| Summary: | We report the discovery in K2's Campaign 10 of a transiting terrestrial planet in an ultra-short-period orbit around an M3-dwarf. K2-137 b completes an orbit in only 4.3 h, the second shortest orbital period of any known planet, just 4 min longer than that of KOI 1843.03, which also orbits an M-dwarf. Using a combination of archival images, adaptive optics imaging, radial velocity measurements, and light-curve modelling, we show that no plausible eclipsing binary scenario can explain the K2 light curve, and thus confirm the planetary nature of the system. The planet, whose radius we determine to be 0.89 ± 0.09 R⊕, and which must have an iron mass fraction greater than 0.45, orbits a star of mass 0.463 ± 0.052 M⊙ and radius 0.442 ± 0.044 R⊙. © 2017 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2017 November 3. Received 2017 November 2; in original form 2017 July 14. Published: 08 November 2017. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. We greatly thank the NOT staff members for their precious support during the observations. Based on observations obtained with the NOT, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de AstrofÃsica de Canarias. The data presented here were obtained in part with ALFOSC, which is provided by the Instituto de AstrofÃsica de Andalucia under a joint agreement with the University of Copenhagen and NOTSA. DG gratefully acknowledges the ...
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