Atmospheric and evolutionary characterisation of K2-18b

Cool sub-Neptune planets within the habitable zone of M-dwarf stars have become a central focus of investigation in exoplanetary science. To date, K2-18b remains the only sub-Neptune with equilibrium temperature below 300 K in that star environment that has been observed with the James Webb Space Telescope. Although it shows an extensive transmission spectrum, both its atmospheric composition and internal structure remain debated. Since the atmospheric study alone cannot fully determine the nature of K2-18b, we present a comprehensive analysis that combines atmospheric retrievals with models of planetary formation and evolution.Using updated stellar parameters, we perform a uniform reduction of all the JWST transmission datasets using the Eureka! package. We obtain a transmission spectrum spanning 0.6-12 micrometers, combining spectra observed with NIRISS/SOSS, NIRSpec/G235H, NIRSpec/G395H, and MIRI/LRS instrumentations. We perform several Bayesian free-chemistry retrieval models using the TauREx3 framework, exploring different molecules and temperature-pressure profiles. In addition, we test a power-law cloud parameterisation through a new TauRex3 plugin, specifically implemented for this project. Our favoured atmospheric model indicates a hydrogen-dominated atmosphere containing  1.6% CH4,  0.13% CO2 and a weak signature of C2H4, together with photochemical hazes. We determine that the best-fitting atmospheric model for K2-18b has a low mean molecular weight of about 2.8 amu, mainly composed of light elements. We perform a detailed evolution model of the planetary envelope, finding that at early ages the envelope size was about two times larger than at present age, but its mass was just 10% larger. We find that hydrodynamic photoevaporation processes played a marginal role in shaping the atmospheric content, which instead are mostly driven by the natural gravitational shrinking of the planet. In this way, the current composition of K2-18b is likely primordial, supporting the atmospheric model output. We complement free-chemistry retrieval models with chemical equilibrium computations to interpret the retrieved molecular abundances under different atmospheric scenarios. We test a well-mixed mini-Neptune atmosphere,  a well-mixed Hycean world, and a vertically stratified atmosphere, establishing that the retrieved abundances of CH4, CO2 and C2H4 are best reproduced by the first scenario. This result is further supported by population synthesis simulations, finding that K2-18 b has formed at several astronomical units from its host star and migrated inward during the protoplanetary disk phase. Due to this, we predict a mainly rocky core, with a limited ice fraction of < 25%, which is in agreement with the mini-Neptune scenario.Our findings indicate that the use of multiple types of analysis together leads to a deeper understanding of complex planets like K2-18 b. Furthermore, our results may be used to investigate how other sub-Neptunes evolve within the habitable zone of M-dwarf stars, in order to build a solid sample and finally understand the nature of these planets.