Testing modified-gravity theories via wide binaries and GAIA

Abstract

The standard ΛCDM model based on General Relativity (GR) including cold dark matter (CDM) is very successful at fitting cosmological observations, but recent nondetections of candidate dark matter (DM) 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 (WB) 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 MOND or 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 MONDlike 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, followup 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.

The distribution of relative proper motions of wide binaries in Gaia DR2: MOND or multiplicity?

“…It has long been recognised that ultra-wide binaries offer a potential opportunity to scrutinise alternative gravity theories (see e.g. Hernandez et al (2012), Pittordis & Sutherland (2018)). This derives from the fact that the gravitational acceleration experienced in solar type binaries with separations of order 10 4 AU is starting to become comparable to that experienced in the outer reaches of spiral galaxies, where the anomalously large circular velocity provides some of the most convincing evidence for dark matter.…”

A new line on the wide binary test of gravity

“…Fortunately, these systems can be utilized in a statistical sense if one uses their accurately known sky-projected separation r sky (Pittordis & Sutherland 2018). Thus, the WBT in the short term will be based on r sky and v rel .…”

“…It offers modest benefits in bin 3 and substantial benefits in bins 1 and 2 ( Figure 3). These are the critical bins for the WBT (Pittordis & Sutherland 2018;Banik & Zhao 2018). Although the uncertainties in these bins are slightly larger than with v line alone, using v sky has the advantage of utilizing two components of v rel instead of just one.…”

The geometric challenge of testing gravity with wide binaries

“…However, for a statistical sample of binaries observed at random snapshots in their orbits, GR and modified gravity theories predict different relations between the projected physical separation, s, and the instantaneous one-dimensional velocity difference between the two stars (typically measured with proper motions and/or radial velocities), ∆V. The magnitude of the difference compared to GR varies significantly between modified gravity theories and is much larger in theories that do not include an external field effect than in theories that do (Banik & Zhao 2018;Pittordis & Sutherland 2018). GR (in the Newonian limit) predicts ∆V ∼ s −1/2 ; at s ∼ 1 pc, it predicts bound solar-type binaries to have ∆V of only a few tens of m s −1 .…”

“…GR (in the Newonian limit) predicts ∆V ∼ s −1/2 ; at s ∼ 1 pc, it predicts bound solar-type binaries to have ∆V of only a few tens of m s −1 . Measurements of binaries with wide separations and large ∆V can in principle rule out both GR and modified gravity theories that include an external field effect (Famaey & McGaugh 2012;Pittordis & Sutherland 2018 Hernandez et al (2018) is shown in black; the simulated sample described in Section 2 is shown in red. The simulated sample is constructed to have a similar distribution of distance and proper motion to the observed sample.…”