Optimized transit detection algorithm to search for periodic transits of small planets

<jats:p>We present a new method to detect planetary transits from time-series photometry, the transit least squares (<jats:monospace>TLS</jats:monospace>) algorithm. <jats:monospace>TLS</jats:monospace> searches for transit-like features while taking the stellar limb darkening and planetary ingress and egress into account. We have optimized <jats:monospace>TLS</jats:monospace> for both signal detection efficiency (SDE) of small planets and computational speed. <jats:monospace>TLS</jats:monospace> analyses the entire, unbinned phase-folded light curve. We compensated for the higher computational load by (i.) using algorithms such as “Mergesort” (for the trial orbital phases) and by (ii.) restricting the trial transit durations to a smaller range that encompasses all known planets, and using stellar density priors where available. A typical K2 light curve, including 80 d of observations at a cadence of 30 min, can be searched with <jats:monospace>TLS</jats:monospace> in ∼10 s real time on a standard laptop computer, as fast as the widely used box least squares (<jats:monospace>BLS</jats:monospace>) algorithm. We perform a transit injection-retrieval experiment of Earth-sized planets around sun-like stars using synthetic light curves with 110 ppm white noise per 30 min cadence, corresponding to a photometrically quiet <jats:italic>K</jats:italic><jats:sub>P</jats:sub> = 12 star observed with <jats:italic>Kepler</jats:italic>. We determine the SDE thresholds for both <jats:monospace>BLS</jats:monospace> and <jats:monospace>TLS</jats:monospace> to reach a false positive rate of 1% to be SDE = 7 in both cases. The resulting true positive (or recovery) rates are ∼93% for <jats:monospace>TLS</jats:monospace> and ∼76% for <jats:monospace>BLS</jats:monospace>, implying more reliable detections with <jats:monospace>TLS</jats:monospace>. We also test <jats:monospace>TLS</jats:monospace> with the K2 light curve of the TRAPPIST-1 system and find six of seven Earth-sized planets using an iterative search for increasingly lower signal detection efficiency, the phase-folded transit of the seventh planet being affected by a stellar flare. <jats:monospace>TLS</jats:monospace> is more reliable than <jats:monospace>BLS</jats:monospace> in finding any kind of transiting planet but it is particularly suited for the detection of small planets in long time series from <jats:italic>Kepler</jats:italic>, TESS, and PLATO. We make our <jats:monospace>python</jats:monospace> implementation of <jats:monospace>TLS</jats:monospace> publicly available.</jats:p>