Luminous Fast Blue Optical Transients as “Failed” Gravitational-wave Sources: Helium Core–Black Hole Mergers Following Delayed Dynamical Instability

Abstract Binaries in which a massive donor star undergoes an extended (≳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 delayed dynamical instability (DDI), culminating in the BH plunging into the partially stripped donor and potentially disrupting and accreting its helium core (HeC) at super-Eddington rates. Combining binary evolution models with analytic estimates and population synthesis, we predict the population of luminous transients from DDI and attribute them to the “luminous” class of fast blue optical transients (LFBOTs). The initial BH plunge typically ejects ∼10 M ⊙ of H/He-enriched material at ∼10 2 –10 3 km s −1 , generating a compact circumstellar medium (CSM) of ≲1000 R ⊙ before the BH tidally disrupts the HeC. Rapid BH accretion generates a highly aspherical wind-driven explosion into the (already aspherical) environment, powering UV/optical emission via CSM interaction and X-ray reprocessing, peaking after several days at ∼10 44 –10 45 erg s −1 before fading as the disk spreads and the accretion rate drops. If the BH is rapidly spinning, its relativistic jet may power an ultralong gamma-ray transient for on-axis observers. Luminous radio/submillimeter emission arises over months as the jet collides with the slow quasi-spherical outflow generated by the stable mass transfer preceding DDI, extending to ∼10 17 cm, consistent with the remarkable CSM of LFBOTs. We estimate event rates of 5–300 Gpc −3 yr −1 , with a preference for low metallicity (≲0.4 Z ⊙ ), consistent with LFBOT demographics. Taken together, our results support LFBOTs as luminous signposts of “failed” gravitational-wave sources.