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Possible reasons for the non-detection of absorption in the metastable He  i (23S) line at transit observations of warm Neptune GJ436b, in spite of the well-pronounced strong absorption features measured earlier in Lyα for this planet, are investigated. We perform numeric simulations of the escaping upper atmosphere of this planet and its He  i (23S) triplet absorption with a global 3D multifluid, self-consistent hydrodynamic model. By fitting the model parameters to the lowest detection level of absorption measurements, we constrain an upper limit for the He/H abundance three times smaller than the solar value. We demonstrate that neither the significant changes of the stellar wind related to possible stellar coronal mass ejections (CMEs), or possible variations in the stellar ionization radiation, nor the presence of heavy trace elements have a crucial effect on the absorption at the 10   830 Å line of He  i (23S) triplet. The main reason of weak signature is that the region populated by the absorbing metastable helium is rather small (<3 R p), as well as the small size of the planet itself in comparison to the host star. We show that the radiation pressure force acting on the He  i (23S) atoms spreads them along the line of sight and around the planet, thus further reducing peak absorption. [ABSTRACT FROM AUTHOR]

We simulate with a global 3D aeronomy code two warm Neptunes in the TOI-421 system and show that both planets experience significant escape of their upper atmospheres. The double shock structures, generated around the planets in course of their interaction with the stellar wind (SW) plasma flow are revealed. The calculations of stellar Ly α transit absorption by the planets reveal that it reaches a detectable level only for a moderate or strong SW, with a sufficiently high density. In this case, the energetic neutral atoms provide significant absorption at the high velocity blue wing of the Ly α line, whereas the corresponding transit light curves exhibit an early ingress and extended egress features. With the same code, we also modelled the absorption at the position of the 10 830 Å line of the metastable helium, showing that it can be detected only for the farthest planet of the considered two, if the helium abundance is comparable to the solar value. [ABSTRACT FROM AUTHOR]