TOI-837 b: characterisation, formation and evolutionary history of an infant warm Saturn-mass planet

We aim to determine the fundamental properties of the $\sim$35 Myr old star TOI-837 and its close-in Saturn-sized planet, and to investigate the system's formation and evolutionary history. We analysed TESS photometry and HARPS spectroscopic data, measured stellar and planetary parameters, and characterised the stellar activity. We performed population synthesis simulations to track the formation history of TOI-837 $b$, and to reconstruct its possible internal structure. We investigated the planetary atmospheric evolution through photo-evaporation, and quantified the prospects for atmospheric characterisation with JWST. TOI-837 $b$ has radius and mass similar to those of Saturn ($r_b$=9.71$^{+0.93}_{-0.60}$ \rearth, $m_b$=116$^{+17}_{-18}$ M$_\odot$, and $\rho_b$=0.68$^{+0.20}_{-0.18}$ gcm$^{-3}$), on a primordial circular orbit. Population synthesis and early migration simulations suggest that the planet could have originated between 2-4 au, and have either a large and massive core, or a smaller Saturn-like core, depending on the opacity of the protoplanetary gas and on the growth rate of the core. We found that photo-evaporation produced negligible effects even at early ages (3-10 Myr). Transmission spectroscopy with JWST is very promising, and expected to provide constraints on atmospheric metallicity, abundance of H$_2$O, CO$_2$, CH$_4$ molecules, and to probe the presence of refractory elements. TOI-837 offers valuable prospects for follow-up observations, which are needed for a thorough characterisation. JWST will help to better constraining the formation and evolution history of the system, and understand whether TOI-837 $b$ is a Saturn-analogue.