Improved constraints on modified Newtonian gravity from Cassini radio tracking data

TL;DR

This work tightens the Solar System constraint on the MOND external field effect by estimating the quadrupole parameter $Q_2$ from an extended Cassini data set within the DE440 ephemerides. The analysis demonstrates that Jupiter has a negligible influence on $Q_2$, and the updated bound $Q_2=(1.6 ext{±}1.8) imes10^{-27} ext{s}^{-2}$ is a 40% improvement over previous limits. When juxtaposed with SPARC galaxy rotation curves, the Solar System constraint reveals substantial tension for standard MOND modified gravity limits (AQUAL/QUMOND), implying that any viable MOND-based theory must involve an additional scale or a different mechanism, such as modified inertia. The results also place tight implications for Milky Way modeling, constraining the local MOND boost to near-Newtonian values and reinforcing that Solar System tests currently dominate over wide-binary tests in constraining these theories.

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-$σ$), 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 $3$-$15σ$ 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.

Figures (7)

• Figure 1: Distribution of the phantom density for the $\delta=\gamma=1$ IF (the RAR IF), computed using Eq. (\ref{['eq:rho_p']}) including both the Sun and Jupiter as sources. The Galactic Center is located in the $+z$ direction, i.e. towards the right of the figure. All scales are logarithmic. Clearly, the phantom density is essentially zero within 100 au and the QUMOND quadrupole is entirely related to the aspherical phantom density at much larger distances.
• Figure 2: Simulation of the deviation of the Earth-Saturn 1-way range over time when including a quadrupole as in Eq. \ref{['eq:Phi_EFE']} with $Q_2 = 10^{-26} {\rm s}^{-2}$.
• Figure 3: Residuals of the Cassini range data against the "All Data" case. The weighted root-mean-square residual is about 4 m.
• Figure 4: Posteriors on $a_0$ (in $10^{-10}$ m s$^{-2}$) and $\delta$ from the RAR and SS quadrupole. Left: Fiducial SPARC $M/L$ model; center: free Gaussian hyperprior model; right: as center but excluding galaxies with bulges.
• Figure 5: Posterior predictive distribution of $\alpha_\text{grav}$ for the three IF families from the updated $Q_2$ constraint.