Does MOND Underestimate Excess Gravity For Wide Binaries?

Wide binary stars are one of the strongest arguments for modified gravity rather than dark matter as a correct solution to dark matter phenomena.

Simply put, the kind of diffuse dark matter distribution which dark matter propose exists in galaxies would be too slight and would exert too homogeneous a pull to explain systems of two stars at distance of, for example 7000 AU.

Yet, wide binary stars do display the same excessively strong attraction to each other that dark matter theories and various modified gravity theories observe and try to explain in galaxy scale systems. 

But, the plot thickens.

According to Mike McCulloch, MOND underestimates the effect seen, which he argues that his theory, now called quantified inertia but in February 2012 when he made this post called MiHsC, explains better. He explains:

There has been a great observational study done recently by Hernandez et al. (see: http://arxiv.org/abs/1105.1873). They have looked at wide binary stars and found that when they are separated by 7000AU or more, so that their accelerations decrease below 2*10^-10 m/s^2, then their behaviour becomes non-Newtonian, in that their orbital speeds are so large that the centrifugal (inertial) forces separating them should be greater than the gravitational pull inwards from the mass that we can see, so they should zoom off to infinity. A similar behaviour is seen in galaxy rotation curves, which deviate from Newtonian behaviour below this same acceleration. For these simple binary systems, it is hard to see how dark matter (DM) could kick in at a particular acceleration, and Newton and MoND both predict only about 1/10th of the orbital speeds seen. 

This provides a experimentum crucis, and so I have recently been testing MiHsC on these data: because of their low acceleration, MiHsC predicts a decrease in the stars’ inertial masses so they manage to orbit each other at the faster speed without inertia separating them. The orbital speed predicted by MiHsC is still only 1/2 of that seen, but this is much better than the 1/10th from Newtonian dynamics and MoND. I have just today submitted an abstract on this to the UK’s National Astronomy Meeting (NAM 2012).

This would be particularly notable, because somebody else also predicts an enhanced gravitational force that is greater in a two point particle system than in a spiral galaxy system, because it is further from spherical symmetry and uses that observation to explain why "dark matter phenomena" seem to be greater in galactic clusters than in spiral galaxies. That person would be Alexandre Deur who, while noting the result more in passing than rigorously proving it, discussed the applications of his approach to two point systems in a peer reviewed journal article in 2009, two years before Hernandez had published his wide binary star observations in 2011.

Hernandez updated the wide binary study in 2014, and this continued to show non-Newtonian behavior not plausibly explained by dark matter. But, MOND seems to be a bit closer to the mark in the more recent study as noted in a more recent post from McCulloch.