Characterising TOI-732 b and c: New insights into the M-dwarf radius and density valley

TOI-732 is an M dwarf hosting two transiting planets that are located on the two opposite sides of the radius valley. Inferring a reliable demographics for this type of systems is key to understanding their formation and evolution mechanisms. By doubling the number of available space-based observations and increasing the number of radial velocity (RV) measurements, we aim at refining the parameters of TOI-732\,b and c. We also use the results to study the slope of the radius valley and the density valley for a well-characterised sample of M-dwarf exoplanets. We performed a global Markov chain Monte Carlo analysis by jointly modelling ground-based light curves and CHEOPS and TESS observations, along with RV time series both taken from the literature and obtained with the MAROON-X spectrograph. The slopes of the M-dwarf valleys were quantified via a support vector machine (SVM) procedure. TOI-732\,b is an ultrashort-period planet $ d) with a radius $R_b=1.325_ oplus $, a mass $M_b=2.46 oplus $, and thus a mean density $ $, while the outer planet at $P=12.252284 d has oplus $, $M_c=8.04_ oplus $, and thus $ $. Even with respect to the most recently reported values, this work yields uncertainties on the transit depths and on the RV semi-amplitudes that are smaller up to a factor of sim \,1.6 and sim \,2.4 for TOI-732\,b and c, respectively. Our calculations for the interior structure and the location of the planets in the mass-radius diagram lead us to classify TOI-732\,b as a super-Earth and TOI-732\,c as a mini-Neptune. Following the SVM approach, we quantified $ $, which is flatter than for Sun-like stars. In line with former analyses, we note that the radius valley for M-dwarf planets is more densely populated, and we further quantify the slope of the density valley as $ Compared to FGK stars, the weaker dependence of the position of the radius valley on the orbital period might indicate that the formation shapes the radius valley around M dwarfs more strongly than the evolution mechanisms.