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This is: Dark Matters, published by Diffractor on the LessWrong.
This post will be about the main points of evidence for the existence of dark matter. To evaluate whether a competing theory to dark matter is plausible, it's important to know what the actual arguments in favor of dark matter are in more detail than just "dark matter is the stuff you have to add to get galactic rotation curves to work out". A competitor has to address the strongest arguments in favor of the existence of dark matter, not just the weaker fare like galactic rotation curves.
So, when reading some hot new arxiv paper about dark matter or the lack thereof, it is fairly useful to know the top five lines of evidential support for dark matter (in my own personal estimation, others may differ). This lets you at least check whether the result is directly addressing the major cruxes that the case for dark matter rests upon, or just picking off one particular piece of evidence and sweeping the rest under the rug, even if you lack the full technical ability to evaluate the claimed result.
This post will be saving the best for last, so if you're not going to read the whole thing, skip down to sections 4 and 5.
Also, what exactly is meant when the term "dark matter" is used in this post? Anything with mass (so it's affected by gravity and gravitationally influences other things) which does not interact via the electromagnetic force. Electrons, protons, nuclei, and atoms emphatically do not count. Black holes, neutrinos, WIMPS (weakly interacting massive particles), and axions would count under this definition. The last two are theoretical, the first two are very much established. Of course, it would be a massive cop-out to go "neutrinos exist, therefore dark matter does", so "dark matter" will be used with a followup connotation of "and whatever the heck is (we don't know yet), there must be 5x more of it in the universe than matter made of atoms or atom parts, no way around that whatsoever"
Point 1: Galactic Rotation Curves
The story begins with galaxy rotation curves, which were the original motivation for postulating dark matter in the first place. Given a point gravitational mass, it's pretty simple to calculate the velocity of something orbiting around it, depending only on how far away the object is orbiting and how much mass is in the central point. Stuff orbiting further out from a point mass will be orbiting at a lower velocity.
With a bit more work, given a disc of mass, you can calculate the velocity of something orbiting around or within it. For this, the graph of orbital velocity vs distance from the center of the disc first rises, then falls. Orbital velocities are low in the center because stuff orbiting near the center of the disc isn't orbiting around very much mass, and orbital velocities are low at the outside of the disc, because you get closer to being able to approximate things by the situation "your distant object is orbiting around a central point mass", which, as previously discussed, already exhibits the "stars on further-out orbits move more slowly" behavior.
Computing this in practice requires knowledge of two things, however. First, you need to know how fast the stars in the galaxy are orbiting around the center. Second, you need to know the radial distribution of mass in the disc or ellipse.
It's pretty easy to tell how fast stars in a galaxy are orbiting around the center, for suitably chosen galaxies. Stars have emission and absorption lines at very specific frequencies measured to very high accuracy, which only depend on details of atomic physics that don't change in different galaxies. So, as an example, you could pick an edge-on spiral galaxy, and look at the position of the absorption lines in the center of the galaxy. Then, you can look at the two edges of the galaxy, and i...
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