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

TL;DR

The paper tackles the problem of distinguishing true tidal orbital decay of hot Jupiters from LTTE induced by distant companions. It introduces a joint transit-timing and radial-velocity framework, including a Taylor-expanded LTTE term for long-period companions, and applies it to WASP-4 b, WASP-12 b, and Kepler-1658 b. The main findings are that WASP-4 b's timing variations arise from LTTE due to a ~7 $M_{\mathrm{Jup}}$ companion at ~8 AU, WASP-12 b shows genuine orbital decay, and Kepler-1658 is not a planet but an eclipsing binary bound to the primary, with LTTE explaining its timing changes. Consequently, among known hot Jupiters, only WASP-12 b currently shows compelling evidence for orbital decay; the study underscores the necessity of joint timing+RV analyses to correctly attribute observed period changes.

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. By 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 an ~7 Jupiter-mass companion at ~8 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.

Figures (1)

• Figure 1: WASP-4.Upper left.---Radial velocities, Radial velocities, after shifting the data from each spectrograph to have zero mean. Lower left.---Deviations between transit times and the best-fit constant-period model ($P=1.338231293$ days, $t_{\rm c} = 2456180.558583$ BJD$_{\rm TDB}$). In this panel and others, the black curve is the best-fit model including the hot Jupiter and a wide-orbiting companion, and the gray curves are random draws from the posterior. Upper right.---Radial velocities as a function of folded time (i.e. relative to the nearest transit time), after subtracting the best-fit contribution from the wide-orbiting companion. Lower right.---Radial velocities after subtracting the best-fit contribution of the hot Jupiter.