Wide Binary Star Tests Of Modified Gravity

Wide binary systems (i.e. stars in gravitationally bound binary star systems with a large separation) should behave in a non-Newtonian fashion in modified gravity theories. But, in LambdaCDM and other dark matter particle halo theories, the dark matter halos should be too large to materially change the dynamics of wide binary systems. 

So, it is a good data set to distinguish the two approaches to phenomena normally attributed to dark matter, and there are at least 9,000 such binary systems that have been detected by GAIA. But the data aren't yet sufficiently precise because it can't rule out that what appear to be binary systems are really three or four star systems in which not all of the stars have been seen. Fortunately, progress is being made in distinguishing false positive binary systems in order to allow the dynamics of wide binaries to be rigorously studies with a large data set.

Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt to emulate dark matter; in essence, MOND-like theories (with external field effect included) predict that wide binaries (wider than ∼7 kAU) should orbit ∼15% faster than Newtonian for similar orbit parameters; such a shift is readily detectable in principle in the sample of 9,000 candidate systems selected from GAIA EDR3 by Pittordis and Sutherland (2022). However, the main obstacle at present is the observed ``fat tail" of candidate wide-binary systems with velocity differences at ∼1.5−6× circular velocity; this tail population cannot be bound pure binary systems, but is likely to be dominated by triple or quadruple systems with unresolved or undetected additional star(s).

While this tail can be modelled and subtracted, obtaining an accurate model for the triple population is crucial to obtain a robust test for modified gravity. Here we explore prospects for observationally constraining the triple population: we simulate a population of hierarchical triples ``observed" as in PS22 at random epochs and viewing angles; then evaluate various possible methods for detecting the third star, including GAIA astrometry, RV drift, and several imaging methods from direct Rubin images, speckle imaging and coronagraphic imaging. Results are encouraging, typically 90 percent of the triple systems in the key regions of parameter space are detectable; there is a moderate ``dead zone" of cool brown-dwarf companions at ∼25−100 AU separation which are not detectable with any of our baseline methods. A large but feasible observing campaign can clarify the triple/quadruple population and make the gravity test decisive.

Dhruv Manchanda, Will Sutherland, Charalambos Pittordis, "Wide Binaries as a Modified Gravity test: prospects for detecting triple-system contamination" arXiv:2210.07781 (October 14, 2022) (Submitting to Open Journal of Astrophysics).

The introduction to the paper explains:

A number of recent studies have shown that velocity differences of wide stellar binaries offer an interesting test for modified-gravity theories similar to MoND, which attempt to eliminate the need for dark matter (see e.g. Hernandez et al. (2012a), Hernandez et al. (2012b) Hernandez et al. (2014), Matvienko & Orlov (2015), Scarpa et al. (2017) and Hernandez (2019)). Such theories require a substantial modification of standard GR below a characteristic acceleration threshold a0 ∼ 1.2×10−10 m s−2 (see review by Famaey & McGaugh (2012)). A key advantage of wide binaries is that at separations > 7 kAU, the relative accelerations are below this threshold, so MoND-like theories predict significant deviations from GR; while wide binaries should contain negligible dark matter, so DM theories predict no change from GR/Newtonian gravity. Thus in principle the predictions of DM vs modified gravity in wide binaries are unambiguously different, unlike the case for galaxy-scale systems where the DM distribution is uncertain. 

Wide binaries in general have been studied since the 1980s ((Weinberg et al. 1987; Close et al. 1990)), but until recently the precision of ground-based proper motion measurements was a serious limiting factor: wide binaries could be reliably selected based on similarity of proper motions, see e,g, Yoo et al. (2004), L´epine & Bongiorno (2007), Kouwenhoven et al. (2010), Jiang & Tremaine (2010), Dhital et al. (2013), Coronado et al. (2018). However, the typical proper motion precision ∼ 1 mas yr−1 from ground-based or Hipparcos measurements was usually not good enough to actually measure the internal velocity differences, except for a limited number of nearby systems. 

The launch of the GAIA spacecraft (Gaia Collaboration 2016) in 2014 offers a spectacular improvement in precision; the proper motion precision of order 30 µas yr−1 corresponds to transverse velocity precision 0.0284 km s−1 at distance 200 parsecs, around one order of magnitude below wide-binary orbital velocities, so velocity differences can be measured to good precision over a substantial volume; and this will steadily improve with future GAIA data extending eventually to a 10-year baseline. Recent studies of WBs from GAIA include e.g. El-Badry et al. (2021) and Hernandez et al. (2022). 

