A PSF-based Approach to TESS High quality data Of Stellar clusters (PATHOS) -- IV. Candidate exoplanets around stars in open clusters: frequency and age-planetary radius distribution.

The knowledge of the ages of stars hosting exoplanets allows us to obtain an overview on the evolution of exoplanets and understand the mechanisms affecting their life. The measurement of the ages of stars in the Galaxy is usually affected by large uncertainties. An exception are the stellar clusters: for their coeval members, born from the same molecular cloud, ages can be measured with extreme accuracy. In this context, the project PATHOS is providing candidate exoplanets orbiting members of stellar clusters and associations through the analysis of high-precision light curves obtained with cutting-edge tools. In this work, we exploited the data collected during the second year of the TESS mission. We extracted, analysed, and modelled the light curves of $\sim 90000$ stars in open clusters located in the northern ecliptic hemisphere in order to find candidate exoplanets. We measured the frequencies of candidate exoplanets in open clusters for different orbital periods and planetary radii, taking into account the detection efficiency of our pipeline and the false positive probabilities of our candidates. We analysed the Age--$R_{\rm P}$ distribution of candidate and confirmed exoplanets with periods $<100$ days and well constrained ages. While no peculiar trends are observed for Jupiter-size and (super-)Earth-size planets, we found that objects with $4\,R_{\rm Earth} \lesssim R_{\rm P} \lesssim 13\,R_{\rm Earth}$ are concentrated at ages $\lesssim 200$ Myr; different scenarios (atmospheric losses, migration, etc.) are considered to explain the observed age-$R_{\rm P}$ distribution.