Constraining planet occurrence around ultracool dwarfs observed by K2

Abstract

Though we expect many planets around ultracool dwarfs, few have been detected. The K2 mission presents a unique opportunity to search for transiting planets around a large sample of ultracool dwarfs and place constraints on planet occurrence at the bottom of the main sequence. Planet detection using the transit method is dependent not only on geometric transit probability but also the effectiveness of transit-searching methods. In this work, we use K2 observations to measure transit detection efficiency in ultracool dwarfs and use our transit detection efficiency to calculate an upper limit on the planet occurrence rate. We measure our ability to recover various types of transits around dwarfs at the M/L transition. We inject synthetic planetary transits of radii from 0.1 to 3.5 Earth radii and of periods from 0.3 to 26 days into 382 K2 light curves of late-type M and L dwarfs. We attempt to recover them using Box-Least Squares and Levenberg-Marquardt optimization methods. We then calculate a detection efficiency, or fraction recovered, and a threshold of detectability relating to orbital period and radius for each dwarf. We present an upper limit on the planet occurrence rate, as well as constraints on the probability of seeing no planets around a given number of ultracool dwarfs.