In earlier papers in this series, Pittordis & Sutherland (2018) (hereafter PS18) compared simulated WB orbits in MoND versus GR, to investigate prospects for the test in advance of GAIA DR2. This was applied to a sample of candidate WBs selected from GAIA DR2 data by Pittordis & Sutherland (2019) (hereafter PS19), and an expanded sample from GAIA EDR3 by Pittordis & Sutherland (2022) (hereafter PS22). To summarise results, simulations show that (with MoND external field effect included), wide binaries at & 10 kAU show orbital velocities typically 15 to 20 percent faster in MOND than GR, at equal separations and masses. This leads to a substantially larger fraction of “faster” binaries with observed velocity differences between 1.0 to 1.5 times the Newtonian circular-orbit value. In Newtonian gravity, changing the eccentricity distribution changes the shape of the distribution mainly at lower velocities, but has little effect on the distribution at the high end from 1.0 to 1.5 times circular velocity. Therefore, the predicted shift from MOND is distinctly different from changing the eccentricity distribution within Newtonian gravity; so given a large and pure sample of several thousand WBs with precise 2D velocity difference measurements, we could decisively distinguish between GR and MOND predictions. 

The main limitation at present is that PS19 and PS22 showed the presence of a “fat tail” of candidate binaries with velocity differences ∼ 1.5 to 6× the circular-orbit velocity; these systems are too fast to be pure bound binaries in either GR or MOND, and a likely explanation (Clarke 2020) is higher-order multiples e.g. triples where either one star in the observed “binary” is itself an unresolved closer binary, or the third star is at resolvable separation but is too faint to be detected by GAIA; the third star on a closer orbit thus substantially boosts the velocity difference of the two observed stars in the wide “binary”. 

In PS22 we made a simplified model of this triple population, then fitted the full distribution of velocity differences for WB candidates using a mix of binary, triple and flyby populations. These fits found that GR is significantly preferred over MOND if the rather crude PS22 triple model is correct, but we do not know this at present. Allowing much more freedom in the triple modelling is computationally expensive due to many degrees of freedom, and is likely to lead to significant degeneracy between gravity modifications and varying the triple population. Therefore, observationally constraining the triple population, or eliminating most of it by additional observations, is the next key step to make the WB gravity test more secure. 

In this paper we explore prospects for observationally constraining the triple population: we generate simulated triple systems “observed” at random epochs, inclinations and viewing angles, and then test whether the presence of the third star is detectable by any of various methods including direct, speckle or coronagraphic imaging; radial velocity drift; or astrometric non-linear motion in the future GAIA data; we see below that prospects are good, in that 80 to 95% of triple systems in the PS22 sample should be potentially detectable as such by at least one of the methods.

Should Wide Binaries Be Different In Deur's Analysis?

Quoting from the sidebar:

How strong are the gravitational self-interaction? 

This is a function, roughly speaking, of system mass and system size:

Near a proton GM_p/r_p=4×10^-38 with M_p the proton mass and r_p its radius. ==>Self-interaction effects are negligible. . . . 

For a typical galaxy: Magnitude of the gravity field is proportionate to GM/size_system which is approximately equal to 10^-3.

A binary star system has about 10¹¹ times fewer stars than the Milky Way galaxy which can be a proxy for mass.

There are about 62,340 astronomical units (AUs) in a light year. A binary star system is defined as a separation of 7kAU (kilo-astronomical units) or more, which is about 0.11 light years. The Milky Way galaxy is about 87,400 ± 3,590 light years, so the separation of wide binary stars is up to about 10⁶ times smaller than the Milky Way galaxy.

So, the gravitational self-interaction in a minimum distance defined binary star system is about 10^-8 compared to about 10^-3  in a typical galaxy. 

Even allowing for stars ten times a massive as average at this separation and this would be about 10^-7 which would be 10,000 times weaker than in a typical galaxy and the effect would be weaker in binary star systems wider than 7kAU. 

So Deur's approach would not predict a noticeable effect in a binary star system unless its two point geometry similar to that which is dominant in clusters and the observable universe as a whole, as opposed to spiral geometry had that effect. According to this source:

Even if that geometry increased the self-interaction effect by a hundred fold (more than the roughly 40x difference between inferred dark matter proportions in galaxy clusters v. spiral galaxies) and the stars in question had masses ten times those of the average Milky Way galaxy stars, the self-interaction of gravitational fields effect would still be only about one percent of the effect size in galaxies (about 0.1% to 0.15% in the quantity measured in the proposed analysis, which is much less than the measurement errors involved).  

So, unlike MOND which predicts a significant wide binary effect from gravity modification, Deur's approach does not appear to predict significant non-Newtonian behavior from the self-interaction of gravitational fields in wide binary star systems. Deur's model performs better than MOND in the tentative data so far.

The outcome of the study of wide binary stars should be a good way to distinguish between the predictions of MOND and the predictions of Deur's approach.