Wide Binaries and Modified Gravity (STVG/MOG)

I guess the main problem in interpretation of wide binaries data is, that dark matter is contextual - especially in the sense of background buyoancy. That is in dark matter dense fields of large ensemble of bodies the dark matter effects between individual bodies tend to vanish as if no dark matter would be there. Which is also why we don't observe dark matter effects at the scope of planets within solar system, but at the scope of asteroids and more lightweight bodies (i.e. Pioneer spaceprobes) these effects emerge again. Binary stars reside preferably at the center of galaxies (analogously to presence of binaries within Kuiper belt) and this is actually a dark matter effect by itself . But just because the dark matter density is already high there, the dark matter affects mutual path of binaries relatively less there. As a whole these binary stars still revolve center of galaxy with strong dark matter deceleration - they just move accordingly to Newtonian law with respect to each other. See also:

Modified Gravity Strikes Back

The most widely used version of modified gravity is modified Newtonian dynamics, and in that approach the modification kicks in at low acceleration. This means, loosely speaking, it becomes relevant once the average gravitational pull is sufficiently small. The issue with wide binaries is now that the further away the two stars in the binary system are from each other, the lower the acceleration. So they cross over from the range where gravity should be unmodified to where it should be modified. And the data seem to say that there’s no such cross over. For wide binaries you have normal gravity, end of story.

However the Canadian physicist John Moffat before twenty years developed a different model of modified gravity which is not Newtonian so it works together nicely with Einstein’s theories. He just calls it modified gravity, MOG. But the MOG is more difficult than MOND as it introduces two new fields, a scalar and a vector (hence the original STVG name of the MOG theory). The major difference between MOND and MOG is that in MOG the modification does not kick in with acceleration. It kicks in at a particular length and how it kicks in depends on the type of system. In his new paper, John shows that in MOG there just aren’t any changes in wide binaries, no matter how wide, so that negative dark matter effects for wide binaries don't really exclude MOG with compare to MOND/QI theories.