Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars. II. Planetary Systems Observed During Campaigns 1-7

We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. 29 of these worlds were new discoveries that had not previously been published. We calculate the false positive probabilities that the transit-like signals are actually caused by non-planetary astrophysical phenomena and reject five new transit-like events and three previously reported events as false positives. We also statistically validate 17 planets (7 of which were previously unpublished), confirm the earlier validation of 22 planets, and announce 17 newly discovered planet candidates. Revising the properties of the associated planet candidates based on the updated host star characteristics and refitting the transit photometry, we find that our sample contains 21 planets or planet candidates with radii smaller than 1.25 solar radii, 18 super-Earths (1.25-2 solar radii), 21 small Neptunes (2-4 solar radii), three large Neptunes (4-6 solar radii), and eight giant planets (greater than 6 solar radii). Most of these planets are highly irradiated, but EPIC 206209135.04 (K2-72e, 1.29 from plus 0.19 to minus 0.18 solar radii), EPIC 211988320.01 (perihelion radius equals 2.86 from plus 0.16 to minus 0.15 solar radii), and EPIC 212690867.01 (2.20 from plus 0.19 to minus 0.18 solar radii) orbit within optimistic habitable zone boundaries set by the "recent Venus" inner limit and the "early Mars" outer limit. In total, our planet sample includes eight moderately irradiated 1.5-3 solar radii planet candidates (planetary flux greater than or approximately 20 times Earth's flux) orbiting brighter stars (Ks less than 11) that are well-suited for atmospheric investigations with the Hubble, Spitzer, and/or James Webb Space Telescopes. Five validated planets orbit relatively bright stars (Kp less than 12.5) and are expected to yield radial velocity semi-amplitudes of at least 2 meters per second. Accordingly, they are possible targets for radial velocity mass measurement with current facilities or the upcoming generation of red optical and near-infrared high-precision RV (Radial Velocity) spectrographs.