Activity of the Young Solar Analog HD 109833 and Estimates of the Mass Loss Rate from the Atmospheres of Its Two Planets

Abstract

We present the results of our analysis of the manifestations of activity in the young solar analog HD 109833 and estimate the mass loss rate from the atmospheres of its two planets. HD 109833 probably belongs to the Lower Centaurus Crux (LCC) association with an age of 27 \(\pm\) 3 Myr, but it is not inconceivable that the star is only spatially associated with the association and may be older, although in any case its age does not exceed 100–200 Myr. Based on data from the TESS archive for HD 109833, we have determined the stellar rotation period \(P=5.08\pm 0.30\) days and the photometric variability amplitude (about 0.6\({\%}\) of the mean stellar brightness) and estimated the spot areas on its surface, which exceed the maximum sunspot area and are 15 200–17 700 m.s.h. Based on data from the All-Sky Automated Survey archive, we have revealed a stellar activity cycle with a duration \({\sim}1950\) days (5.3 years). Both planets in the HD 109833 system are characterized as sub-Neptunes with radii of 2.9 and 2.6 \(R_{\oplus}\) and periods of 9.2 and 13.9 days. The mass loss rates by the planetary atmospheres have been found using an approximate formula corresponding to the energy-limited atmospheric escape model. To estimate the \(XUV\) flux, we have applied analytical dependences relating the flux and the parameter \(\log R^{\prime}_{HK}\) and information about the distribution of these quantities for G-type stars, suggesting that there are two pronounced peaks with maxima for values \({\sim}-5.0\) and \(-4.5\) dex in low-activity and active stars, respectively. In addition, we have used the relation between the X-ray flux from the star and \(\log F_{XUV}\). The value found is comparable to the estimate obtained by applying the parameter \(\log R^{\prime}_{HK}\) for active stars and exceeds it by a factor of 4. Both exoplanets HD 109833 b and c being considered by us fall into the region on the \((M-R)\) diagram in which the populations of rocky and volatile-rich exoplanets overlap and do not allow their masses to be estimated unambiguously. Our calculations were performed for two cases—rocky exoplanets and volatile-rich exoplanets. The masses of the exoplanets HD 109833 b and c are, respectively, 34.9 and 24 \(M_{\oplus}\) for rocky exoplanets and 9.3 and 7.8 \(M_{\oplus}\) for volatile-rich exoplanets. We present the results of our calculations of the atmospheric mass loss rates by the planets HD 109833 b and c while varying the parameters related to the estimates of the planetary masses and the UV flux incident on the planets. The parameter \(\dot{M}\) for HD 109833 b and c varies in the ranges from \(9.60\times 10^{7}\) to \(1.38\times 10^{10}\) g s\({}^{-1}\) and from \(4.56\times 10^{7}\) to \(5.28\times 10^{9}\) g s\({}^{-1}\), respectively. The high mass loss rates found can be a consequence of a fairly high \(XUV\) flux from the solar-type star (an analog of the young active Sun) and a fairly close location of the planets from the host star.