Testing modified-gravity theories via wide binaries and GAIA

The standard Lambda cold dark matter model based on general relativity (GR) including cold dark matter (DM) is very successful at fitting cosmological observations, but recent non-detections of candidate dark matter particles mean that various modified-gravity theories remain of significant interest. The latter generally involve modifications to GR below a critical acceleration scale {∼ } 10^{-10} {m s^{-2}}. Wide-binary star systems with separations {≳ } 5 kau provide an interesting test for modified gravity, due to being in or near the low-acceleration regime and presumably containing negligible DM. Here, we explore the prospects for new observations pending from the GAIA spacecraft to provide tests of GR against modified Newtonian dynamics (MOND)- or tensor-vector-scalar (TeVeS)-like theories in a regime only partially explored to date. In particular, we find that a histogram of (3D) binary relative velocities, relative to equilibrium circular velocity predicted from the (2D) projected separation, predicts a rather sharp feature in this distribution for standard gravity, with an 80th (90th) percentile value close to 1.025 (1.14) with rather weak dependence on the eccentricity distribution. However, MOND/TeVeS theories produce a shifted distribution, with a significant increase in these upper percentiles. In MOND-like theories without an external field effect, there are large shifts of order unity. With the external field effect included, the shifts are considerably reduced to ∼0.04-0.08, but are still potentially detectable statistically given reasonably large samples and good control of contaminants. In principle, follow-up of GAIA-selected wide binaries with ground-based radial velocities accurate to {≲ } 0.03 { km s^{-1} } should be able to produce an interesting new constraint on modified-gravity theories.