Analysing surveys of our Galaxy -- II. Determining the potential

TL;DR

This paper introduces a new method for determining the Milky Way's gravitational potential from star catalogues, reducing numerical noise compared to orbit-based methods, and demonstrates its effectiveness with Gaia-like data.

Contribution

The paper presents an alternative approach to orbit-based methods, achieving lower numerical noise and more accurate potential parameter estimation from star catalogues.

Findings

Potential scaleheight can be determined with less than 20pc uncertainty using Gaia-like data.

Potential scalelength uncertainty is significantly below 0.25kpc.

The new method outperforms traditional orbit-based approaches in numerical stability.

Abstract

We consider the problem of determining the Galaxy's gravitational potential from a star catalogue. We show that orbit-based approaches to this problem suffer from unacceptable numerical noise deriving from the use of only a finite number of orbits. An alternative approach, which requires an ability to determine the model's phase-space density at predetermined positions and velocities, has a level of numerical noise that lies well below the intrinsic uncertainty associated with the finite size of the catalogue analysed. A catalogue of 10000 stars brighter than V=17 and distributed over the sky at b>30 degrees enables us to determine the scaleheight of the disc that contributes to the potential with an uncertainty below 20pc if the catalogue gives proper motions, line-of-sight velocities and parallaxes with errors typical of the Gaia Catalogue, rising to 36pc if only proper motions are available. The uncertainty in the disc's scalelength is significantly smaller than 0.25kpc.