Heat transfer between baryons and millicharged dark matter has been invoked as a possible explanation for the anomalous 21-cm absorption signal seen by EDGES. Prior work has shown that the solution requires that millicharged particles make up only a fraction $(m_chi/{rm MeV}) 0.0115% lesssim f lesssim 0.4%$ of the dark matter and that their mass $m_chi$ and charge $q_chi$ have values $0.1 lesssim (m_chi/{rm MeV})lesssim 10$ and $10^{-6} lesssim (q_chi/e)lesssim 10^{-4}$. Here we show that such particles come into chemical equilibrium before recombination, and so are subject to a constraint on the effective number $N_{rm eff}$ of relativistic degrees of freedom, which we update using Planck 2018 data. We moreover determine the precise relic abundance $f$ that results for a given mass $m_chi$ and charge $q_chi$ and incorporate this abundance into the constraints on the millicharged-dark-matter solution to EDGES. With these two results, the solution is ruled out if the relic abundance is set by freeze-out.
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