High-Precision Differential Radial Velocities of C3PO Wide Binaries: A Test of Modified Newtonian Dynamics (MOND)

TL;DR

This study develops a high-precision spectroscopic method to measure differential radial velocities of wide binary stars, enabling a rigorous test of Modified Newtonian Dynamics (MOND) predictions against Newtonian gravity in low-acceleration regimes.

Contribution

It introduces a novel high-resolution spectroscopic technique to measure differential RVs with unprecedented precision, allowing for the first detailed Bayesian analysis of wide binaries to test MOND.

Findings

Achieved 8-15 m/s differential RV precision, significantly better than Gaia.

Found tension with MOND at the canonical acceleration scale, especially for the simple interpolating function.

Excluded the standard MOND value at 3.1 sigma for one interpolating function.

Abstract

Wide-binary stars, separated by thousands of AU, reside in low-acceleration regimes where Modified Newtonian Dynamics (MOND) predicts deviation from Newtonian gravity. However, Gaia radial velocities (RVs) lack the precision to resolve the small velocity differences expected in these systems, limiting previous MOND analyses to two-dimensional kinematics. In this paper, we introduce a technique to measure differential RVs of wide binary stars using high resolution, high signal-to-noise spectra. We apply this method to measure differential RVs of 100 wide-binaries from the C3PO survey and achieved precisions of $8-15$ m/s per binary pair, a $\sim 10-100 \times$ improvement (median $\sim 24 \times$) over Gaia DR3. Combining these measurements with Gaia astrometry, we construct a hierarchical Bayesian model to infer the orbital elements of all wide-binary pairs and the global MOND acceleration scale ($a_0$). We test two commonly used interpolating functions in MOND formulation: the simple form ($b=1, \mu = x/(1+x)$) and the standard form ($b=2, \mu = x/\sqrt{1+x^2}$). Our results indicate tension with MOND at the presently accepted $a_0$ value: for $b=1$, the canonical value is excluded at $3.1\sigma$, while for $b=2$, the exclusion is at $1.9\sigma$.