A Study of the Shortest-Period Planets Found With Kepler
  We present the results of a survey aimed at discovering and studying transiting planets with orbital periods shorter than one day (ultra--short-period, or USP, planets), using data from the {\em Kepler} spacecraft. We computed Fourier transforms of the photometric time series for all 200,000 target stars, and detected transit signals based on the presence of regularly spaced sharp peaks in the Fourier spectrum. We present a list of 106 USP candidates, of which 18 have not previously been described in the literature. In addition, among the objects we studied, there are 26 USP candidates that had been previously reported in the literature which do not pass our various tests. All 106 of our candidates have passed several standard tests to rule out false positives due to eclipsing stellar systems. A low false positive rate is also implied by the relatively high fraction of candidates for which more than one transiting planet signal was detected. By assuming these multi-transit candidates represent coplanar multi-planet systems, we are able to infer that the USP planets are typically accompanied by other planets with periods in the range 1-50 days, in contrast with hot Jupiters which very rarely have companions in that same period range. Another clear pattern is that almost all USP planets are smaller than 2 $R_\oplus$, possibly because gas giants in very tight orbits would lose their atmospheres by photoevaporation when subject to extremely strong stellar irradiation. Based on our survey statistics, USP planets exist around approximately $(0.51\pm 0.07)\%$ of G-dwarf stars, and $(0.83\pm 0.18)\%$ of K-dwarf stars. 
Roberto Sanchis-Ojeda, Saul Rappaport, Joshua N. Winn, Michael C.   Kotson, Alan M. Levine and Ileyk El Mellah
astro-ph.EP