The apparent tidal decay of WASP-4 b can be explained by the R{\o}mer effect

Tidal orbital decay plays a vital role in the evolution of hot Jupiter systems. As of now, this was only observationally confirmed for the WASP-12 system. There are a few other candidates, including WASP-4 b, but no conclusive result could be obtained for these systems as of yet. In this study, we present an analysis of new TESS data of WASP-4 b together with archival data, taking the light-time effect (LTE), induced by the second planetary companion, into account as well. We make use of three different Markov-Chain-Monte-Carlo models; a circular orbit with a constant orbital period, a circular orbit with a decaying orbit, and an elliptical orbit with apsidal precession. This analysis is repeated for four cases. The first case features no LTE correction, with the remaining three cases featuring three different timing correction approaches. Comparison of these models yields no conclusive answer to the cause of WASP-4\,b's apparent transit timing variations. A broad range of values of the orbital decay and apsidal precession parameters are possible, depending on the LTE correction. This work highlights the importance of continued photometric and spectroscopic monitoring of hot Jupiters.