A new preprint rigorously derives a fairly robust lower bound on the possible mass of dark matter particles, if they exist. The new bound is close to a previous back of napkin estimate based upon the same line of reasoning, but this preprint reaches a slightly higher lower mass bound with more precise data to back it up and more rigorous mathematical analysis.
The most promising dark matter particle theories at this point propose dark matter candidates that hover around this minimum mass.
Folk wisdom dictates that a lower bound on the dark matter particle mass, m, can be obtained by demanding that the de Broglie wavelength in a given galaxy must be smaller than the virial radius of the galaxy, leading to m ≳ 10^−22 eV when applied to typical dwarf galaxies.
This lower limit has never been derived precisely or rigorously. We use stellar kinematical data for the Milky Way satellite galaxy Leo II to self-consistently reconstruct a statistical ensemble of dark matter wavefunctions and corresponding density profiles. By comparison to a data-driven, model-independent reconstruction, and using a variant of the maximum mean discrepancy as a statistical measure, we determine that a self-consistent description of dark matter in the local Universe requires m > 2.2 × 10^−21eV (CL > 95%).
This lower limit is free of any assumptions pertaining to cosmology, microphysics (including spin), or dynamics of dark matter, and only assumes that it is predominantly composed of a single bosonic particle species.
Tim Zimmermann, et al., "Dwarf galaxies imply dark matter is heavier than 2.2 × 10^−21eV" arXiv:2405.20374 (May 30, 2024).
2 comments:
and only assumes that it is predominantly composed of a single bosonic particle species.
there could be many types of dark matter
"there could be many types of dark matter"
There could be.
But, even if there are, how many would be phenomenologically important? Usually, a few of the possibilities dominate observed phenomena.
There are hundreds of kinds of hadrons (i.e. strong force bound composite particles). But, of those, only two fermions (protons and neutrons) have much practical importance, because only they are stable (and neutrons are only stable if bound) and only about four to six light mesons, the ones that carry almost all of the nuclear binding force in atoms have much practical relevance. If you simply assume that atomic nuclei are bound without asking why, you can manage with just two hadrons, only one of which can appear by itself, and that provide a pretty good model for lots of purposes (e.g. all of chemistry).
There are 118 known atomic elements with proton/neutron nuclei with about 3,400 isotopes that have been observed, and a few more atomic elements and many more isotopes of them could be synthesized in the future. But only 92 of those elements have one of the 339 isotopes stable enough to be found in nature, and only 250 of which are truly stable.
Yet out of all of them, 74% of the baryonic matter in the universe is hydrogen and 24% of all matter in the universe is helium. For astronomy purposes, a model with just two atomic elements, with no known substructure, would get you pretty far.
The fact that a toy-model as simple as MOND with just one post-Newtonian/post-GR parameter can explain as wide a range of phenomena from the local scale to the galaxy scale as it does, and can make a big dent of the inferred dark matter budget of clusters as well, suggests that if there is a dark matter particle model, it probably doesn't have much more than about three kinds of particles that would provide three degrees of freedom which account for essentially everything that we can observe with telescopes. You can estimate the number of degrees of freedom in a system without actually knowing what those degrees or freedom are, or the equations that govern them, just by looking at how many independent dimensions of variation appear in the data.
So, even if there are lots of kinds of dark matter, it is unlikely that more than two or three would be necessary for a highly accurate astronomy/cosmology model.
Maybe the dark sector, if there is one, actually has hundreds of particles, but only two or three matter to any meaningful degree for astronomy and cosmology purposes. Given how weak the interactions between the dark sector and ordinary matter are constrained by observations to be (although they must be stronger than gravity alone), the remainder of the dark sector may be as a practical matter unobservable.
And, even if the dark sector has three significant particles, they are probably unequal in importance, so a model based upon the primary one would be close and would allow you to home in on the residual effects attributable to the other two.
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