From there, a good question is "How do we model it?". And sqrt(GM/R^2 * cH/(2pi)) works really well.
By the way, cH/(2pi) = c^2 / (2pi * 13.8 bly), which looks like centripetal acceleration.
I'm also struggling to find what MOND has to say about all the astrophysics observed that LCDM people try to model to get their Tully-Fisher to work. If MOND is true, why would all these astrophysical feedback effects (such as supernovae) not matter for Tully-Fisher?
- galaxy clusters
- lensing
- Bullet Cluster, El Gordo
all have answers in the work of modified gravity (MOND) cosmologists. Stacy McGaugh does a really good job going through each one.
The essential thing, and I mean really essential, is that modified gravity (MOND) uses fewer free parameters than cold dark matter (CDM), by a long shot.
[1] https://twitter.com/dudedarkmatter/status/109452639162072268... [2] https://twitter.com/DudeDarkmatter/status/109452792999493222...
certainly, these are still open questions in cosmology
Meanwhile it's good to restate the obvious.
Modified gravity (MOND), where acceleration at galactic scales isn't just GM/R^2 but modeled as sqrt(GM/R^2 * cH/(2pi)), works for 100s of galaxies, and is more precise than cold dark matter (CDM).
Modified gravity only has one free parameter. cH/(2pi) = c^2 / 87 bly.
Perhaps the "dark matter" of a galaxy is the rest of the galaxies of the universe.
The only MOND formulations that actually work are ones that simply reduce cold dark matter from 80% of the universe to 30% of the universe. MOND has all -- literally all, as in 100% of them -- the free parameters of lCDM plus the parameters for MOND.
I like MOND. It's elegant. It's intuitive. It's simple. You get to put your name at the end of the sequence Aristotle, Copernicus, Kepler, Newton, Einstein. When I first started reading about dark matter in the '90s I thought MOND was the obvious solution. (MACHO was still a leading theory at the time, they were still analyzing the data from the microlensing surveys) lCDM is messy and existentially unsatisfying. We don't know what what it is, and if it has the properties we think it has, we could not conceivably ever know what it is. But regardless of the fact that MOND is nicer than lCDM, lCDM explains all of our observations, but MOND only explains some of them, and depending on which formulation of MOND you subscribe to, is falsified by the the bullet cluster, or by galaxies whose rotation curves show a lack of dark matter, or by the LIGO/VIRGO observations that show gravity moves at the speed of light.
MOND reminds me of the meme of Homer Simpson where he's standing there looking fairly fit and then the camera turns around him and he's just got all his fat and loose skin pinned and tied up on his back. It looks great on the face of it but once you really, really start digging into the details it doesn't work anymore. lCDM wears all of its warts on its face.
What kinds of relativistic effects have been postulated for explaining our observations?
Something about dark matter which always struck me was that I have not seen explanations which incorporate the very limited perspective we have on galaxies -- being singular beings on a tiny rock very far away -- and how the light follows geodesics which may be significantly different from straight lines in the non-relativistic view. If these galaxies are large enough to lens light from elsewhere, doesn't it follow that this should be happening in places of high mass/energy density like the interior of galaxies, too? In other words, are the edges of the galaxies really where we think they are?
Is there any "whirlpool" effect that gravitational waves may have that would sweep or twist these geodesics as the galaxy rotates?