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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 &#39;temperate&#39; 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.