# Stellar Accelerations and the Galactic Gravitational Field

## TL;DR

Measuring stellar accelerations with high precision can test Newtonian gravity, detect dark matter inhomogeneities, and improve understanding of the galaxy's mass distribution, leveraging upcoming spectrograph advancements.

## Contribution

This paper explores the potential of future high-precision spectroscopic measurements to directly test gravitational theories and map dark matter in the galaxy.

## Key findings

- High-precision stellar acceleration measurements are feasible with upcoming spectrographs.
- Such measurements can test non-Newtonian gravity and detect dark matter inhomogeneities.
- Strategies to mitigate confounding effects are discussed.

## Abstract

Typical stars in the Milky Way galaxy have velocities of hundreds of kilometres per second and experience gravitational accelerations of $\sim 10^{-10}$ m s$^{-2}$, resulting in velocity changes of a few centimetres per second over a decade. Measurements of these accelerations would permit direct tests of the applicability of Newtonian dynamics on kiloparsec length scales and could reveal significant small scale inhomogeneities within the galaxy, as well increasing the sensitivity of measurements of the overall mass distribution of the galaxy. Noting that a reasonable extrapolation of progress in exoplanet hunting spectrographs suggests that centimetre per second level precision will be attainable in the coming decade(s), we explore the possibilities such measurements would create. We consider possible confounding effects, including apparent accelerations induced by stellar motion and reflex velocities from planetary systems, along with possible strategies for their mitigation. If these issues can be satisfactorily addressed it will be possible to use high precision measurements of changing stellar velocities to perform a "blind search" for dark matter, make direct tests of theories of non-Newtonian gravitational dynamics, detect local inhomogeneities in the dark matter density, and greatly improve measurements of the overall properties of the galaxy.