A comprehensive Rossiter-Mclaughlin Modelling Framework in TLCM: Application to HD 2685 = TOI-135 system

We present an updated Rossiter-McLaughlin modelling framework in the exoplanet analysis code TLCM. We describe our model in detail. The model and the code were validated by nine systems where we use TESS photometric measurements and archive radial velocity data (WASP-15, HAT-P-1, HAT-P-3, HAT-P-6, HAT-P-7, HAT-P-11, HAT-P-14, HAT-P-20, HAT-P-32). In addition, new observations were obtained from HD 2685 = TOI-135 which is an evolved, hot (T eff=6801 K), single star hosting a about 1.15 Jupiter-mass transiting hot Jupiter in a about 4.1 days orbit. We obtained new HARPS radial velocity measurements in-transit and out-of-transit. Also, there are new photometric observations from six additional, yet not-analyzed TESS-sectors since the time of the discovery of its transits. This allowed us to refine the planetary, orbital and system parameters and to detect Rossiter-Mclaughlin effect in it. We find an intermediate sky-projected obliquity, lambda =+-, for our fiducial spectroscopic V I prior. Tests with broader V I priors show that the central value of lambda remains stable, although the uncertainty increases.