tokens: unaffected by the Milky Way potential. We see in the lower panel that even for V peak the relation is broadly flat with significant scatter. For example, without including pericentre information, the V peak error bars for CVenI and Draco overlap, suggesting that these two galaxies with similar stellar masses could have formed within haloes of the same size. The revised estimate suggest that Draco I likely formed within a halo that was more massive. Improving constraints on the dynamical mass of the dSphs at present combined with better constraints on their pericentres from Gaia can provide deeper understanding of the past evolution and the mass of the progenitor haloes of MW dwarf spheroidal galaxies. Among the galaxies we have considered, Draco and Ursa Minor are affected the most by including pericentre information. These, the densest dSph satellites, have relatively small pericentres ( r peri ≲ 50 kpc) and this pushes their inferred V max values lower than they would have been without pericentre information. We find that both Draco and Ursa Minor appear to inhabit subhaloes with V max ≃ 20–27 km s −1 (at one sigma) and are less dense than would be expected for the most massive subhaloes with small pericentres (see Fig. 1 ). This exacerbates the traditional TBTF problem (Boylan-Kolchin et al. 2011 , 2012 ). The inferred range of V peak values is also tightened for these galaxies. Both galaxies have inferred peak maximum circular velocities (prior to infall) that put them in range to have been significantly affected by reionization, V peak ≃ 25–37 km s −1 (e.g. Bullock, Kravtsov Weinberg 2000 ; Gnedin 2000 ; Benítez-Llambay et al. 2017 ; Fitts et al. 2017 ). It is worth considering whether our results are affected by numerical resolution. There is a fair amount of evidence to suggest that simulations such as ours do not accurately track halo survival after they have lost a significant () amount of mass, with ∼3000 particles appearing to be a critical limit below which haloes disrupt unphysically (e.g. Van den Bosch Ogiya 2018 ; Errani Navarro 2020 ). In terms of halo counts alone, this effect should not affect current cosmological zoom simulations significantly, since accreted halo mass functions rise steeply with increasing mass, d n /d M ∼ M −1.8 (e.g. Giocoli, Tormen van den Bosch 2008 ). This means that for every halo of mass M that was accreted long ago and has lost 99 per cent of its original mass (100 M ), there are as many as ∼4000 haloes of mass M that were accreted more recently and that can be accurately counted. As discussed in Kelley et al. ( 2019 ), convergence tests suggest that our halo counts are mostly complete down to V max > 4.5 km s −1 , or only ∼150 particles. Of particular relevance to this work is whether or not internal halo structures, e.g. V max / V peak distributions at fixed V max , are tracked appropriately. We have limited our analysis to haloes with V max > 10 km s −1 , or ≳ 3000 particles. According to the
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