In models of minicharged dark matter associated with a hidden $U(1)$ symmetry, astrophysical black holes may acquire a dark charge, in such a way that the inspiral dynamics of binary black holes can be formally described by an Einstein-Maxwell theory. Charges enter the gravitational wave signal predominantly through a dipole term, but their effect is known to effectively first post-Newtonian order in the phase, which enables measuring the size of the charge-to-mass ratios, $|q_i/m_i|$, $i = 1,2$, of the individual black holes in a binary. We set up a Bayesian analysis to discover, or constrain, dark charges on binary black holes. After testing our framework in simulations, we apply it to selected binary black hole signals from the second Gravitational Wave Transient Catalog (GWTC-2), namely those with low masses so that most of the signal-to-noise ratio is in the inspiral regime. We find no evidence for charges on the black holes, and place typical 1-$sigma$ bounds on the charge-to-mass ratios of $|q_i/m_i| lesssim 0.2 - 0.3$.
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