Improved constraints on modified Newtonian gravity from Cassini radio tracking data

TL;DR

This paper refines the constraints on the Solar System quadrupole parameter $Q_2$ related to modified gravity theories, using Cassini data, and discusses implications for MOND and galaxy rotation curves.

Contribution

It provides an improved estimate of $Q_2$ from Cassini data, validating the Sun-only approximation and analyzing tensions with galaxy rotation curves and galactic acceleration limits.

Findings

$Q_2 = (1.6 1.8) imes 10^{-27}\,s^{-2}$, 40% better than previous

Jupiter's contribution to $Q_2$ is negligible at 0.05% level

Solar System constraints challenge modified gravity explanations of galaxy rotation curves

Abstract

We report an updated constraint on the Solar System quadrupole parameter $Q_2$, which encodes the external field effect predicted by modified gravity versions of the MOND paradigm. Using the dataset employed to compute the DE440 planetary ephemerides, and estimating it simultaneously with other parameters included in the planetary ephemerides, we find $Q_2 = (1.6 \pm 1.8) \times 10^{-27}\,\mathrm{s}^{-2}$ (1-$\sigma$), representing an improvement of 40% over previous estimates. We also show explicitly that the contribution to the MOND prediction of $Q_2$ from the Solar System's largest planet, Jupiter, is at the 0.05% level, validating the approximation of retaining only the Sun in theoretical calculations. With this new constraint on $Q_2$, we update previously acknowledged tensions with external galaxy rotation curves, now leading to discrepancies at the $3$-$15\sigma$ level depending on the detailed mass modeling or the subset of galaxies considered. Within the Milky Way itself, the $Q_2$ constraint imposes an upper bound of only 2% (at 95% confidence) on the MOND boost to the galactic radial acceleration (i.e., the ratio of the observed over baryonic Newtonian acceleration) at the position of the Sun, in strong tension with current observational limits. The updated $Q_2$ posterior finally confirms that Solar System measurements provide stronger constraints than current wide-binary data on classical modified gravity versions of MOND.