0.5 mas ($30\mathrm{km}/\mathrm{s}$); TMT-like improved accuracy, $15\mu \mathrm{as}$ ($5\mathrm{km}/\mathrm{s}$).