At least three members of the recently identified class of fast luminous blue optical transients show evidence of late-time electromagnetic activity in great excess of what was predicted by an extrapolation of the early time emission. In particular, AT2022tsd displays fast, bright optical fluctuations approximately a month after the initial detection. Here we propose that these transients are produced by exploding stars in black hole binary systems and that the late-time activity is due to the accretion of clumpy ejecta onto the companion black hole. We derive the energetics and timescales involved, compute the emission spectrum, and discuss whether the ensuing emission is diffused or not in the remnant. We find that this model can explain the observed range of behaviors for reasonable ranges of the orbital separation and the ejecta velocity and clumpiness. Close separation and clumpy, high-velocity ejecta result in bright variable emission, as seen in AT2022tsd. A wider separation and smaller ejecta velocity, conversely, give rise to fairly constant emission at a lower luminosity. We suggest that high-cadence, simultaneous, panchromatic monitoring of future transients should be carried out to better understand the origin of the late emission and the role of binarity in the diversity of explosive stellar transients.
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