tokens: zones leads to the depletion of stars in the regions around these resonances. These results do not strongly depend on the choice for the gravitational potential assumed for the Milky Way, provided this is generic enough (and not integrable, e.g., of Stäckel form). We also find that in two other commonly used Galactic potentials ( Piffl et al. 2014 ; Bovy 2015 ), very similar substructures can be observed in R max vs. z max , as is shown in Appendix A , and that they are associated with resonant families, and hence with the presence of non-integrability in the system. Our analysis (as also concluded by Amarante et al. 2020 ) therefore directly shows that not all substructures are related to accretion, as is often considered in the literature, nor to the settling of the gravitational potential after major merger activity as had been suggested by Haywood et al. (2018) . Nonetheless, the characteristics of substructures from merger events may sometimes be related to the presence of resonances. For example, we see that some of the stars in the Helmi streams appear to be close to a resonance, Ω z : Ω R ∼ 1:2. This perhaps explains why its stars are distributed asymmetrically in velocity space (the stream with v z 0 has more stars than that with v z > 0). This asymmetry was used to constrain its time of accretion to approximately 5-8 Gyr ago, which is a puzzlingly low value given that these stars are on relatively bound orbits. Since stars near a resonance take longer to spread out in space ( Vogelsberger White 2008 ), this can lead to an underestimation of their time of accretion. This means that chaotic dynamics may have to be considered when modelling the evolution of tidal debris, as already hinted by Price-Whelan et al. (2015) in their modelling of cold thin streams farther away in the halo. Probably the best way to tell whether substructures are related to accretion events is via a chemical tagging analysis. Stars that originate from a satellite will follow characteristic tracks in chemical abundance space. On the other hand, stars that group together because of dynamical resonances have no reason to be chemically distinct from other stars. How stars populate different resonant families depends on their distribution function and the gravitational potential in which they move. In this work, we only considered that of the Milky Way, but a recent analysis of nearby thin-disc stars has shown that the Sagittarius dwarf also plays a role in their dynamics (see Antoja et al. 2018 ). Interestingly, if we integrate the orbit of Sagittarius in the McMillan (2017) potential for 40 Gyr with the initial conditions derived by the Gaia Collaboration (2018c) and apply the SuperFreq code to obtain its frequencies (i.e. we repeat the analysis done for the stars in our sample), we find that Sagittarius falls on the Ω z : Ω R = 1:2 and Ω z : Ω φ = 1:1 resonance. The stars in our sample on the Ω z : Ω R = 1:2 resonance (green points in Figs. 7 – 9 ) define a
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O B-CelestialObjectRegion O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject O O B-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O