Constraints on a MOND effect for isolated aspherical systems in deep Newtonian regime from orbital motions

Non-spherical systems described by MOND theories of modified gravity arising from generalizations of the Poisson equations are affected by a MONDian extra-quadrupolar potential \phi_M even if they are isolated and they are in deep Newtonian regime. In general MOND theories quickly approaching Newtonian dynamics for accelerations beyond A_0, \phi_M is proportional to a multiplicative scaling coefficient \alpha \sim 1, while in MOND models becoming Newtonian beyond \kappa A_0, \kappa » 1, it is enhanced by \kappa^2. We analytically work out some orbital effects due to \phi_M in the framework of QUMOND, and compare them with the latest observational determinations of Solar System’s planetary dynamics, exoplanets and double lined spectroscopic binary stars. The current admissible range for the anomalous perihelion precession of Saturn yields |\kappa| <= 3.5 x 10^3, while the radial velocity of \alpha Cen AB allows to infer |\kappa|<= 6.2 x 10^4 (A) and |\kappa|<= 4.2 x 10^4 (B). In evaluating such preliminary constraints it must be recalled that QUMOND is not the nonrelativistic limit of TeVeS.

💡 Research Summary

The paper investigates a previously overlooked consequence of Modified Newtonian Dynamics (MOND) in the quasi‑linear formulation known as QUMOND. While MOND is designed to deviate from Newtonian gravity only at accelerations below the characteristic scale A₀≈1.2×10⁻¹⁰ m s⁻², the authors show that for isolated, non‑spherical mass distributions a residual quadrupolar potential φ_M persists even in the deep Newtonian regime (a≫A₀). This extra potential originates from the anisotropic part of the mass distribution and is proportional to a dimensionless scaling factor α (≈1 for generic MOND models). In theories where Newtonian behaviour is recovered only beyond a higher threshold κ A₀ (with κ≫1), the amplitude of φ_M is amplified by κ².

Using the QUMOND field equations, the authors derive analytic expressions for the secular perturbations induced by φ_M on orbital elements: the peri‑centre precession Δϖ, long‑term changes in the semi‑major axis, and the induced radial‑velocity signal in spectroscopic binaries. They then confront these predictions with the most precise contemporary data sets:

• Solar System: The anomalous peri‑helion precession of Saturn, constrained by Cassini tracking and planetary ephemerides, yields |κ| ≤ 3.5 × 10³.
• Exoplanets: Current radial‑velocity and transit timing data are not yet precise enough to improve the bound, but the methodology is outlined for future missions.
• Double‑lined spectroscopic binaries: The α Centauri AB system provides the tightest constraints. High‑precision radial‑velocity measurements give |κ| ≤ 6.2 × 10⁴ for component A and |κ| ≤ 4.2 × 10⁴ for component B.

The authors stress that these limits are preliminary because QUMOND is not the non‑relativistic limit of TeVeS, the relativistic MOND theory most often cited. Consequently, the derived κ‑bounds apply specifically to the quasi‑linear framework. They also discuss systematic uncertainties: simplifications in the mass‑distribution model (e.g., treating bodies as homogeneous ellipsoids), neglect of external field effects, and measurement errors in radial velocities and planetary ephemerides.

Finally, the paper outlines prospects for tightening the constraints. Upcoming astrometric missions (e.g., Gaia’s final data release), next‑generation radial‑velocity spectrographs, and laser ranging to planetary probes could reduce the observational uncertainties by orders of magnitude, potentially pushing the κ limit down to the few‑hundred range. Such improvements would provide a stringent, high‑acceleration test of MOND‑type theories, complementing the traditional low‑acceleration tests based on galaxy rotation curves and dwarf‑galaxy dynamics.