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The star S0-2, which orbits the supermassive black hole (SMBH) in our Galaxywith a period of 16 years, provides the strongest constraint on both the massof the SMBH and the distance to the Galactic center. S0-2 will soon provide thefirst measurement of relativistic effects near a SMBH. We report the firstlimits on the binarity of S0-2 from radial velocity monitoring, which hasimplications for both understanding its origin and robustness as a probe of thecentral gravitational field. With 87 radial velocity measurements, whichinclude 12 new observations presented, we have the data set to look for radialvelocity variations from S0-2's orbital model. Using a Lomb-Scargle analysisand orbit fitting for potential binaries, we detect no radial velocityvariation beyond S0-2's orbital motion and do not find any significant periodicsignal. The lack of a binary companion does not currently distinguish betweendifferent formation scenarios for S0-2. The upper limit on the mass of acompanion star ($M_{\text{comp}}$) still allowed by our results has a medianupper limit of $M_{\text{comp}}$ $\sin i \leq$ 1.6 M$_{\odot}$ for periodsbetween 1 and 150 days, the longest period to avoid tidal break up of thebinary. We also investigate the impact of the remaining allowed binary systemon the measurement of the relativistic redshift at S0-2's closest approach in2018. 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 therelativistic redshift.

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