Ultra-short-period Planets in K2. III. Neighbors are Common with 13 New Multiplanet Systems and 10 Newly Validated Planets in Campaigns 0-8 and 10

Using the EVEREST photometry pipeline, we have identified 74 candidate ultra-short-period planets (USPs; orbital period P < 1 day) in the first half of the K2 data (Campaigns 0-8 and 10). Of these, 33 candidates have not previously been reported. A systematic search for additional transiting planets found 13 new multiplanet systems containing a USP, doubling the number known and representing a third (32%) of USPs in our sample from K2. We also identified 30 companions, which have periods from 1.4 to 31 days (median 5.5 days). A third (36 of 104) of the candidate USPs and companions have been statistically validated or confirmed in this work, 10 for the first time, including 7 USPs. Almost all candidates, and all validated planets, are small (radii R ( p ) <= 3 R (circle plus)) with a median radius of R ( p ) = 1.1 R (circle plus); the validated and confirmed USP candidates have radii between 0.4 R (circle plus) and 2.4 R (circle plus) and periods from P = 0.18 to 0.96 days. The lack of candidate (a) ultra-hot-Jupiter (R ( p ) > 10 R (circle plus)) and (b) short-period-desert (3 <= R ( p ) <= 10 R (circle plus)) planets suggests that both populations are rare, although our survey may have missed some of the very deepest transits. These results also provide strong evidence that we have not reached a lower limit on the distribution of planetary radius values for planets at close proximity to a star and suggest that additional improvements in photometry techniques would yield yet more USPs. The large fraction of USPs in known multiplanet systems supports origins models that involve dynamical interactions with exterior planets coupled to tidal decay of the USP orbits.