Self-lensing flares from black hole binaries IV: the number of detectable shadows

Sub-parsec supermassive black hole (SMBH) binaries are expected to be common in active galactic nuclei (AGN), as a result of the hierarchical build-up 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 AGN red-noise, additional evidence is needed to confirm their binary nature. Recurring self-lensing flares (SLF), 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 VLBI. Here we estimate the number of quasars for which these dips may be detectable by 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.