Estimates of Atmospheric Mass Loss for Two Planets of the Young Solar Analog HD 109833

Abstract

We present the results of a further investigation of the planetary system HD 109833, whose central star is a young, active solar analog, presumably a member of the Lower Centaurus Crux association (age: \(27\pm 3\) Myr). Using digitized photographic plates from the Digital Access to a Sky Century@Harvard project (providing data on HD 109833 spanning a 100 year observation period) we made an additional attempt to study possible activity cycles of the star. Taking into account all uncertainties, it should be noted that the derived estimates of the activity cycle period \(P_{\textrm{cycl}}\) (including the earlier value obtained from ASAS-3 data, \(P_{\textrm{cycl}}=5.3\) years) are on the edge of statistical reliability. Based on measurements of the chromospheric activity index \(\log R^{\prime}_{HK}\) for HD 109833 from the updated HARP SRV database and its empirical relation with \(\log F_{\textrm{XUV}}\), we estimated the XUV photon flux to be \(2.0\times 10^{29}\) erg s\({}^{-1}\). The exoplanets HD 109833 b and c are located in the overlapping region of two distinct populations on the ‘‘mass–radius’’ diagram: rocky planets and planets rich in volatile compounds. We present calculations of atmospheric mass loss rates \(\dot{M}\) for HD 109833 b and c based on both the energy-limited escape model (EL) and the hydrodynamic approximation model (HA), using different planetary mass estimates. We also provide the ratios of mass loss rates \(\dot{M}\) obtained from EL and HA models (Ratio), and the values of the Jeans parameter \(\Lambda\). It is suggested that the HA model significantly underestimates \(\dot{M}\) in the case of rocky planets, rendering this model inapplicable for such high values of \(\Lambda\). Our results are in reasonable agreement with those of Foster et al. (2022), which describe the general behavior of \(\dot{M}\), and fall within the observed spread of this parameter.