Searching for GEMS The Occurrence of Giant Planets Orbiting M Dwarfs within 100 pc

We present results from a systematic search for transiting short-period giant exoplanets around M dwarf stars (GEMS; P < 10 days, R_p ≳ 8R_⊕) within a distance-limited 100 pc sample of 149,316 M dwarfs using TESS-Gaia Light Curve (or TGLC) data. We describe the development and application of the TESS-miner package and associated vetting procedures used in this analysis. To assess detection completeness, we conducted ∼72 million injection-recovery tests across ∼26,000 stars with an average of ∼3 sectors of data per star, subdivided into early-type (M0–M2.5), mid-type (M2.5–M4), and late-type (M4 or later) M dwarfs. Our pipeline demonstrates high sensitivity across all subtypes within the injection bounds. We estimate the occurrence rates of short-period GEMS as a function of stellar mass, and combine our measured rates with those derived for FGK stars, fitting an exponential trend with stellar mass, consistent with core-accretion theory predictions. We find GEMS occurrence rates of 0.118% ± 0.068% for early-type M dwarfs, 0.153% ± 0.069% for mid-type M dwarfs, and 0.036% ± 0.024% for late-type M dwarfs, with a mean rate of 0.068% ± 0.024% across the full sample. While our search spanned 1.0 day < P < 10.0 days, these rates were calculated using planets orbiting with 1.0 day < P < 5.0 days. This work establishes the basis for future occurrence-rate studies of transiting GEMS.