TOI-431/HIP 26013: a super-Earth and a sub-Neptune transiting a bright, early K dwarf, with a third RV planet

We present the bright (V_mag = 9.12), multiplanet system TOI-431, characterized with photometry and radial velocities (RVs). We estimate the stellar rotation period to be 30.5 ± 0.7 d using archival photometry and RVs. Transiting Exoplanet Survey Satellite (TESS) objects of Interest (TOI)-431 b is a super-Earth with a period of 0.49 d, a radius of 1.28 ± 0.04 R_⊕, a mass of 3.07 ± 0.35 M_⊕, and a density of 8.0 ± 1.0 g cm^-3; TOI-431 d is a sub-Neptune with a period of 12.46 d, a radius of 3.29 ± 0.09 R_⊕, a mass of $9.90^{+1.53}_{-1.49}$ M_⊕, and a density of 1.36 ± 0.25 g cm^-3. We find a third planet, TOI-431 c, in the High Accuracy Radial velocity Planet Searcher RV data, but it is not seen to transit in the TESS light curves. It has an Msin i of $2.83^{+0.41}_{-0.34}$ M_⊕, and a period of 4.85 d. TOI-431 d likely has an extended atmosphere and is one of the most well-suited TESS discoveries for atmospheric characterization, while the super-Earth TOI-431 b may be a stripped core. These planets straddle the radius gap, presenting an interesting case-study for atmospheric evolution, and TOI-431 b is a prime TESS discovery for the study of rocky planet phase curves.