Self-lensing binaries in globular clusters -- predictions for ELT

Self-lensing (SL) represents a powerful technique for detecting compact objects in binary systems through gravitational microlensing effects, when a compact companion transits in front of its luminous partner. We present the first comprehensive study of SL probability within globular cluster (GC) environments, utilizing synthetic stellar populations from MOCCA simulations to predict detection rates for the Extremely Large Telescope (ELT). Our analysis incorporates finite-size lens effects for white dwarf (WD) lenses and the specific observational characteristics of the ELT/MICADO instrument. We find that present-day GCs contain 1-50 SL sources with magnifications $\mu_\mathrm{sl} > 1+10^{-8}$, strongly dependent on initial binary fraction, with systems dominated by WD lenses paired with low-mass main-sequence companions. The predicted populations exhibit characteristic bimodal magnitude distributions with peaks at $m \approx 24$ and 32 mag at 10 kpc distance, and typical Einstein ring crossing times of $\tau_\mathrm{eff} \sim 2$ hours. ELT observations should achieve detection efficiency of 0.015-10 sources in $\sim150$ nearby GC after a year of observations depending on distance and survey strategy, with nearby clusters ($D \lesssim 10$ kpc) offering the highest yields. Multi-year monitoring campaigns with daily cadence provide order-of-magnitude improvements over single observations through enhanced photometric precision and increased detection probability. Our results demonstrate that coordinated ELT surveys of Galactic GCs represent a viable approach for probing hidden binary populations and compact object demographics in dense stellar environments, with comprehensive programs potentially yielding up to 10-100 well-characterized SL sources after first 5 years of observations suitable for statistical studies of binary evolution in extreme environments.