We present the detection and follow-up observations of planetary candidates around low-mass stars observed by the K2 mission. Based on light-curve analysis, adaptive-optics imaging, and optical spectroscopy at low and high resolution (including radial velocity measurements), we validate 16 planets around 12 low-mass stars observed during K2 campaigns 5-10. Among the 16 planets, 12 are newly validated, with orbital periods ranging from 0.96-33 days. For one of the planets (K2-151b) we present ground-based transit photometry, allowing us to refine the ephemerides. Combining our K2 M-dwarf planets together with the validated or confirmed planets found previously, we investigate the dependence of planet radius R p on stellar insolation and metallicity [Fe/H]. We confirm that for periods P 2 days, planets with a radius R p 2 R ⊕ are less common than planets with a radius between 1-2 R ⊕ . We also see a hint of the "radius valley" between 1.5 and 2 R ⊕ that has been seen for close-in planets around FGK stars. These features in the radius/period distribution could be attributed to photoevaporation of planetary envelopes by high-energy photons from the host star, as they have for FGK stars. For the M dwarfs, though, the features are not as well defined, and we cannot rule out other explanations such as atmospheric loss from internal planetary heat sources, or truncation of the protoplanetary disk. There also appears to be a relation between planet size and Hirano et al.metallicity: those few planets larger than about 3 R ⊕ are found around the most metal-rich M dwarfs.

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We present observations of two bright M dwarfs (TOI-1634 and TOI-1685: J = 9.5-9.6) hosting ultra-short-period (USP) planets identified by the TESS mission. The two stars are similar in temperature, mass, and radius (T eff ≈ 3500 K, M å ≈ 0.45-0.46 M e , and R å ≈ 0.45-0.46 R e ), and the planets are both super-Earth size (1.25 R ⊕ < R p < 2.0 R ⊕ ). For both systems, light curves from ground-based photometry exhibit planetary transits, whose depths are consistent with those from the TESS photometry. We also refine the transit ephemerides based on the ground-based photometry, finding the orbital periods of P = 0.9893436 ± 0.0000020 days and P = 0.6691416 ± 0.0000019 days for TOI-1634b and TOI-1685b, respectively. Through intensive radial velocity (RV) observations using the InfraRed Doppler (IRD) instrument on the Subaru 8.2 m telescope, we confirm the planetary nature of the TOIs and measure their masses: 10.14 ± 0.95 M ⊕ and 3.43 ± 0.93 M ⊕ for TOI-1634b and TOI-1685b, respectively, when the observed RVs are fitted with a single-planet circular-orbit model. Combining those with the planet radii of R p = 1.749 ± 0.079 R ⊕ (TOI-1634b) and 1.459 ± 0.065 R ⊕ (TOI-1685b), we find that both USP planets have mean densities consistent with an Earth-like internal composition, which is typical for small USP planets. TOI-1634b is currently the most massive USP planet in this category, and it resides near the radius valley, which makes it a benchmark planet in the context of discussing the size limit of rocky planet cores as well as testing the formation scenarios for USP planets. Excess scatter in the RV residuals for TOI-1685 suggests the presence of a possible secondary planet or unknown activity/instrumental noise in the RV data, but further observations are required to check those possibilities.