Using the motion of S2 to constrain vector clouds around Sgr A*

The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass $M_{\bullet } \sim 4.3 \times 10^6 \, {\rm M}_{\odot }$, but the nature of its environment is still under debate. In this work, we used astrometric and spectroscopic measurements of the motion of the star S2, one of the closest stars to the massive black hole, to determine an upper limit on an extended mass composed of a massive vector field around Sagittarius A*. For a vector with effective mass $10^{-19} \lesssim m_\mathrm{ s} \lesssim 10^{-18} \, \rm eV$, our Markov chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound $M_{\rm cloud} \lesssim 0.1 \% \, M_{\bullet }$ at 3σ confidence level. We show that dynamical friction exerted by the medium on S2 motion plays no role in the analysis performed in this and previous works, and can be neglected thus.