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If dark matter were to be partly composed of fermions (such as hypothetical neutralinos), then could these particles be subject to degeneracy pressure if they were trapped in the potential well of a galaxy?

If so, would that make them even harder to interact with, because of a lack of available energy levels for them to move into?

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  • $\begingroup$ The mass would then have to be about 16 eV to match the known local DM density of 0.3 GeV/cm^3. The question is then how such extremely light DM particles could end up collapsing in such dense states. $\endgroup$ – Count Iblis May 6 '15 at 20:43
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This is an interesting suggestion, and I don't claim to know much about neutralinos, but to be degenerate they would need to have a temperature $$ T \ll \frac{p_F^{2}}{2mk_{B}}, $$ where $p_{F}$ is the Fermi momentum and $m$ is the neutralino mass, thought to be in the range 100 GeV/$c^2$ - 1 TeV/$c^2$.

The present mass density of dark matter in the solar neighbourhood is thought to be of order 0.4 GeV/cm$^3$ (maybe an absolute maximum of 400 GeV/cm$^{3}$ nearer the centre?), so if this were made of say 400 GeV neutralinos, their number density would be of order just $n=10^3$ m$^{-3}$ ($10^{6}$ m$^{-3}$).

The Fermi momentum $p_{F} = (3n/8\pi)^{1/3} h \simeq 3\times 10^{-33}$ ($3 \times 10^{-32}$) kg m/s, which leads to a requirement on the temperature of $T \ll 10^{-18}$ ($10^{-16}$ K) if they were to be considered a degenerate gas.

Are such low temperatures realistic? It sounds a bit cold to me. I know that there are strong claims in the literature that dark matter needs to be at least warm(ish) - of order 10,000 K - to account for the non-cuspiness of dark matter profiles in dwarf spheroidal galaxies (e.g. Gilmore et al. 2007).

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