Uncovering 3D dark-matter distribution of the Milky Way using an empirical triaxial orbit-superposition model: Method validation

¹ Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China
² National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
³ Department of Astronomy, Westlake University, Hangzhou, Zhejiang 310030, China
⁴ School of Physics and Optoelectronic Engineering, Hainan University, 58 Renmin Avenue, Haikou 570228, China
⁵ Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China

^★ Corresponding author: lzhu@shao.ac.cn

Received: 19 June 2025
Accepted: 26 August 2025

Abstract

We introduce the empirical, triaxial orbit-superposition model, a novel dynamical model for the Milky Way halo. This model relies on minimal physical assumptions that the system is stationary, meaning the distribution function in 6D phase space does not change when the stars orbit in the correct gravitational potential. We validated our method by applying it to mock datasets that mimic the observations of the Milky Way halo from LAMOST + Gaia with stars’ 3D positions and 3D velocities observed. By removing the stellar disc and substructures and correcting the selection function, we obtain a sample of smooth halo stars considered stationary and complete. We constructed a gravitational potential including a highly flexible, triaxial dark-matter halo with adaptable parameters. Within each specified gravitational potential, we integrated orbits of these halo stars and built a model by superposing the orbits together taking the weights of stars derived from the selection function correction. The goodness of each model was evaluated by comparing the density distributions as well as 3D velocity distributions numerically represented in the model to that in the data. The shape and radial density distribution of the underlying dark-matter halo can be constrained well simultaneously. We applied it to three mock galaxies with different intrinsic shapes of their dark-matter halos and achieved accurate recovery of the 3D dark-matter density distributions for all of them.