TFAW survey - I. Wavelet-based denoising of K2 light curves. Discovery and validation of two new Earth-sized planets in K2 campaign 1

The wavelet-based detrending and denoising method TFAW is applied for the first time to EVEREST 2.0-corrected light curves to further improve the photometric precision of almost all K2 observing campaigns (C1-C8, C12-C18). The performance of both methods is evaluated in terms of 6 h combined differential photometric precision (CDPP), simulated transit detection efficiency, and planet characterization in different SNR regimes. On average, TFAW median 6 h CDPP is ${\sim} 30{\rm {per \, cent}}$ better than the one achieved by EVEREST 2.0 for all observing campaigns. Using the TRANSIT LEAST-SQUARES (TLS) algorithm, we show that the transit detection efficiency for simulated Earth-Sun-like systems is ∼8.5× higher for TFAW-corrected light curves than that for EVEREST 2.0 ones. Using the light curves of two confirmed exoplanets, K2-44 b (high SNR) and K2-298 b (low SNR), we show that TFAW yields better Markov chain Monte Carlo posterior distributions, transit parameters compatible with the catalogued ones but with smaller uncertainties, and narrows the credibility intervals. We use the combination of TFAW's improved photometric precision and TLS enhancement of the signal detection efficiency for weak signals to search for new transit candidates in K2 observing campaign 1. We report the discovery of two new K2-C1 Earth-sized planets statistically validated, using the VESPA software: EPIC 201170410.02, with a radius of 1.047 $^{+0.276}_{-0.257}\mathrm{ R}_{\oplus }$ planet orbiting an M-type star, and EPIC 201757695.02, with a radius of 0.908 $^{+0.059}_{-0.064}\mathrm{ R}_{\oplus }$ planet orbiting a K-type star. EPIC 201757695.02 is the 9th smallest planet ever discovered in K2-C1, and the 39th smallest in all K2 campaigns.