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From its discovery, the WASP-18 system with its massive transiting planet ona tight orbit was identified as a unique laboratory for studies on tidalplanet-star interactions. In an analysis of Doppler data, which include fivenew measurements obtained with the HIRES/Keck-I instrument between 2012 and2018, we show that the radial velocity signal of the photosphere following theplanetary tidal potential can be distilled for the host star. Its amplitude isin agreement with both theoretical predictions of the equilibrium tideapproximation and an ellipsoidal modulation observed in an orbital phase curve.Assuming a circular orbit, we refine system parameters using photometric timeseries from TESS. With a new ground-based photometric observation, we extendthe span of transit timing observations to 28 years in order to probe the rateof the orbital period shortening. Since we found no departure from aconstant-period model, we conclude that the modified tidal quality parameter ofthe host star must be greater than 3.9x10^6 with 95% confidence. This result isin line with conclusions drawn from studies of the population of hot Jupiters,predicting that the efficiency of tidal dissipation is 1 or 2 orders ofmagnitude weaker. As the WASP-18 system is one of the prime candidates fordetection of orbital decay, further timing observations are expected to pushthe boundaries of our knowledge on stellar interiors.

Planet-star interactions with precise transit timing. II. The  radial-velocity tides and a tighter constraint on the orbital decay rate in  the WASP-18 system