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.

中文翻译：

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年轻太阳模拟 HD 109833 的活动及其两颗行星大气层的质量损失率估计

摘要

我们展示了对年轻太阳模拟 HD 109833 活动表现的分析结果，并估计了其两颗行星大气层的质量损失率。HD 109833 可能属于下半人马座十字星 (LCC) 星团，年龄为 27 \(\pm\) 3 Myr，但这并不是不可想象的，这颗恒星仅在空间上与该星团相关，并且可能更老，尽管在任何如果其年龄不超过 100–200 Myr。根据HD 109833的TESS档案数据，我们确定了恒星自转周期\(P=5.08\pm 0.30\)天和平均恒星亮度的光度变化幅度（约0.6 \({\%}\)）并估计了其表面的黑子面积，超过了最大太阳黑子面积，为 15 200–17 700 msh 根据全天自动巡天档案的数据，我们揭示了一个持续时间为 \({ \ sim}1950\）天（5.3年）。HD 109833 系统中的两颗行星均属于亚海王星，半径分别为 2.9 和 2.6 \(R_{\oplus}\)，周期分别为 9.2 和 13.9 天。行星大气的质量损失率是使用与能量限制大气逃逸模型相对应的近似公式得出的。为了估计\(XUV\)通量，我们应用了与通量和参数\(\log R^{\prime}_{HK}\)相关的分析依赖性以及有关 G 型恒星这些量分布的信息，表明在低活动星和活跃星中分别有两个明显的峰值，其最大值为\({\sim}-5.0\)和\(-4.5\) dex。此外，我们还使用了来自恒星的 X 射线通量与\(\log F_{XUV}\)之间的关系。发现的值与通过对活跃恒星应用参数\(\log R^{\prime}_{HK}\)获得的估计值相当，并超过其 4 倍。同时考虑了系外行星 HD 109833 b 和 c我们落入\((MR)\)图上的区域，其中岩石和富含挥发物的系外行星的数量重叠，并且不允许明确地估计它们的质量。我们的计算针对两种情况进行：岩石系外行星和富含挥发物的系外行星。对于岩石系外行星，HD 109833 b 和 c 的质量分别为 34.9 和 24 \(M_{\oplus}\)，对于富含挥发物的系外行星，其质量分别为 9.3 和 7.8 \(M_{\oplus}\) 。我们展示了行星 HD 109833 b 和 c 的大气质量损失率的计算结果，同时改变了与行星质量和入射到行星上的紫外线通量估计相关的参数。参数\(\dot{M}\)对于 HD 109833 b 和 c，变化范围为\(9.60\times 10^{7}\)到\(1.38\times 10^{10}\) gs \({}^{-1}\)以及分别为\(4.56\times 10^{7}\)到\(5.28\times 10^{9}\) gs \({}^{-1}\) 。发现的高质量损失率可能是来自太阳型恒星（年轻活跃太阳的类似物）的相当高的\(XUV\)通量以及行星距离主恒星相当近的位置的结果。