The MUSE-Faint survey. II. The dark matter-density profile of the ultra-faint dwarf galaxy Eridanus 2

Aims. We use stellar line-of-sight velocities to constrain the dark matter-density profile of Eridanus 2, an ultra-faint dwarf galaxy ($M_\mathrm{V} = -7.1$, $M_* \approx 9 \times 10^4\,M_\odot$). We furthermore derive constraints on fundamental properties of self-interacting and fuzzy dark matter. Methods. We present new observations of Eridanus 2 from MUSE-Faint, a survey of ultra-faint dwarf galaxies with MUSE on the Very Large Telescope, and determine line-of-sight velocities for stars inside the half-light radius. Combined with literature data, we have 92 stellar tracers out to twice the half-light radius. We constrain models of cold dark matter, self-interacting dark matter, and fuzzy dark matter with these tracers, using CJAM and pyGravSphere for the dynamical analysis. Results. We find substantial evidence for cold dark matter over self-interacting dark matter and also substantial evidence for fuzzy dark matter over cold dark matter. We find a virial mass $M_{200} \sim 10^8\,M_\odot$ and astrophysical factors $J(\alpha_\mathrm{c}^J) \sim 10^{11}\,M_\odot^2\,\mathrm{kpc}^{-5}$ and $D(\alpha_\mathrm{c}^D) \sim 10^2$-$10^{2.5}\,M_\odot\,\mathrm{kpc}^{-2}$. We do not resolve a core ($r_\mathrm{c} \lesssim 35\,\mathrm{pc}$, 68-% level) or soliton ($r_\mathrm{sol} \lesssim 4.7\,\mathrm{pc}$, 68-% level). These limits are equivalent to an effective self-interaction coefficient $f\Gamma \lesssim 2.5 \times 10^{-29}\,\mathrm{cm}^3\,\mathrm{s}^{-1}\,\mathrm{eV}^{-1}\,c^2$ and a fuzzy dark matter-particle mass $m_\mathrm{a} \gtrsim 8.5 \times 10^{-20}\,\mathrm{eV}\,c^{-2}$. The constraint on self-interaction is complementary to those from gamma-ray searches. The constraint on fuzzy dark matter-particle mass is inconsistent with those obtained for larger dwarf galaxies, suggesting that the flattened density profiles of those galaxies are not caused by fuzzy dark matter. (Abridged)