Orbital decay candidates reconsidered: WASP-4 b is not decaying and Kepler-1658 b is not a planet

Abstract: The fate of hot Jupiters is thought to be engulfment by their host stars, the outcome of tidal orbital decay. Transit timing has revealed a few systems with apparently shrinking orbital periods, but such signals can be mimicked by light travel-time effects (LTTE) of a distant companion. Combining transit timings with precise radial-velocity data, including new data, we reassessed three reported cases of orbital decay: WASP-4, WASP-12, and Kepler-1658. For WASP-4, the period change is best explained by LTTE due to a 10-Jupiter-mass companion at 4 AU, with no need to invoke orbital decay. For WASP-12, in contrast, the data firmly exclude LTTE and confirm genuine orbital decay. For Kepler-1658, spectroscopic and photometric anomalies reveal the "planet" to be an eclipsing K/M binary bound to the F-type primary, with LTTE explaining the observed period change. Thus, among the known hot Jupiters, only WASP-12 b currently shows compelling evidence for orbital decay.