One question I’ve had for a while but didn’t seem worth the look is if there any consideration for local gravitational interaction between stars exchanging momentum between them and thus flattening the rotation curve.
I’m assuming that’s one of the first things looked at but couldn’t find a paper on the subject. Remember any references on the topic?
Note that most "rotation curves" are actually measured from gas, not stars, and also that strong gravitational interactions between individual stars are extremely rare except in very dense star clusters and galactic nuclei, due to the increasingly large distances between stars as you go out from galactic centers. The time required for individual stellar interactions in the main or outer parts of galaxies to significantly affect their motions is much larger than the age of the universe (see, e.g., https://en.wikipedia.org/wiki/Stellar_dynamics).
Finally, this wouldn't address other evidence for dark matter, like the halos of hot (millions or tens of millions of K) intergalactic gas in galaxy clusters. The pressure of the gas should have driven the gas to expand way billions of years ago, if you assume that only the gravity of the individual galaxies and the gas itself is restraining it.
> strong gravitational interactions between individual stars are extremely rare except in very dense star clusters
We’re talking 225 million years for the sun to orbit the galaxy, rare events become commonplace on those timescales. Anyway, I’m sure someone has actually done this kind of simulation I’m just curious about what the result is and how they did it.
The mean time for the orbit of a star to be significantly randomized by weak, intermediate-distance interactions (e.g., the kind the Sun is experiencing now from neighboring stars) is the relaxation time, and for a star like the Sun it's of order several trillion years.
The mean time between strong gravitational interactions, where the gravity of a single nearby star significantly changes the orbit of a star (perhaps more like what you were imagining), is of order one quadrillion (10^15) years.
(Note that the numbers are for the density of the stars at the Sun's orbit; further out, where you start to get to the point where dark-matter effects really show up, the density is lower, and so these times would be even longer.)
Those are examples of "extremely rare" even on timescales of the age of the universe.
- keplerian rotation curves ("no dark matter") in elliptical and lenticular galaxies
- EFE (a group tried to find evidence against EFE and found it instead)
- early galaxies in the universe
- renzo's rule
- keplerian descent in the milky way (due to the effects of the magellanic clouds)
There's also explaining the tully-fisher relation, which is a post-hoc rationalization, so not really a prediction, but the model wasn't fine tuned to obtain the exact numerical solution.
Some of the "there's no DM" or "there's almost entirely DM" diffuse galaxies are likely due to measurement error in the distance to the diffuse galaxy, for example.
Cheers all. I think it’s interesting how many of us are seriously interested laymen on this topic. I think it’s fun and fascinating.
thats a common misunderstanding of MOND and means you did not stop to understand the definition. look at the formula carefully; in high gravitational regimes it looks newtonian (obviously, e.g. solar system). MOND, by definition predicts keplerian curves when the galaxies are rotating quickly (high gravitation). You will find that ellpitical and lenticular galaxies are almost always rotating fast. it also can through EFE but i dont fully understand the math enough to explain that.
For galaxies, which are extended objects, the rotation curve is not Keplerian when you are well inside the galaxy: it first rises to larger radii, then levels off. But since the baryonic matter (stars, gas, dust) in galaxy is rather centrally concentrated, the rotation curve should start looking more and more Keplerian as you get further and further into the outskirts and outside the galaxy.
But that is not what we see. Instead, we see the rotation curves staying roughly constant with radius ("flat"); we call this "non-Keplerian". This is true for almost all galaxies, including ellipticals and lenticulars (this is a recent study of three lenticular galaxies: https://www.aanda.org/articles/aa/full_html/2020/09/aa38184-.... Note the rotation curves in the bottom panels of Figure 3: they do not at any point start decaying, let alone decaying as fast as R^(-1/2).)
Figure 5 of that paper (https://www.aanda.org/articles/aa/full_html/2020/09/aa38184-...) shows the observed rotation curves; it also shows the predicted curves if just the stars and standard Newtonian gravity were operating, with the dotted red lines. Note how these lines first rise to a local peak at small radii, and then decline to larger radii: this is a (quasi-)Keplerian decline. It fails to match the actual rotation curve at large radii.
The conventional response is to postulate some additional form of matter, distributed in a much more extended fashion than the baryonic matter (this produces the dashed black lines in Figure 5 of that paper). The MOND response is to modify gravity (or: to modify the acceleration due to gravity) such that it doesn't show anything like a Keplerian falloff at large radii, even at radii where the gravitating matter (assumed to be just the visible baryonic matter) is well inside.
In the case of the Solar System, the Keplerian decline starts right outside the Sun, where the acceleration is strong enough to be above the MOND threshold. But if you went far enough out and could measure the circular orbital speed, MOND would start to deviate from Keplerian. In the case of galaxies, the outer radii where the rotation curves appear "flat" are where the acceleration due to gravity is low enough for MOND to matter, and so the predicted MOND curves will not be Keplerian.
(I should perhaps point out that I'm a professional astronomer whose been studying galaxies, including lenticulars and ellipticals, for almost 30 years, so attempts to mansplain my field to me won't really impress me.)