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We present a new method to detect planetary transits from time-seriesphotometry, the Transit Least Squares (TLS) algorithm. TLS searches fortransit-like features while taking the stellar limb darkening and planetaryingress and egress into account. We have optimized TLS for both signaldetection efficiency (SDE) of small planets and computational speed. TLSanalyses the entire, unbinned phase-folded light curve. We compensate for thehigher computational load by (i.) using algorithms like "Mergesort" (for thetrial orbital phases) and by (ii.) restricting the trial transit durations to asmaller range that encompasses all known planets, and using stellar densitypriors where available. A typical K2 light curve, including 80d of observationsat a cadence of 30min, can be searched with TLS in ~10s real time on a standardlaptop computer, as fast as the widely used Box Least Squares (BLS) algorithm.We perform a transit injection-retrieval experiment of Earth-sized planetsaround sun-like stars using synthetic light curves with 110ppm white noise per30min cadence, corresponding to a photometrically quiet KP=12 star observedwith Kepler. We determine the SDE thresholds for both BLS and TLS to reach afalse positive rate of 1% to be SDE~7 in both cases. The resulting truepositive (or recovery) rates are ~93% for TLS and ~76% for BLS, implying morereliable detections with TLS. We also test TLS with the K2 light curve of theTRAPPIST-1 system and find six of seven Earth-sized planets using an iterativesearch for increasingly lower signal detection efficiency, the phase-foldedtransit of the seventh planet being affected by a stellar flare. TLS is morereliable than BLS in finding any kind of transiting planet but it isparticularly suited for the detection of small planets in long time series fromKepler, TESS, and PLATO. We make our Python implementation of TLS publiclyavailable.

Transit Least Squares: Optimized transit detection algorithm to search for periodic transits of small planets