Investigating the Binarity of S0-2: Implications for its Origins and Robustness as a Probe of the Laws of Gravity around a Supermassive Black Hole

The star S0-2, which orbits the supermassive black hole (SMBH) in our Galaxy with a period of 16 years, provides the strongest constraint on both the mass of the SMBH and the distance to the Galactic center. S0-2 will soon provide the first measurement of relativistic effects near a SMBH. We report the first limits on the binarity of S0-2 from radial velocity monitoring, which has implications for both understanding its origin and robustness as a probe of the central gravitational field. With 87 radial velocity measurements, which include 12 new observations presented, we have the data set to look for radial velocity variations from S0-2's orbital model. Using a Lomb-Scargle analysis and orbit fitting for potential binaries, we detect no radial velocity variation beyond S0-2's orbital motion and do not find any significant periodic signal. The lack of a binary companion does not currently distinguish between different formation scenarios for S0-2. The upper limit on the mass of a companion star ($M_{\text{comp}}$) still allowed by our results has a median upper limit of $M_{\text{comp}}$ $\sin i \leq$ 1.6 M$_{\odot}$ for periods between 1 and 150 days, the longest period to avoid tidal break up of the binary. We also investigate the impact of the remaining allowed binary system on the measurement of the relativistic redshift at S0-2's closest approach in 2018. While binary star systems are important to consider for this experiment, we find plausible binaries for S0-2 will not alter a 5$\sigma$ detection of the relativistic redshift.