Andromeda XXI -- a dwarf galaxy in a low density dark matter halo

Andromeda XXI (And XXI) has been proposed as a dwarf spheroidal galaxy with a central dark matter density that is lower than expected in the Standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmology. In this work, we present dynamical observations for 77 member stars in this system, more than doubling previous studies to determine whether this galaxy is truly a low density outlier. We measure a systemic velocity of $v_r=-363.4\pm1.0\,{\rm kms}^{-1}$ and a velocity dispersion of $\sigma_v=6.1^{+1.0}_{-0.9}\,{\rm kms}^{-1}$, consistent with previous work and within $1\sigma$ of predictions made within the modified Newtonian dynamics framework. We also measure the metallicity of our member stars from their spectra, finding a mean value of ${\rm [Fe/H]}=-1.7\pm0.1$~dex. We model the dark matter density profile of And~XXI using an improved version of \GravSphere, finding a central density of $\rho_{\rm DM}({\rm 150 pc})=2.7_{-1.7}^{+2.7} \times 10^7 \,{\rm M_\odot\,kpc^{-3}}$ at 68\% confidence, and a density at two half light radii of $\rho_{\rm DM}({\rm 1.75 kpc})=0.9_{-0.2}^{+0.3} \times 10^5 \,{\rm M_\odot\,kpc^{-3}}$ at 68\% confidence. These are both a factor ${\sim}3-5$ lower than the densities expected from abundance matching in $\Lambda$CDM. We show that this cannot be explained by `dark matter heating' since And~XXI had too little star formation to significantly lower its inner dark matter density, while dark matter heating only acts on the profile inside the half light radius. However, And~XXI's low density can be accommodated within $\Lambda$CDM if it experienced extreme tidal stripping (losing $>95\%$ of its mass), or if it inhabits a low concentration halo on a plunging orbit that experienced repeated tidal shocks.