Self-lensing binaries as probes of Supernova physics

Self-lensing (SL) in binary systems has the potential to provide a unique observational window into the Galactic population of compact objects. Using the $\mathtt{startrack}$ and COSMIC population synthesis codes, we investigate how different supernova mechanisms affect the observable population of SL systems, with particular attention to the mass gap (2$\mathrm{-}$5 M$_\odot$) in compact object distributions. We test three supernova remnant formation models with different convective growth timescales ($f_{\rm mix}$ = 0.5, 1.0, and 4.0), simulating SL binary systems across the Galactic disk and bulge. We identify distinct groupings of SL sources based on lens mass and Einstein crossing time, clearly differentiating neutron star from black hole systems and close from wide orbits. Notably, the delayed $f_{\rm mix} = 0.5$ model predicts a significantly higher fraction of systems with lens masses in the mass gap region (up to $\sim10$ times more for certain surveys), suggesting that SL observations could help constrain this controversial population. Our analysis reveals a strong preference for systems with low centre-of-mass velocities ($v_{\rm cm}\leq20$ km/s) across all models, resulting primarily from physical processes governing compact object formation and binary survival. While many potential detections will have limited observational coverage, ZTF is predicted to yield several dozen well-covered systems that should enable detailed characterization. When applying simple detection criteria including photometric precision and signal-to-noise requirements, predicted rates decrease by approximately two orders of magnitude, but still yield up to a few tens of expected detections for LSST and ZTF in the Galactic disk population.