Self-lensing flares from black hole binaries. IV. The number of detectable shadows

Subparsec supermassive black hole (SMBH) binaries are expected to be common in active galactic nuclei as a result of the hierarchical buildup of galaxies via mergers. While direct evidence for these compact binaries is lacking, a few hundred candidates have been identified, most based on the apparent periodicities of their optical light curves. Since these signatures can be mimicked by active galactic nuclei red noise, additional evidence is needed to confirm their binary nature. Recurring self-lensing flares, occurring whenever the two BHs are aligned with the line of sight within their Einstein radii, have been suggested as additional binary signatures. Furthermore, in many cases, lensing flares are also predicted to contain a ``dip,'' whenever the lensed SMBH's shadow is comparable in angular size to the binary's Einstein radius. This feature would unambiguously confirm binaries and additionally identify SMBH shadows that are spatially unresolvable by high-resolution Very Long Baseline Interferometry (VLBI). Here we estimate the number of quasars for which these dips may be detectable by Legacy Survey of Space and Time (LSST) by extrapolating the quasar luminosity function to faint magnitudes and assuming that SMBH binaries are randomly oriented and have mass ratios following those in the Illustris simulations. Under plausible assumptions about quasar lifetimes, binary fractions, and Eddington ratios, we expect tens of thousands of detectable flares, of which several dozen contain measurable dips.