Activity of the Star Gl 414A with Two Planets and its Effect on the Loss of Mass of the Atmosphere of the Planet Gl 414A b

Results are presented from a study of manifestations of the activity of the dwarf Gl 414A of spectral class K7 with two planets, one of which (the planet Gl 414A b) with an eccentricity e=0.45 was found to be within the habitable zone over a large part of its orbit. Our analysis showed that the most reliable determination of the rotation period of Gl 414A was obtained from an analysis of photometric observations of the star in the KELT (Kilodegree Extremely Little Telescope) survey which yield a rotation period of P=42 days. However, the existence of this period is not confirmed by periodograms constructed from other observations of Gl 414A. The long-term activity cycle of the star is on the order of 3800 days (10.4 years). The obtained data on the activity of the star were used to estimate the loss of matter from the atmosphere of the planet Gl 414A b using an approximation formula for a model of atmospheric loss with a limit on energy. Based on 486 estimates of the parameter S_HK, the loss of matter by the atmosphere of Gl 414A b over an interval of 5805 days (15.9 years) was calculated. The magnitude of these losses mainly lies within a range of log(M_loss) from 7.15 to 7.50 with a median of 7.30. For an eccentricity of 0.45 the distance from the central star to Gl 414A b ranges from 0.13 to 0.34 a.u., and for these distances the estimated losses of matter by the atmosphere are 16.21·10¹⁷ and 2.37·10¹⁷ g/s, respectively.