Testing gravity with wide binary stars like α Centauri

Abstract

We consider the feasibility of testing Newtonian gravity at low accelerations\nusing wide binary (WB) stars separated by $\\ge 3$ kAU. These systems probe the\naccelerations at which galaxy rotation curves unexpectedly flatline, possibly\ndue to Modified Newtonian Dynamics (MOND). We conduct Newtonian and MOND\nsimulations of WBs covering a grid of model parameters in the system mass,\nsemi-major axis, eccentricity and orbital plane. We self-consistently include\nthe external field (EF) from the rest of the Galaxy on the Solar neighbourhood\nusing an axisymmetric algorithm. For a given projected separation, WB relative\nvelocities reach larger values in MOND. The excess is ${\\approx 20\\%}$ adopting\nits simple interpolating function, as works best with a range of Galactic and\nextragalactic observations. This causes noticeable MOND effects in accurate\nobservations of ${\\approx 500}$ WBs, even without radial velocity measurements.\n We show that the proposed Theia mission may be able to directly measure the\norbital acceleration of Proxima Centauri towards the 13 kAU-distant $\\alpha$\nCentauri. This requires an astrometric accuracy of $\\approx 1 \\, \\mu$as over 5\nyears. We also consider the long-term orbital stability of WBs with different\norbital planes. As each system rotates around the Galaxy, it experiences a\ntime-varying EF because this is directed towards the Galactic Centre. We\ndemonstrate approximate conservation of the angular momentum component along\nthis direction, a consequence of the WB orbit adiabatically adjusting to the\nmuch slower Galactic orbit. WBs with very little angular momentum in this\ndirection are less stable over Gyr periods. This novel direction-dependent\neffect might allow for further tests of MOND.\n