Atmospheric Loss Estimates in Two Planets of the Young Sun-Like Star TIC 434398831 from the Moving Group Theia 116

We present here the results of analyzing the activity of the young solar-type star (spectral class G4 V) TIC 434398831 belonging to the Moving Group Theia 116 aged approximately 61 Myr. The atmospheric mass loss estimates of the TIC 434398831 b and c planets are also found. Using the data from the TESS mission, the rotation period of the star ( P≈ 1d.75 ) is determined, and a hypothesis is put forward regarding the possible evolution of spots (cool regions) on its surface. For TIC 434398831, the differential rotation parameter of the star is found to be ΔΩ=0.081 rad/day. The areas of cool spots on the surface of the star are estimated to exceed manifold the maximum area of spots on the Sun varying for different sectors in the range of 47 140–103 090 MSH. In addition, the properties of the TIC 434398831 flare activity are studied. For the most reliable event, the relative duration of the flare is measured (about 50 s), the emitted energy was 2.1× 10³³ erg. According to the Kamogata Wide-field Survey (KWS), the long-term activity cycle of the star is found to be 2500 days (6.8 years). The results of calculations of the atmospheric mass loss values for the planets TIC 434398831 b and c ( Ṁ ) are presented using two atmospheric loss models: with an energy constraint (EC) and with a hydrodynamic approximation (HA) for two values of the log R^HK parameter (the XUV photon-flux values). Calculations with the HA model yield lower estimates of the Ṁ parameter. The ranges of the Ṁ parameter variations for TIC 434398831 b lie in the interval from 1.8× 10¹⁰ to 1.7× 10⁹ g s ⁻¹ (the model with EC) and from 5.1× 10⁹ to 4.8× 10⁸ g s ⁻¹ (the model with HA), and for TIC 434398831 c they are from 1.7× 10¹⁰ to 1.6× 10⁹ g s ⁻¹ (the model with EC) and from 4.3× 10⁹ to 4.0× 10⁸ g s ⁻¹ (the model with HA).