Constraining a Companion of the Galactic Center Black Hole Sgr A*

Abstract

We use 23 yr 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 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 intermediate-mass black hole outside the orbit of S0-2 (1020 au), we find that a companion black hole with mass m c between 10 3 and 10 5 M ⊙ is excluded, with a boundary behaving as a c ∼ m c 1 / 3 . For a companion with a c < 1020 au, a black hole with mass between 10 3 and 10 5 M ⊙ is excluded, with a c ∼ m c − 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 M ⊙ at 200 au; the numerical simulations suggest a bound from these effects varying as a c ∼ m c − 1 . We compare and contrast our results with those from a recent analysis by the GRAVITY collaboration.