Examining the orbital decay targets KELT-9 b, KELT-16 b and WASP-4 b, and the transit-timing variations of HD 97658 b

Tidal orbital decay is suspected to occur especially for hot Jupiters, with the only observationally confirmed case of this being WASP-12 b. By examining this effect, information on the properties of the host star can be obtained using the so-called stellar modified tidal quality factor $Q_*'$, which describes the efficiency with which kinetic energy of the planet is dissipated within the star. This can help to get information about the interior of the star. In this study, we aim to improve constraints on the tidal decay of the KELT-9, KELT-16 and WASP-4 systems, to find evidence for or against the presence of this particular effect. With this, we want to constrain each star's respective $Q_*'$ value. In addition to that, we also aim to test the existence of the transit timing variations (TTVs) in the HD 97658 system, which previously favoured a quadratic trend with increasing orbital period. Making use of newly acquired photometric observations from CHEOPS and TESS, combined with archival transit and occultation data, we use Markov chain Monte Carlo (MCMC) algorithms to fit three models, a constant period model, an orbital decay model, and an apsidal precession model, to the data. We find that the KELT-9 system is best described by an apsidal precession model for now, with an orbital decay trend at over 2 $\sigma$ being a possible solution as well. A Keplerian orbit model with a constant orbital period fits the transit timings of KELT-16 b the best due to the scatter and scale of their error bars. The WASP-4 system is represented the best by an orbital decay model at a 5 $\sigma$ significance, although apsidal precession cannot be ruled out with the present data. For HD 97658 b, using recently acquired transit observations, we find no conclusive evidence for a previously suspected strong quadratic trend in the data.