Probing dense environments around Sgr A* with S-stars dynamics

The orbits of stars around Sgr A*, the Milky Way's supermassive black hole, provide a unique laboratory for testing its environment with unprecedented precision. In this work, we compute the apsidal precession induced by extended matter distributions through Lagrange's equations and compare it with the measured precession of S2, reproducing and extending GRAVITY's constraints. In particular, we push bounds on boson clouds to larger gravitational couplings $α$ and to the second-fastest superradiant mode. We also show that environments with mass of order $1\%$ of Sgr A* drive stellar orbits to decay by dynamical friction within a few Myr. The inner star cluster is however efficiently replenished, masking this effect observationally. We also show that orbital resonances from boson clouds have no impact on relevant timescales. While S2 currently provides the cleanest dataset, our framework is readily applicable to other stars that we identify as particularly promising, whose orbits will be measured with increasing accuracy, opening up new opportunities to probe the environment of Sgr A*.