A search for self-lensing binaries with TESS and constraints on their occurrence rate

Five self-lensing binaries (SLBs) have been discovered with Kepler light curves. They contain white dwarfs (WDs) in AU-scale orbits that gravitationally lens solar-type companions. Forming SLBs likely requires common envelope evolution when the WD progenitor is an AGB star and has a weakly bound envelope. No SLBs have yet been discovered with data from the Transiting Exoplanet Survey Satellite (TESS), which observes far more stars than Kepler did. Identifying self-lensing in TESS data is made challenging by the fact that TESS only observes most stars for $\sim$25 days at a time, so only a single lensing event will be observed for typical SLBs. TESS's smaller aperture also makes it sensitive only to SLBs a factor of $\sim$100 brighter than those to which Kepler is sensitive. We demonstrate that TESS has nevertheless likely already observed $\sim$4 times more detectable SLBs than Kepler. We describe a search for non-repeating self-lensing signals in TESS light curves and present preliminary candidates for which spectroscopic follow-up is ongoing. We calculate the sensitivity of our search with injection and recovery tests on TESS and Kepler light curves. Based on the 5 SLBs discovered with Kepler light curves, we estimate that $(1.1 \pm 0.6)\%$ of solar-type stars are orbited by WDs with periods of 100-1000 d. This implies a space density of AU-scale WD + main sequence (MS) binaries a factor of 20-100 larger than that of astrometrically-identified WD + MS binaries with orbits in Gaia DR3. We conclude that the Gaia sample is still quite incomplete, mainly because WD + MS binaries can only be unambiguously identified as such for high mass ratios.