Constraining a companion of the galactic center black hole, Sgr A*

We use 23 years of astrometric and radial velocity data on the orbit of the star S0-2 to constrain a hypothetical intermediate-mass black hole orbiting the massive black hole Sgr A* at the Galactic center. The data place upper limits on variations of the orientation of the stellar orbit at levels between 0.02 and 0.07 degrees per year. We use a combination of analytic estimates and full numerical integrations of the orbit of S0-2 in the presence of a black-hole binary. For a companion IMBH outside the orbit of S0-2 (a > 1020 a.u.), we find that a companion black hole with mass between 10³ and 10⁵ solar masses is excluded, with a boundary behaving as a ~ m^1/3. For a companion with semimajor axis < 1020 a.u., a black hole with mass between 10³ and 10⁵ solar masses is excluded, with a ~ m^-1/2. These bounds arise from quadrupolar perturbations of the orbit of S0-2. Significantly stronger bounds on an inner companion arise from the fact that the location of S0-2 is measured relative to the bright emission of Sgr A*, and that separation is perturbed by the wobble of Sgr A* about the center of mass between it and the companion. The result is a set of bounds as small as 400 solar masses at 200 a.u.; numerical simulations suggest a bound from these effects varying as a ~ m^-1.