Abstract
Dwarf spheroidal galaxies of the Local Group obey a relationship between the line-of-sight velocity dispersion and half-light radius, although there are a number of dwarfs that lie beneath this relation with suppressed velocity dispersion. The most discrepant of these (in the Milky Way) is the `feeble giant' Crater II. Using analytic arguments supported by controlled numerical simulations of tidally-stripped flattened two-component dwarf galaxies, we investigate interpretations of Crater II within standard galaxy formation theory. Heavy tidal disruption is necessary to explain the velocity-dispersion suppression which is plausible if the proper motion of Crater II is $(\mu_{\alpha*},\mu_\delta)=(-0.21\pm0.09,-0.24\pm0.09)\mathrm{mas\,yr}^{-1}$. Furthermore, we demonstrate that the velocity dispersion of tidally-disrupted systems is solely a function of the total mass loss even for weakly-embedded and flattened systems. The half-light radius evolution depends more sensitively on orbital phase and the properties of the dark matter profile. The half-light radius of weakly-embedded cusped systems rapidly decreases producing some tension with the Crater II observations. This tension is alleviated by cored dark matter profiles, in which the half-light radius can grow after tidal disruption. The evolution of flattened galaxies is characterised by two competing effects: tidal shocking makes the central regions rounder whilst tidal distortion produces a prolate tidally-locked outer envelope. After $\sim70$ per cent of the central mass is lost, tidal distortion becomes the dominant effect and the shape of the central regions of the galaxy tends to a universal prolate shape irrespective of the initial shape.
Highlights
The dwarf spheroidal galaxies of the Local Group lie at the extreme low mass end of all known galaxies
We reject samples that imply Crater II is on first infall (| μ| 0.46 mas yr−1), as we have shown tidal mass loss is essential to explain Crater II if it is embedded in an NFW-like dark halo
Our modelling approach uses a number of simplifications that merit validation: (i) no correlations between flattening and tidal disruption – we have found that tidal disruption is intrinsically linked to a galaxy’s shape (Fig. 3) and highly flattened galaxies are inconsistent with heavy mass loss
Summary
The dwarf spheroidal galaxies (dSphs) of the Local Group lie at the extreme low mass end of all known galaxies As such they present a number of challenges for any theory of galaxy formation (Weinberg et al 2015). Their typically high dynamical-mass-to-light ratios (Mateo 1998) indicate the presence of massive dark matter haloes. The velocity dispersion and half-light radius of dSphs are approximately related as σlos ∝ Rh1/2 which can be interpreted as all dSphs residing in a universal dark matter halo (Strigari et al 2008; Walker et al 2009; Wolf et al 2010; Sawala et al 2016) corresponding to the smallest dark matter halo that can form and retain stars in ΛCDM galaxy formation theory (Okamoto & Frenk 2009).
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