Alleviating the transit timing variation bias in transit surveys II. RIVERS: Twin resonant Earth-sized planets around Kepler-1972 recovered from a Kepler false positive

Transit timing variations (TTVs) can provide useful information for systems observed in this way, putting constraints on the masses and eccentricities of the observed planets, and in some cases even revealing the existence of non-transiting companions. However, TTVs can also prevent the detection of small planets in transit surveys, or bias the recovered planetary and transit parameters. Here we show that Kepler-1972 c, initially the 'not transit-like' false positive KOI-3184.02, is an Earth-sized planet whose orbit is perturbed by Kepler-1972 b (initially KOI-3184.01). The pair is locked in a 3:2 mean-motion resonance, each planet displaying TTVs of more than 6h of amplitude over the duration of the Kepler mission. The two planets have similar masses m(b)/m(c) = 0.956(-0.051)(+0.056) and radii R-b = 0.802(-0.041)(+0.042) R-Earth, R-c= 0.868(-0.050)(+0.051)R(Earth), and the whole system, including the inner candidate KOI-3184.03, appears to be coplanar. Despite the faintness of the signals (signal-to-noise ratio (S/N) of 1.35 for each transit of Kepler-1972 b and 1.10 for Kepler-1972 c), we recovered the transits of the planets using the RIVERS method, which is based on recognition of the tracks of planets in river diagrams using machine learning, and a photo-dynamic fit of the light curve. Recovering the correct ephemerides of the planets is essential to obtaining a complete picture of the observed planetary systems. In particular, we show that in Kepler-1972, not taking into account planet-planet interactions yields an error of similar to 30% on the radii of planets b and c, in addition to generating in-transit scatter, which is why KOI3184.02 was mistaken for a false positive. Alleviating this bias is essential for an unbiased view of Kepler systems, some of the TESS stars, and the upcoming PLATO mission.