Abstract The gravitational potential of the Milky Way encodes information about the distribution of all matter—including dark matter—throughout the Galaxy. Gaia Data Release 3 has revealed a complex structure that necessitates flexible models of the Galactic gravitational potential. We make use of a sample of 5.6 million upper-main-sequence stars to map the full three-dimensional gravitational potential in a 1 kpc radius from the Sun using a data-driven approach called “Deep Potential.” This method makes minimal assumptions about the dynamics of the Galaxy—that the stars are a collisionless system that is statistically stationary in a rotating frame (with pattern speed to be determined). We model the distribution of stars in six-dimensional phase space using a normalizing flow and the gravitational network using a neural network. We recover a local pattern speed of Ω p = 28.2 ± 0.1 km s −1 kpc −1 , a local total matter density of ρ = 0.086 ± 0.010 M ⊙ pc −3 , and local dark matter density of ρ DM = 0.007 ± 0.011 M ⊙ pc −3 . The full three-dimensional model exhibits spatial fluctuations, which may stem from the model architecture and nonstationarity in the Milky Way.
Kalda et al. (2025) studied this question.