Dynamical clock of the Helmi stream -- Analysis of the clumping of stars in the orbital frequency-space

Abstract

Reconstructing the assembly history of the Milky Way requires precise constraints on the dynamical age of its merger remnants -- the time elapsed since a progenitor satellite was disrupted by the Galactic tidal force. We present a new framework to derive this dynamical age for disrupted stellar systems by extending the Fourier analysis of the orbital frequency distribution proposed by Gomez and Helmi. To overcome the smearing of frequency-space structures caused by observational noise, we introduce the Greedy Optimistic Clustering algorithm. This method allows for an optimistic exploration of the density contrasts in the orbital frequency space by taking into account the observational uncertainty in the data, effectively sharpening the signal required for age estimation. By applying this method to the Helmi stream, we derive a dynamical age of $6.8 \pm 0.8$ Gyr. Our derived accretion epoch is consistent with the observed kinematic properties of the Helmi stream. In particular, the marked asymmetry in the vertical velocity distribution -- where approximately two-thirds of the stars have negative $v_z$ in the solar neighborhood -- supports a relatively recent arrival. This suggests that the progenitor of the Helmi stream was accreted during an epoch of Galactic growth distinct from the much earlier Gaia-Sausage-Enceladus merger ($\sim 10$ Gyr ago). We validate our methodology using error-added mock simulations, demonstrating the reliability of our approach. Our results establish the Greedy Optimistic Clustering framework as a powerful chronometric tool for reconstructing the hierarchical assembly of the Milky Way using current and future high-precision astrometric datasets.