2025ApJ...992...84K

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.