Ergodic Considerations in the Gravitational Potential of the Milky Way

TL;DR

This paper introduces an ergodic-based method to constrain the Milky Way's gravitational potential using high-precision phase space data, assessing model validity through statistical comparison over time.

Contribution

It presents a novel, model-independent approach leveraging ergodic assumptions to evaluate Galactic potential models with precise observational data.

Findings

Method effectively constrains gravitational potential without symmetry assumptions

Requires high-precision data from missions like SIM and GAIA

Provides a statistical framework for model validation

Abstract

A method is proposed for constraining the Galactic gravitational potential from high precision observations of the phase space coordinates of a system of relaxed tracers. The method relies on an "ergodic" assumption that the observations are representative of the state of the system at any other time. The observed coordinates serve as initial conditions for moving the tracers forward in time in an assumed model for the gravitational field. The validity of the model is assessed by the statistical equivalence between the observations and the distribution of tracers at randomly selected times. The applicability of this ergodic method is not restricted by any assumption on the form or symmetry of the potential. However, it requires high recision observations as those that will be obtained from missions like SIM and GAIA.