Deep Potential: Recovering the gravitational potential and local pattern speed in the solar neighborhood with GDR3 using normalizing flows

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 3D gravitational potential in a one-kiloparsec 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 6D phase space using a normalizing flow and the gravitational network using a neural network. We recover a local pattern speed of $\Omega_p = 28.2\pm0.1\mathrm{\,km/s/kpc}$, a local total matter density of $\rho=0.086\pm0.010\mathrm{\,M_\odot/pc^3}$ and local dark matter density of $\rho_\mathrm{DM}=0.007\pm0.011\mathrm{\,M_\odot/pc^3}$. The full 3D model exhibits spatial fluctuations, which may stem from the model architecture and non-stationarity in the Milky Way.