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I have heard that dwarf galaxy masses can be used to determine the mass of a dark matter particle. I have tried looking online for methods cosmologists use (https://cds.cern.ch/record/2702846, De Simeone, Introduction to Cosmology and Dark Matter, 2018), etc, but I am unsure how they do this. In particular, I am considering dark matter that was initially relativistic and later froze out. I did some of the math on my own to find the equilibrium densities as a function of temperature (which I verified with the above source) to get familiar with the mathematics and calculations. Can anyone explain how the math is done to determine a mass for dark matter particles from the dark matter mass of a dwarf galaxy, assuming that the dark matter was produced in a relativistic freeze-out process? For instance suppose the total mass of dark matter in a dwarf galaxy is about 10^{7} solar masses.

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  • $\begingroup$ Maybe this link will help academic.oup.com/mnras/article/321/4/713/997689 $\endgroup$
    – anna v
    Feb 14, 2021 at 18:07
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    $\begingroup$ Could there be a misunderstanding? Dwarf galaxies can be used to place a constraint on the minimum mass of dark matter particles (from the requirement that their Compton wavelength is smaller than said galaxy). I am not aware of any way whatsoever to determine the mass of the dark matter particle though (other through a future signal in a direct or indirect detection experiment) $\endgroup$
    – rfl
    Feb 15, 2021 at 12:54

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First of all we don't get the mass of Dark matter particle from dwarf galaxy mass. Of course you can determine how much dark matter is there in the galaxy but that is it. First let's try to start with what we know about dark matter(DM)-

  1. We know they are there! This in itself is a very strong statement. We have enough evidence of its existence in the Universe. MOND (Modified Newtonian dynamics) is one idea against DM but that simply doesn't explain everything.

  2. Dark matter density in present day Universe is known. Around 24% of energy density is occupied by DM in present day.

Now the fun part is that we don't know if it is made up particles or massive astrophysical objects. A better understanding of the whole mass range of DM can be obtained from the figure below. https://cds.cern.ch/record/2764484/plots

There are various DM candidates depending on their mass. From Standard LambdaCDM model of Cosmology we know that DM has to be cold (non-relativistic), though some fraction of DM can be warm or hot.

Now dwarf galaxy, being dominated by DM, is one of the most ideal places to look for DM decay/annihilation signatures (the amount of stars in dwarfs is very less, so the astrophysical background is negligible). What people try to do generally is to try and constrain properties of DM from known dwarf galaxies. A good place to start understanding this idea is this: Shining Light on Dark Matter

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