# name
Data-driven diagnosis of the Milky Way disk dynamics

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Universitat de Barcelona. Departament de Física Quàntica i Astrofísica

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[eng] The Milky Way (MW) galaxy is a complex dynamic system that, thanks to the Gaia mission, is now understood to show significant departures from dynamical equilibrium. In galactic dynamics, we study how the mass distribution of the galaxy shapes the stellar motions, and how these motions - our observables - reveal the structure and history of the Galaxy. The Gaia mission has provided an unprecedented high-precision map of stellar positions and velocities, revolutionizing our field of research by showing detailed kinematic substructures that contain the dynamical information of our Galaxy. This thesis investigates the dynamics of the MW disc by analysing Gaia observational data, and using state-of-the-art numerical simulations and advanced data analysis methods. We began by studying substructures in the Gaia data using a method based on the wavelet transform and graph theory algorithms. This method allowed for a blind search and detailed characterization of kinematic substructures, some of which are usually referred to as moving groups, across extended regions of the disc in the full 6D phase-space. We applied it to Gaia EDR3 data and found that their morphology and spatial evolution across extended regions of the disc displayed a complexity not expected from simple dynamical principles. Some of our findings, such as deviations from constant angular momentum lines in the radial direction and vertical asymmetries for certain groups, suggest a strong influence from bar resonances and possibly incomplete vertical mixing. We then applied this methodology to Gaia DR3 data, and quantified the radial and azimuthal gradients in velocity of prominent moving groups. For Hercules, a key feature often linked to the bar, we measured a radial gradient of 28.1±2.8kms−1 kpc−1 and an azimuthal gradient of −0.63±0.13kms−1deg−1. Comparing these measurements with simple galaxy models including a bar revealed that such models cannot reproduce the observed radial gradient. This strong quantitative constraint indicates that understanding the kinematic substructure of the Milky Way disc requires more complex models than a fixed-pattern-speed bar alone; contributions from spiral arms, a secularly evolving bar (slowing down), a more complex potential, or external perturbations are likely necessary. Motivated by the observed complexity and the need to account for multiple components, we used simulations to show that stellar spiral arms induce a corresponding spiral structure within the dark matter (DM) halo. These DM spiral arms are consistently found across various types of simulations, from idealized test-particle models to full N-body and cosmological hydrodynamical simulations, confirming their ubiquitous presence. Our analysis confirmed that they form through the forced response of the halo to the stellar spiral potential. We quantified the strength of the DM spiral, finding it to be approximately 10% that of the stellar spiral, showed that it had distinct kinematic signatures compared to the stellar component, and that the DM spiral are consistently trailing the stellar arms, typically by about 10◦ in these simulations. These findings highlight a significant dynamic coupling between the stellar disk and the DM halo. Finally, we explored the dynamics of tidally induced spiral arms, that is, those that arise from interactions with satellite galaxies like the Sagittarius dwarf galaxy (Sgr). We combined numerical simulations with a data-driven equation discovery technique, Sparse Identification of Non-linear Dynamics (SINDy), to empirically identify the partial differential equations (PDEs) that govern the evolution of these spiral arms and their corresponding features in phase-space. This approach successfully recovered a known linear PDE for small perturbations and discovered a simple, previously unknown non-linear PDE for larger perturbations. We then analytically solved these discovered equations, obtaining explicit descriptions of the properties of the generated waves, such as their amplitude and pattern speed, and their shape and evolution in phase-space. Comparing the predictions derived from this analytical framework, with the Lz − VR waves in the Gaia data, we found that a single-impact scenario is inconsistent with the observed amplitude ratios of the resulting waves. This suggests that the actual origin of these features is more complex, likely involving multiple satellite passages or coupled effects from the bar and/or spiral arms from different origins. This work demonstrates the power of merging data-driven discovery with classical analytical theory to create simple, insightful dynamic models applicable to observations. By deriving quantitative constraints from high-precision observations, identifying and characterizing phenomena involving complex coupling like DM spiral arms, and developing novel methods that bridge empirical discovery with theoretical analysis, this thesis contributes to solving the puzzle of the dynamical history of our Galaxy.

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cc by-nc-sa (c) Bernet Martí, Marcel, 2025

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Tesis Doctorals - Departament - Física Quàntica i Astrofísica

# metadata.dc.title[].value
Data-driven diagnosis of the Milky Way disk dynamics