TESS discovery of two super-Earths orbiting the M-dwarf stars TOI-6002 and TOI-5713 near the radius valley

We present the validation of two TESS super-Earth candidates transiting the mid-M dwarfs TOI-6002 and TOI-5713 every 10.90 and 10.44 days, respectively. The first star (TOI-6002) is located $32.038\pm0.019$ pc away, with a radius of $0.2409^{+0.0066}_{-0.0065}$ \rsun, a mass of $0.2105^{+0.0049}_{-0.0048}$ \msun, and an effective temperature of $3229^{+77}_{-57}$ K. The second star (TOI-5713) is located $40.946\pm0.032$ pc away, with a radius of $0.2985^{+0.0073}_{-0.0072}$ \rsun, a mass of $0.2653\pm0.0061$ \msun, and an effective temperature of $3225^{+41}_{-40}$ K. We validated the planets using TESS data, ground-based multi-wavelength photometry from many ground-based facilities, as well as high-resolution AO observations from Keck/NIRC2. TOI-6002 b has a radius of $1.65^{+0.22}_{-0.19}$ \re\ and receives $1.77^{+0.16}_{-0.11} S_\oplus$. TOI-5713 b has a radius of $1.77_{-0.11}^{+0.13} \re$ and receives $2.42\pm{0.11} S_\oplus$. Both planets are located near the radius valley and near the inner edge of the habitable zone of their host stars, which makes them intriguing targets for future studies to understand the formation and evolution of small planets around M-dwarf stars.