tokens: of the WASP-South data for WASP-182 from three different years (left) along with folds of the data at the possible rotational periods (right). The folded data have been binned to 20 bins, each corresponding to 1.5 nights. The blue marks are at 30 and 15 d and the dotted horizontal line at 1 per cent false alarm probability (FAP). 4 SYSTEM PARAMETERS The full set of system parameters was modelled jointly using the discovery photometry, follow-up light curves, and RV data with the MCMC code described in detail in Collier Cameron et al. ( 2007 ) and Anderson et al. ( 2015 ). The analytic eclipse expressions derived by Mandel Agol ( 2002 ) are used with a four-parameter, non-linear limb darkening law of Claret ( 2000 , 2004 ). We have interpolated coefficients for stellar temperature and metallicity of each star, and in each photometric filter. The values used were perturbed during the MCMC via T L-D , the ‘limb-darkening temperature’, which has a mean and standard deviation corresponding to the spectroscopic T eff and its uncertainty. We ran the MCMC both with the eccentricity as a free parameter and fixed to zero, to check if the results are compatible with a circular orbit. We expect most giant planets in short-period orbits to have been circularized by tidal forces, and want to avoid overestimating the eccentricity in orbits that have none. Each circular model has six fitted parameters: orbital period, P , epoch, T C , transit depth in the absences of dark limb effects, ( R p / R s ) 2 , transit duration, T 14 , impact parameters, b , and stellar RV semi-amplitude, K 1 . The RV systemic velocity γ was fitted too, and in the case of WASP-171 along with a linear RV drift, . For WASP-182, where we have data from two different spectrographs, an offset between CORALIE and HARPS was modelled as well. For each target we ran 5000 MCMC steps as a ’burn in phase’ to initialize the main phase that was set to have 50 000 iterations. At each step the free parameters are perturbed and the models are refit. If the χ 2 of the fit is better than the previous step, the current parameters are accepted, if the fit is worse, the parameters are accepted with a probability proportional to exp (−Δχ 2 ). We used Gelman–Rubin statistics (Gelman et al. 2003 ; Ford 2006 ) to check how well the chains converge. In our case the Gelman–Rubin statistics indicated that all fitted parameters were well mixed. Continuing our practice from recent discovery papers (e.g. Hellier et al. 2019 ) we treat the stellar parameters through a two-step process; we first estimate the stellar density, ρ s , from the transit duration alone, independently of stellar models. Secondly, we obtain stellar masses by using ρ s , T eff , and [Fe/H] in the stellar evolution model bagemass , as explained in Section 3.2 . The resulting stellar mass estimate and its uncertainty are finally used as input in the MCMC to derive stellar radii. The stellar density for WASP-182 is poorly constrained by the
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