Luminous Fast Blue Optical Transients as "Failed" Gravitational Wave Sources: Helium Core$-$Black Hole Mergers Following Delayed Dynamical Instability

Binaries in which a massive donor star undergoes an extended ($\gtrsim$ kyr) phase of stable mass transfer onto a black hole (BH) accretor offer a promising channel for creating LIGO gravitational wave sources. However, in many systems the mass transfer terminates prematurely in a dynamical instability at orbital periods of a few days, culminating in the BH plunging into the donor and potentially disrupting and accreting its helium core at highly super-Eddington rates. Combining a suite of binary evolution models with analytic estimates and population synthesis, we predict the population of luminous transients from delayed dynamical instability (DDI) and attribute them to the "luminous" class of fast blue optical transients (LFBOTs). The initial plunge of the BH into the partially stripped envelope typically ejects $\sim 10M_{\odot}$ of H/He-enriched material at speeds $\sim 10^{2}-10^{3}$ km s$^{-1}$, generating a compact circumstellar medium (CSM) of radius $\lesssim 1000R_{\odot}$ by the time the BH meets and tidally disrupts the HeC. Rapid BH accretion generates a highly aspherical wind-driven explosion into the environment, powering UV/optical emission via CSM interaction and X-ray reprocessing that rises over a few days to a luminosity $\sim 10^{44}-10^{45}$ erg s$^{-1}$ before fading as the disk spreads outwards and accretion rate drops. Luminous radio/sub-mm emission is generated over several months as the jet collides with the slow quasi-spherical binary outflow, generated by the stable mass transfer preceding DDI, extending to radii $\sim 10^{17}$ cm, in agreement with the inferred CSM environments of LFBOTs. We estimate local rates of DDI merger transients $5-300$ Gpc$^{-3}$ yr$^{-1}$, with a preference for low-metallicities, in agreement with LFBOT demographics. Taken together, our results support LFBOTs as being luminous signposts of "failed" gravitational wave sources.