The face-on galaxy image is credited to Stefan Payne-Wardenaar (https://stefanpw.myportfolio.com/home), whose Twitter and Bluesky bios say, "I make astronomy visualizations in Blender."
> is there some sort of gravitational body in the middle that makes everything orbit in galaxies?
No. The Sun's orbit is determined by the total mass of stars, gas, and dark matter interior to the orbit. This is mostly due to the stars (we're not far enough out from the center for dark matter to be the dominant component) and is on the order of several tens of billions of solar masses.
(There is a supermassive black hole at the center of our galaxy, but its mass is only about 4 million solar masses, so it's negligibly small compared to the mass of all the stars.)
It's kind of amusing that you present "keplerian rotation curves" as a "prediction" of MOND, given that the whole point of MOND is a kludge to produce non-Keplerian rotation curves. That is, by definition MOND cannot produce Keplerian rotation curves. This is why the (small) number of dwarf galaxies (not "elliptical and lenticular galaxies"!) which apparently lack dark matter -- and which do not follow the Tully-Fisher relation-- are serious problems for MOND.
> by definition MOND cannot produce Keplerian rotation curves.
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.
"Keplerian" is a term of art based on the rotation curve in Newtonian gravity when all the mass of a system is concentrated at its center. For the Solar System, the rotation curve outside the radius of the Sun is pretty much pure Keplerian: the velocity decreases proportional to the square root of the radius.
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.)
The "batting average" is a bit higher than that. For example, measurements of the proper motion (motion across the sky) of Sirius led to the prediction in 1844 that it was in an orbit with an (observed) faint or dark companion; the latter (the white dwarf Sirius B) was not directly observed until 1862, when better telescopes were available.
One could also argue that detections of planets from spectroscopic observations of stars is another example. The first observations of transiting exoplanets -- where the planet blocks some of the light of the star -- were actually cases where the existence of the planet had been previously inferred from Doppler shifting of the parent star (e.g., https://en.wikipedia.org/wiki/HD_209458_b).
As another example, the first evidence for dark matter came from observations in the 1930s of the Doppler shifts of galaxies in galaxy clusters, which suggested much more mass in the clusters than could be explained by the masses of the individual galaxies. Some of this "missing mass" was actually observed in the 1960s and 1970s, when orbiting X-ray telescopes showed X-ray emission from very hot, dilute gas within the clusters (unobservable from the ground because the Earth's atmosphere blocks X-rays). It turns out that the hot, X-ray-emitting gas has about five times the mass of the (stars in) the individual galaxies. So some of the missing mass has been found -- though you still need significant, as-yet-undetected extra mass in clusters to explain why they haven't flown apart long ago.
The problem isn't so much the flatness of the rotation curve, but its continued high value: as you go farther and farther out in distance, it should drop rapidly because most of the visible matter is concentrated toward the center of the galaxy, but it doesn't. This implies that there is more matter, less centrally concentrated than the visible matter.
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.
You don't need a simulation; you just need an understanding of Newtonian gravity, basic algebra and a bit of calculus, and some knowledge of stellar masses, velocities, and space densities. This is a standard part of the grad school curriculum (even the advanced undergrad level) in astronomy; here's an example with the math in some lecture notes from an undergrad course at Caltech (by George Djorgovski):
https://sites.astro.caltech.edu/~george/ay20/Ay20-Lec15x.pdf
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.
I appreciate that link, but Dynamic relaxation is a much larger impact on velocity than required to be significant here. It’s still large enough to probably make such interactions meaningless on these timescales but it’s close.
I think "if the training pool is large enough" is a real issue here. We're not talking about living languages with large, properly attested and annotated corpuses.
Indeed, one of the thing you'd probably like the translators to do is identify rare or unique words that can be added to our existing knowledge of these languages.
> I think "if the training pool is large enough" is a real issue here.
It would be really neat to set up something like a wiki populated with the existing translations and machine translations done via LLM, and to periodically re-train the LLM on all the newly manually verified translations and automatically re-run the machine translations after. The whole thing could move incrementally toward high quality output.
"From 1877 to 1882, while undertaking four expeditions on behalf of the British Museum, Rassam made some important discoveries. Numerous finds of significance were transported to the museum, thanks to an agreement made with the Ottoman Sultan by Rassam's old colleague Austen Henry Layard, now Ambassador at Constantinople, allowing Rassam to return and continue their earlier excavations and to 'pack and dispatch to England any antiquities [he] found ... provided, however, there were no duplicates.' A representative of the Sultan was instructed to be present at the dig to examine the objects as they were uncovered."
> there could be empty regions of space in which billions of years more have elapsed than in e.g. a galaxy.
A problem with that idea would be that the ages of galaxies in low-density regions (including voids) tend to be younger than galaxies in denser regions, suggesting that galaxy evolution proceeds more slowly in voids.
> When I was getting my PhD in condensed matter physics I was going to the department colloquium all the time and seeing astrophysics talks about how some people thought the hubble constant was 40 km/s/Mpc and others thought it was 80 km/s/Mpc. With timescape cosmology maybe they were both right.
You're (mis)remembering a different (old) problem and confusing it with a new one. The problem in the 1970s and 1980s was: what is the local expansion rate of the universe? Where "local" mean "within a few hundred megaparsecs". There were two main groups working on the problem: one group tended to find values of around 50 km/s/Mpc and other values of around 100. Gradually they began to converge (in the early 1990s, the low-H0 group getting values of around 60, the high-H0 group values of around 80), until a consensus emerged that it was in the low 70s, which is where we are now.
The "Hubble tension" is a disagreement between what we measure locally (i.e., a value in the low 70s) and what theory (e.g., LCDM) says we should measure locally, if you extrapolate the best-fitting cosmological models -- based on cosmological observations of the CMB, etc. -- down to now (a value in the upper 60s). This has only become a problem very recently, because the error bars on the local measurement and the cosmological predictions are now small enough to suggest (maybe/probably) meaningful disagreement.
> Another longstanding problem in astronomy is that since the 1970s it's been clear we have no idea of how supermassive black holes could have formed in the time we think the universe has existed. With the JWST there are a flood of results that show the first 500 million years of the universe probably lasted a lot more than 500 million years
https://iopscience.iop.org/article/10.3847/2041-8213/ac9b22
That's not a "longstanding" problem, it's a problem from the last 25 years or so. In order for there to be a problem, you have to have what you think are reliable estimates for the age of the universe and evidence for large supermassive black holes very early in the universe. This is something that has emerged only relatively recently.
(Your link, by the way, is to a paper that has nothing to do with black holes.)
