A statistical method for measuring the Galactic potential and testing gravity with cold tidal streams

TL;DR

The paper presents the Minimum Entropy Method, a statistical approach to constrain the Milky Way's gravitational potential and test gravity theories using 6D phase-space data from tidal streams, without relying on dynamical models.

Contribution

It introduces a new entropy-based technique to analyze tidal streams for gravitational potential and gravity theory testing, applicable directly to observational data.

Findings

Separable orbital energy distributions indicate correct gravitational assumptions.

Systematic energy distribution variations quantify biases in potential models.

Method successfully distinguishes between Newtonian, Dirac, MONDian, and f(R) gravity in simulations.

Abstract

We introduce the Minimum Entropy Method, a simple statistical technique for constraining the Milky Way gravitational potential and simultaneously testing different gravity theories directly from 6D phase-space surveys and without adopting dynamical models. We demonstrate that orbital energy distributions that are separable (i.e. independent of position) have an associated entropy that increases under wrong assumptions about the gravitational potential and/or gravity theory. Of known objects, `cold' tidal streams from low-mass progenitors follow orbital distributions that most nearly satisfy the condition of separability. Although the orbits of tidally stripped stars are perturbed by the progenitor's self-gravity, systematic variations of the energy distribution can be quantified in terms of the cross-entropy of individual tails, giving further sensitivity to theoretical biases in the host potential. The feasibility of using the Minimum Entropy Method to test a wide range of gravity theories is illustrated by evolving restricted N-body models in a Newtonian potential and examining the changes in entropy introduced by Dirac, MONDian and f(R) gravity modifications.