Charting the Galactic Acceleration Field with Stellar Streams: A Flexible Model Independent Approach

We present a data-driven method for fully reconstructing the Galactic acceleration field from phase-space measurements of stellar streams. Using a flexible and differentiable neural network that parametrizes the stream in phase space, our approach enables a direct estimation of the acceleration vector along a given stream. The divergence of the acceleration field is constrained to be negative, as required by Poisson’s equation for a positive mass density; this yields smoother results. Our approach is unique in that a model for the galactic gravitational potential does not need to be specified beforehand. Our algorithm treats the stream as a collection of tracer particles on locally similar orbits, rather than assuming that the stream delineates any single stellar orbit in the galaxy. Accordingly, our approach allows for distinct regions of the stream to have different energies, as is the case for real stellar streams. Once the acceleration vector is sampled along the stream, standard analytic models for the Galactic potential can then be constrained. Alternatively, we demonstrate that the potential can be represented with a neural network to enable full model flexibility while minimizing non-physical artifacts through Poisson’s equation. On mock data, our approach recovers the true potential with sub-percent level fractional errors across a range of scales, providing a new avenue to map the Milky Way with stellar streams.