Searching for GEMS: Characterizing Six Giant Planets around Cool Dwarfs

Transiting giant exoplanets around M-dwarf stars (GEMS) are rare, owing to the low-mass host stars. However, the all-sky coverage of TESS has enabled the detection of an increasingly large number of them to enable statistical surveys like the \textit{Searching for GEMS} survey. As part of this endeavour, we describe the observations of six transiting giant planets, which includes precise mass measurements for two GEMS (K2-419Ab, TOI-6034b) and statistical validation for four systems, which includes validation and mass upper limits for three of them (TOI-5218b, TOI-5616b, TOI-5634Ab), while the fourth one -- TOI-5414b is classified as a `likely planet'. Our observations include radial velocities from the Habitable-zone Planet Finder on the Hobby-Eberly Telescope, and MAROON-X on Gemini-North, along with photometry and high-contrast imaging from multiple ground-based facilities. In addition to TESS photometry, K2-419Ab was also observed and statistically validated as part of the K2 mission in Campaigns 5 and 18, which provides precise orbital and planetary constraints despite the faint host star and long orbital period of $\sim 20.4$ days. With an equilibrium temperature of only 380 K, K2-419Ab is one of the coolest known well-characterized transiting planets. TOI-6034 has a late F-type companion about 40\arcsec~away, making it the first GEMS host star to have an earlier main-sequence binary companion. These confirmations add to the existing small sample of confirmed transiting GEMS.