Charting galactic accelerations – II. How to ‘learn’ accelerations in the solar neighbourhood

A P Naik,J An,N W Evans,C Burrage

doi:10.1093/mnras/stac153

Abstract

ABSTRACT Gravitational acceleration fields can be deduced from the collisionless Boltzmann equation, once the distribution function is known. This can be constructed via the method of normalizing flows from data sets of the positions and velocities of stars. Here, we consider application of this technique to the solar neighbourhood. We construct mock data from a linear superposition of multiple ‘quasi-isothermal’ distribution functions, representing stellar populations in the equilibrium Milky Way disc. We show that given a mock data set comprising a million stars within 1 kpc of the Sun, the underlying acceleration field can be measured with excellent, sub-per cent level accuracy, even in the face of realistic errors and missing line-of-sight velocities. The effects of disequilibrium can lead to bias in the inferred acceleration field. This can be diagnosed by the presence of a phase space spiral, which can be extracted simply and cleanly from the learned distribution function. We carry out a comparison with two other popular methods of finding the local acceleration field (Jeans analysis and 1D distribution function fitting). We show our method most accurately measures accelerations from a given mock data set, particularly in the presence of disequilibria.

Highlights

Given a map of the gravitational acceleration field within a kiloparsec of the Sun, we could learn a wealth of information about the current state of our Galaxy, the distribution of matter and the nature of gravity
(ii) From the learned distribution function (DF), we calculate the gravitational acceleration field using an inversion of the collisionless Boltzmann equation (CBE)
Training an ensemble of normalizing flows on the mock data set generated from our Milky Way (MW) model, we arrive at a learned DF describing the local population of disc stars

Summary

Introduction

Given a map of the gravitational acceleration field within a kiloparsec of the Sun, we could learn a wealth of information about the current state of our Galaxy, the distribution of matter (both dark and luminous) and the nature of gravity. If the acceleration due to the luminous component is known, we can calculate the density distribution of dark matter, uncovering any substructures and measuring the ambient dark matter density in the Solar system. This latter number is of great importance in particle physics, as it is a key parameter in the interpretation of results of dark matter direct detection experiments (Read 2014; de Salas & Widmark 2021). Even so, promising steps have been recently taken in this direction employing measurements of pulsar orbital decay, which give the relative acceleration of a few pulsar systems with respect to the Solar system barycentre. If discrete stellar encounters are neglected, the stellar distribution function (DF), i.e. the probability distribution of the stars in six-dimensional (x, ) phase space, can be related to gravitational accelerations via the collisionless Boltzmann equation (CBE),

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Conclusion