TOI-3984 A b and TOI-5293 A b: Two Temperate Gas Giants Transiting Mid-M Dwarfs in Wide Binary Systems

We confirm the planetary nature of two gas giants discovered by TESS to transit M dwarfs with stellar companions at wide separations. TOI-3984 A (J = 11.93) is an M4 dwarf hosting a short-period (4.353326 ± 0.000005 days) gas giant (M _p = 0.14 ± 0.03 M _J and R _p = 0.71 ± 0.02 R _J) with a wide-separation white dwarf companion. TOI-5293 A (J = 12.47) is an M3 dwarf hosting a short-period (2.930289 ± 0.000004 days) gas giant (M _p = 0.54 ± 0.07 M _J and R _p = 1.06 ± 0.04 R _J) with a wide-separation M dwarf companion. We characterize both systems using a combination of ground- and space-based photometry, speckle imaging, and high-precision radial velocities from the Habitable-zone Planet Finder and NEID spectrographs. TOI-3984 A b (T _eq = 563 ± 15 K and $\mathrm{TSM}={138}_{-27}^{+29}$ ) and TOI-5293 A b ( ${T}_{\mathrm{eq}}={675}_{-30}^{+42}$ K and TSM = 92 ± 14) are two of the coolest gas giants among the population of hot Jupiter-sized gas planets orbiting M dwarfs and are favorable targets for atmospheric characterization of temperate gas giants and 3D obliquity measurements to probe system architecture and migration scenarios.