A search for transit-timing variations in the transiting hot-Jupiter systems HIP 65, NGTS-6, NGTS-10, and WASP-173

Hot Jupiters are Jupiter-mass planets with orbital periods of less than 10 d. Their short orbital separations make tidal dissipation within the stellar host especially efficient, potentially leading to a measurable evolution of the orbit. One possible manifestation of this is orbital decay, which presents itself observationally through variations in the orbital period and thus times of transit. Here, we select four promising exoplanetary systems for detecting this effect: HIP65, NGTS-6, NGTS-10, and WASP-173. We present 33 new transit light curves taken with the 1.54m Danish Telescope, and analyse these alongside photometric data from the Transiting Exoplanet Survey Satellite and transit-timing data from the literature. We construct two ephemeris models for each target: a linear ephemeris and a shrinking orbital period due to tidal decay. The linear ephemeris is preferred for three of the four models – the highest significance for the quadratic ephemeris is over 3$\sigma$ for WASP-173. We compare these results to theoretical predictions for tidal dissipation of gravity waves in radiation zones, and find that wave breaking is predicted only in WASP-173, making rapid decay plausible in this system but unclear in the other three. The sensitivity of transit timings to orbital decay depends on the square of the time interval covered by available observations, so our results establish a useful baseline against which future measurements can be compared. NGTS-6 and NGTS-10 are important objects for future study as they are in the first field to be observed by the upcoming PLATO mission.