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 ($4.353326\pm 0.000005$ days) gas giant ($M_p=0.14\pm 0.03{\mathrm{M}}_{\mathrm{J}}$ and $R_p=0.71\pm 0.02{\mathrm{R}}_{\mathrm{J}}$) with a wide separation white dwarf companion. TOI-5293 A ($J=12.47$) is an M3 dwarf hosting a short-period ($2.930289\pm 0.000004$ days) gas giant ($M_p=0.54\pm 0.07{\mathrm{M}}_{\mathrm{J}}$ and $R_p=1.06\pm 0.04{\mathrm{R}}_{\mathrm{J}}$) with a wide separation M dwarf companion. We characterize both systems using a combination of ground-based and space-based photometry, speckle imaging, and high-precision radial velocities from the Habitable-zone Planet Finder and NEID spectrographs. TOI-3984 A b ($T_{eq}=563\pm 15$ K and $\mathrm{T}\mathrm{S}\mathrm{M}=138_{-27}^{+29}$) and TOI-5293 A b ($T_{eq}=675_{-30}^{+42}$ K and $\mathrm{T}\mathrm{S}\mathrm{M}=92\pm 14$) 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 three-dimensional obliquity measurements to probe system architecture and migration scenarios.