Searching for GEMS: TOI-5916 b & TOI-6158 b are two Saturn-density planets orbiting M2 dwarfs

We confirm the planetary nature of (1) TOI-5916 b and (2) TOI-6158 b, two Exoplanets Transiting M-dwarf Stars (GEMS), both discovered by the Transiting Exoplanet Survey Satellite (TESS). Both systems were confirmed with ground-based photometry (Red Buttes Observatory and Swope, respectively) and radial velocity data from the Habitable-zone Planet Finder. Their radii are R₁ = 11.8 (+0.52 / −0.51) R⊕ and R₂ = 10.4 (+2.70 / −1.11) R⊕, and masses are M₁ = 219 ± 28 M⊕ and M₂ = 135 (+19 / −18) M⊕. Both planets have Saturn-like densities (ρ₁ = 0.73 (+0.14 / −0.13) g cm⁻³, ρ₂ = 0.66 (+0.41 / −0.23) g cm⁻³), which appears to be a growing trend among GEMS systems and, more generally, warm Jupiters. In confirming both of these exoplanets, we add to the growing evidence for a population of Saturn-density planets among the GEMS systems. We also find evidence for a preliminary trend in which GEMS exhibit systematically closer orbits compared to FGK giants.