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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]

The signs of an expanding atmosphere of HD209458b have been observed with far-ultraviolet transmission spectroscopy and in the measurements of transit absorption by metastable He  i. These observations are interpreted using the hydrodynamic and Monte Carlo numerical simulations of various degree of complexity and consistency. At the same time, no attempt has been made to model atmospheric escape of a magnetized HD209458b, to see how the planetary magnetic field might affect the measured transit absorption lines. This paper presents the global 3D MHD self-consistent simulations of the expanding upper atmosphere of HD209458b interacting with the stellar wind, and models the observed H  i (Ly α), O  i (1306 Å), C  ii (1337 Å), and He  i (10 830 Å) transit absorption features. We find that the planetary dipole magnetic field with the equatorial surface value of Bp = 1 G profoundly changes the character of atmospheric material outflow and the related absorption. We also investigate the formation of planetary magnetosphere in the stellar wind and show that its size is more determined by the escaping atmosphere flow rather than by the strength of magnetic field. Fitting of the simulation results to observations enables constraining the stellar XUV flux and He abundance at F XUV ∼ 10 erg cm2 s–1 (at 1 au) and He/H ≈ 0.02, respectively, as well as setting an upper limit for the dipole magnetic field of Bp < 0.1 G on the planetary surface at the equator. This implies that the magnetic dipole moment µP of HD209458b should be less than 6 per cent of the Jovian value. [ABSTRACT FROM AUTHOR]