Substructures, resonances, and debris streams: A new constraint on the inner shape of the Galactic dark halo

Context. The local stellar halo of the Milky Way contains the debris from several past accretion events. Aims. Here we study in detail the structure and properties of nearby debris associated with the Helmi streams, which was originally identified as an overdensity in integrals of motion space. Methods. We use 6D phase-space information from Gaia EDR3 combined with spectroscopic surveys, and we analyse the orbits and frequencies of the stars in the streams using various Galactic potentials. We also explore how the Helmi streams constrain the flattening, q, of the Galactic dark matter halo. Results. We find that the streams are split into substructures in integrals of motion space, most notably into two clumps in angular momentum space. The clumps have consistent metallicity distributions and stellar populations, supporting a common progeny. In all the realistic Galactic potentials explored, the Helmi streams' stars depict a diffiuse distribution close to ω/ω_R~ 0:7. At the same time, the reason for the substructure in angular momentum space appears to be a ω_z:ω_φresonance close to 1:1. This resonance is exactly 1:1 in the case where the (density) flattening of the dark halo is q = 1:2. For this halo shape, the substructure in angular momenta is also long-lasting. Conclusions. Our findings suggest that the structure of the Galactic potential leaves a clear imprint on the properties of phase-mixed debris streams.