Prospects for a local detection of dark matter with future missions to Uranus and Neptune

TL;DR

This study explores the potential of future Doppler ranging missions to Uranus and Neptune to detect local dark matter and test modified gravity theories, estimating sensitivity levels and the impact of noise reduction on these measurements.

Contribution

It introduces a method to assess the detectability of dark matter and modified gravity effects using future planetary missions with improved Doppler ranging precision.

Findings

Potential to detect local dark matter densities of ~9×10^{-20} kg/m^3

Improvement in ranging noise could rule out Milgrom's modified gravity

Future missions can significantly refine measurements of solar system gravitational parameters

Abstract

We investigate the possibility of detecting the gravitational influence of dark matter (DM) on the trajectory of prospective Doppler ranging missions to Uranus and Neptune. In addition, we estimate the constraints such a mission can provide on modified and massive gravity theories via extra-precession measurements using orbiters around the ice giants. We employ Monte Carlo-Markov Chain methods to reconstruct fictitious spacecraft trajectories in a simplified solar system model with varying amounts of DM. We characterise the noise on the Doppler link by the Allan deviation $\sigma_{\rm A}$, scaled on the Cassini-era value of $\sigma^{\rm{Cass}}_{\rm A}= 3 \times 10^{-15}$. Additionally, we compare the precision of prospective extra-precession measurements of Uranus and Neptune with the expected rates from simulations, in the context of modifications to the inverse square law. We estimate that the prospective mission will be sensitive to DM densities of the order of $\rho_{\rm{DM}} \sim 9 \times 10^{-20} \, (\sigma_{\rm A}/\sigma_{\rm A}^{\rm{Cass}}) $ kg/m$^3$, while the $1\sigma$ bound on the expected galactic density of $\rho_{\rm{DM}} \sim 5 \times 10^{-22}$ kg/m$^3$ decreases as $1.0 \times 10^{-20} \, (\sigma_{\rm A}/\sigma^{\rm{Cass}}_{\rm A})^{0.8}$ kg/m$^3$. An improvement of two to three orders of magnitude from the baseline Allan deviation would guarantee a local detection of DM. Only a moderate reduction in ranging noise is required to rule out Milgrom's interpolating function with solar system based observations, and improve constraints the graviton mass beyond current local- or gravitational wave-based measurements. Our analysis also highlights the potential of future ranging missions to improve measurements of the standard gravitational parameters in the solar system.