Constraining Axion Dark Matter with Galactic-Centre Resonant Dynamics

We study the influence of fuzzy-dark-matter cores on the orbits of stars at the Galactic centre. This dark matter candidate condenses into dense, solitonic cores, and, if a super-massive black hole is present at the centre of such a core, its central part forms a `gravitational atom'. Here, we calculate the atom's contribution to the gravitational potential felt by a Galactic-centre star, for a general state of the atom. We study the angular-momentum dynamics this potential induces, and show that it is similar to vector resonant relaxation. Its influence is found to be potentially sufficiently strong that such a dynamical component should be accounted for in Galactic-centre modelling. For the Milky Way, the atom is expected to have some spherical asymmetry, and we use this to derive a stability condition for the disc of young, massive stars at the Galactic centre - if the atom's mass is too large, then the disc would be destroyed. Thus, the existence of this disc constrains the mass of the particles comprising the solitonic core. We study an example model of the core, where all of the rotation of the core's inner region is assumed to come from an $l=1$ state, and its amplitude is determined by the halo's spin parameter; such a core is found to be in tension with the stability of the clockwise stellar disc for $4.2\times 10^{-20}\,\textrm{eV} \leq m_a \leq 5.4\times 10^{-20}\,\textrm{eV}$ at $2\sigma$. Other core models would vary the constrained values of $m_a$ somewhat. These constraints will tighten significantly with future, improved data.