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Fig. 13

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Overview of the flattening of the effective potential qΦ and pΦ, as a function of Galactocentric distance along the x-axis for different analytical MW mass models, namely those by Bovy (2015), Price-Whelan (2017), McMillan (2017), and Cautun et al. (2020), and MW mass models constrained by stellar streams, namely Koposov et al. (2010) Küpper et al. (2015), Bovy et al. (2016), Malhan & Ibata (2019), Palau & Miralda-Escudé (2023), and Ibata et al. (2024), by globular cluster dynamics (Posti & Helmi 2019), and by previous work on the HS (Dodd et al. 2022). This figure also shows two Galactic potential models by Vasiliev (2024) with the ℒ3, ℳ11 and ℒ2, ℳ11 halo models at the present day in the left panel, and at different moments in time in the right panel. The black line shows the results obtained in this paper. The uncertainties derived for McMillan (2017), Posti & Helmi (2019), Cautun et al. (2020), Palau & Miralda-Escudé (2023), and this work have been obtained by randomly sampling 100 potentials from the respective chains, while for Küpper et al. (2015) and Malhan & Ibata (2019) we have sampled within the uncertainties quoted in those works. In all cases, we have taken the 16th and 84th percentile values. For Koposov et al. (2010) and Bovy et al. (2016) we show the uncertainties quoted in those works, and for Ibata et al. (2024) no uncertainties could be derived. Models that are based on constraints of the DM halo shape are shown with solid lines, models that assume a spherical DM halo are shown with dashed lines, and their similarity is apparent in qϕ at larger distance, except for the Vasiliev (2024) models, which take into account the infall of the LMC. The differences at small distances are due to varying assumptions on the discs and bulge, but are not relevant for the work presented here.

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