Constraining Axion Dark Matter with Galactic-Centre Resonant Dynamics

TL;DR

The work tests whether fuzzy-dark-matter axions forming a central soliton core around the Galactic Centre can produce a rotating gravitational-atom that exerts VRR-like torques on stars near the SMBH. By deriving an orbit-averaged, multipole potential $\\langle\\Phi\\rangle_{da} = -\\sum_{l,m} J_{lm} Y_{lm}^*(\\hat{\\mathbf{L}})$ and modeling a rotating core with rotating mass parameter $|\\alpha|^2$, the authors show these torques can significantly affect the young stellar disc. They translate disc stability into constraints on the axion mass $m_a$, obtaining 2σ bounds in the range $m_a \\in [3.8,5.98] imes 10^{-20}$ eV, depending on the disc opening angle, and demonstrate how partial FDM fractions modify the limits. The results offer a novel astrophysical probe of $m_a$ and emphasize that improved Galactic Centre data will tighten the constraints and may extend to extragalactic nuclear discs.

Abstract

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 $2σ$. Other core models would vary the constrained values of $m_a$ somewhat. These constraints will tighten significantly with future, improved data.

Figures (4)

• Figure 1: The integral $I_{2,1}$ as a function of the semi-major axis, plotted for various eccentricities, for the wave-function \ref{['eqn:wave function typical']}.
• Figure 2: The upper limit for disc stability from inequality \ref{['eqn:stability']}, for a Galactic-centre-like disc with parameters specified in the text and table \ref{['tab:Parameters']} (in blue). The expected value of the rotating mass $\left\vert\alpha\right\vert^2M_{\rm a}$ is plotted too (red, dashed line). The shaded regions around both curves show estimated $1\sigma$ uncertainties. The disc should be disrupted for values of $m_{a}$ where the maximum rotating mass for disc stability is lower than $\left\vert\alpha\right\vert^2M_{\rm a}$, and are thus constrained.
• Figure 3: The semi-major axes in the disc which the gravitational atom renders unstable. Here $M_{\rm d} = 4000M_\odot$, $\iota = 10^\circ$, $M_{\rm vir} = 1.1\times 10^{12}\, M_\odot$, and $\lambda_{\rm c} = 0.06$; the inner, darker region corresponds to $M_{\rm d} = 10^4M_\odot$ with the same values for the other parameters.
• Figure 4: Values of $m_a$inconsistent with a stable disc, obtained from imposing inequality \ref{['eqn:stability']}, for various values of $\alpha$ (or alternatively, fixing $\alpha$ by equation \ref{['eqn: rotating mass from core properties']}, for the FDM dark-matter fraction, $f_{\rm FDM}$). The shaded blue contours correspond to an opening angle$\iota = 14^\circ \pm 4^\circ$, while the red ones use $\iota = 16^\circ \pm 4.8^\circ$. The darker regions are $2\sigma$ levels, while the lighter ones delineate $1\sigma$ regions, for the field configuration described in the text.