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The two planetary systems TOI-942 and TOI-421 share many similar characteristics, apart from their ages (50~Myr and 9~Gyr). Each of the stars hosts two sub-Neptune-like planets at similar orbits and in similar mass ranges. In this paper, we aim to investigate whether the similarity of the host stars and the configuration of the planetary systems can be taken as proof that the two systems were formed and evolved in a similar way. In paper I of this series, we performed a comparative study of these two systems using 3D modeling of atmospheric escape and its interaction with the stellar wind, for the four planets. We demonstrated that though the strong wind of the young star has a crucial effect on observable signatures, its effect on the atmospheric mass loss is minor in the evolutionary context. Here, we use atmosphere evolution models to track the evolution of planets in the younger system TOI-942 and also to constrain the past of the TOI-421 system. We demonstrate that despite all the similarities, the two planetary systems are on two very different evolutionary pathways. The inner planet in the younger system, TOI-942, will likely lose all of its atmosphere and become a super-Earth-like planet, while the outer planet will become a typical sub-Neptune. Concerning the older system, TOI-421, our evolution modeling suggests that they must have started their evolution with very substantial envelopes, which can be a hint of formation beyond the snow line., Comment: 9 pages, 4 figures; Accepted for publication in MNRAS

At young ages, when radiation from the host star is high, and the planet is hot and inflated after formation, planetary atmospheric mass loss can be extremely strong compared to older planets. In turn, stellar winds are faster and denser for young stars compared to evolved main-sequence stars. Their interaction with escaping planetary atmospheres can substantially affect atmospheric mass loss rates, as well as the observable signatures of escaping atmospheres, with both effects expected to occur differently for young and evolved planets. We perform a comparative study of two systems around stars of similar masses but very different ages (50~Myr and 9~Gyr): TOI-942 and TOI-421. Both stars host two sub-Neptune-like planets at similar orbits and in similar mass ranges, which allows a direct comparison of the atmospheric escape and interactions with the stellar winds in the young and old systems. We perform the 3D atmospheric modeling of the four planets in TOI-942 and TOI-421 systems and make the theoretical predictions of possible observational signatures in Ly-alpha absorption. We find that accounting for the stellar wind interacting with planetary atmospheres is crucial for the interpretation of the observations for young planets. Additionally, we show that a particular energy distribution along the XUV spectra has a minor effect on the atmospheric mass-loss rates, but it is of crucial importance for modeling the Ly-alpha absorption and therefore for interpretation of observations., Comment: 19 pages, 9+3 Figures (including Appendix); Accepted for publication in MNRAS

High-energy stellar irradiation can photoevaporate planetary atmospheres, which can be observed in spectroscopic transits of hydrogen lines. For the exoplanet HD189733b, multiple observations in the Ly-$\alpha$ line have shown that atmospheric evaporation is variable, going from undetected to enhanced evaporation in a $1.5$-year interval. Coincidentally or not, when HD189733b was observed to be evaporating, a stellar flare had just occurred 8h prior to the observation. This led to the question of whether this temporal variation in evaporation occurred due to the flare, an unseen associated coronal mass ejection (CME), or even the effect of both simultaneously. In this work, we investigate the impact of flares (radiation), winds, and CMEs (particles) on the atmosphere of HD189733b using 3D radiation hydrodynamic simulations of atmospheric evaporation that self-consistently include stellar photon heating. We study four cases: first- the quiescent phase of the star including stellar wind, second- a flare, third- a CME, and fourth- a flare that is followed by a CME. Compared to the quiescent case, we find that the flare alone increases the evaporation rate by only 25%, while the CME leads to a factor of 4 increase in escape rate. We calculate Ly-$\alpha$ synthetic transits and find that the flare alone cannot explain the observed high blueshifted velocities seen in the Ly-$\alpha$ observation. The CME, however, leads to an increase in the velocity of the escaping atmosphere, enhancing the transit depth at high blueshifted velocities. While the effects of CMEs show a promising potential to explain the blueshifted line feature, our models are not able to fully explain the blueshifted transit depths, indicating that they might require additional physical mechanisms., Comment: Accepted for publication in MNRAS, 14 pages, 9 figures