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The MUSE-Faint survey: I. Spectroscopic evidence for a star cluster in Eridanus 2 and constraints on MACHOs as a constituent of dark matter

We aim to provide spectroscopic evidence regarding the nature of the putative star cluster in Eridanus 2 and to place constraints on the mass and abundance of massive astrophysical compact halo objects (MACHOs) as a constituent of dark matter. Methods. We present spectroscopic observations of the central square arcminute of Eridanus 2 from MUSE-Faint, a survey of ultra-faint dwarf galaxies with the Multi Unit Spectroscopic Explorer on the Very Large Telescope. We derive line-of-sight velocities for possible member stars of the putative cluster and for stars in the centre of Eridanus 2. We discuss the existence of the cluster and determine new constraints for MACHOs using the Fokker-Planck diffusion approximation. Results. Out of 182 extracted spectra, we identify 26 member stars of Eridanus 2, seven of which are possible cluster members. We find intrinsic mean line-of-sight velocities of $79.7^{+3.1}_{-3.8}\,\mathrm{km}\,\mathrm{s}^{-1}$ and $76.0^{+3.2}_{-3.7}\,\mathrm{km}\,\mathrm{s}^{-1}$ for the cluster and the bulk of Eridanus 2, respectively, and intrinsic velocity dispersions of ${<}7.6\,\mathrm{km}\,\mathrm{s}^{-1}$ (68-$\%$ upper limit) and $10.3^{+3.9}_{-3.2}\,\mathrm{km}\,\mathrm{s}^{-1}$, respectively. This indicates the cluster most likely exists as a distinct dynamical population hosted by Eridanus 2, without surplus of dark matter over the background distribution. Among the member stars in the bulk of Eridanus 2, we find possible carbon stars, alluding to the existence of an intermediate-age population. We derive constraints on the fraction of dark matter that can consist of MACHOs with a given mass between $1$-$10^5\,M_\mathrm{sun}$. For dark matter consisting purely of MACHOs, the mass of the MACHOs must be less than ${\sim}7.6\,M_\mathrm{sun}$ and ${\sim}44\,M_\mathrm{sun}$ at a $68$- and $95$-$\%$ confidence level, respectively. (Abridged)