Two temperate Earth- and Neptune-sized planets orbiting fully convective M dwarfs

As the diversity of exoplanets continues to grow, it is important to revisit assumptions about habitability and classical HZ definitions. In this work, we introduce an expanded 'temperate' zone, defined by instellation fluxes between $0.1<S/\mathrm{S}_\oplus<5$, thus encompassing a broader range of potentially habitable worlds. We also introduce the TEMPOS survey, which aims to produce a catalogue of precise radii for temperate planets orbiting M dwarfs with $T_\mathrm{eff}\leq3400\,$ K. This work reports the discovery and characterisation of two planets in this temperate regime orbiting mid-type M dwarfs: TOI-6716\,b, a $0.98\pm0.07\,\mathrm{R}_\oplus$ planet orbiting its M4 host star ($R_\star=0.231\,\pm0.015\mathrm{R}_\odot$, $M_\star=0.223\pm0.011\,\mathrm{M}_\odot$, $T_\mathrm{eff}=3110\pm80\,\mathrm{K}$) with a period $P=4.7185898^{+0.0000054}_{-0.0000041}\,\mathrm{d}$, and TOI-7384 b, a $3.56\pm0.21\,\mathrm{R}_\oplus$ planet orbiting an M4 ($R_\star=0.319\,\pm0.018\mathrm{R}_\odot$, $M_\star=0.318\pm0.016\,\mathrm{M}_\odot$, $T_\mathrm{eff}=3185\pm75\,\mathrm{K}$) star every $P=6.2340258^{+0.0000034}_{-0.0000036}\,\mathrm{d}$. The radii of TOI-6716 b and TOI-7384 b have precisions of $6.8\%$ and $5.9\%$ respectively. We validate these planets with multi-band ground-based photometric observations, high-resolution imaging and statistical analyses. We find these planets to have instellation fluxes close to the inner (hotter) edge of the temperate zone, with $4.4\pm1.1\,\mathrm{S}_\oplus$ and $4.9\pm1.1\,\mathrm{S}_\oplus$ for TOI-6716 b and TOI-7384 b respectively. Also, with a predicted TSM similar to the TRAPPIST-1 planets, TOI-6716 b is likely to be a good rocky-world JWST target, should it have retained its atmosphere.