Transit least-squares survey. I. Discovery and validation of an Earth-sized planet in the four-planet system K2-32 near the 1:2:5:7 resonance

We apply for the first time the transit least-squares (TLS) algorithm to search for new transiting exoplanets. TLS has been developed as a successor to the box least-squares (BLS) algorithm, which has served as a standard tool for the detection of periodic transits. In this proof-of-concept paper, we demonstrate that TLS finds small planets that have previously been missed. We show the capabilities of TLS using the K2 EVEREST-detrended light curve of the star K2-32 (EPIC 205071984), which has been known to have three transiting planets. TLS detects these known Neptune-sized planets K2-32 b, d, and c in an iterative search and finds an additional transit signal with a high signal detection efficiency (SDE_TLS) of 26.1 at a period of 4.34882_-0.00075^+0.00069 d. We show that this additional signal remains detectable (SDE_TLS = 13.2) with TLS in the K2SFF light curve of K2-32, which includes a less optimal detrending of the systematic trends. The signal is below common detection thresholds if searched with BLS in the K2SFF light curve (SDE_BLS = 8.9), however, as in previous searches. Markov chain Monte Carlo sampling with the emcee software shows that the radius of this candidate is 1.01_-0.09^+0.10 R_⊕. We analyzed its phase-folded transit light curve using the vespa software and calculated a false-positive probability FPP = 3.1 × 10^-3. Taking into account the multiplicity boost of the system, we estimate an FPP < 3.1 × 10^-4, which formally validates K2-32 e as a planet. K2-32 now hosts at least four planets that are very close to a 1:2:5:7 mean motion resonance chain. The offset of the orbital periods of K2-32 e and b from a 1:2 mean motion resonance agrees very well with the sample of transiting multiplanet systems from Kepler, lending further credence to the planetary nature of K2-32 e. We expect that TLS can find many more transits of Earth-sized and even smaller planets in the Kepler and K2 data that have so far remained undetected with algorithms that search for box-like signals.