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

TL;DR

This paper investigates the effects of a MONDian quadrupolar potential on orbital motions in deep Newtonian regimes, deriving constraints from Solar System and stellar observations to test modified gravity theories.

Contribution

It analytically derives orbital effects of the MONDian potential in QUMOND and constrains model parameters using observational data from Solar System and binary stars.

Findings

Constraints on  from Saturn's perihelion precession: ||  3.5  10^3

Limits from  Cen AB radial velocity: ||  6.2  10^4 (A), 4.2  10^4 (B)

MOND effects are constrained to be small within current observational accuracy.

Abstract

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.