We study the general properties of the freeze-out of a thermal relic. We give analytic estimates of the relic abundance for an arbitrary freeze-out process, showing when instantaneous freeze-out is appropriate and how it can be corrected when freeze-out is slow. This is used to generalize the relationship between the dark matter mass and coupling that matches the observed abundance. The result encompasses well-studied particular examples, such as weakly interacting massive particles (WIMPs), strongly interacting massive particles, coannihilation, coscattering, inverse decays, and forbidden channels, and generalizes beyond them. In turn, this gives an approximate perturbative unitarity bound on the dark matter mass for an arbitrary thermal freeze-out process. We show that going beyond the maximal masses allowed for freeze-out via dark matter self-annihilations [WIMP-like, mDM≫O(100 TeV)] predicts that there are nearly degenerate states with the dark matter and that the dark matter is generically metastable.
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