We present theoretical models of chromospheric heating for 55 Cancri, an orange dwarf of relatively low activity. Self-consistent, non-linear, and time-dependent ab initio numerical computations are pursued encompassing the generation, propagation, and dissipation of waves. We consider longitudinal waves operating among arrays of flux tubes as well as acoustic waves pertaining to non-magnetic stellar regions. Additionally, flux enhancements for the longitudinal waves are also taken into account as supplied by transverse tube waves. The Ca ii K fluxes are computed (multi-ray treatment) assuming partial redistribution as well as time-dependent ionization (TDI). The self-consistent treatment of TDI (especially for hydrogen) greatly impacts the atmospheric temperatures and electron densities (especially behind the shocks); it also affects the emergent Ca ii fluxes. Particularly, we focus on the influence of magnetic heating on the stellar atmospheric structure and the emergent Ca ii emission, as well as the impact of non-linearities. Our study shows that a higher photospheric magnetic filling factor entails a larger Ca ii emission; however, an increased initial wave energy flux (e.g. associated with mode coupling) is of little difference. Comparisons of our theoretical results with observations will be conveyed in forthcoming Paper II.

中文翻译：

---

55 Cancri 的色球活动 – I. 理论波研究的结果

我们提出了 55 Cancri 的色球加热理论模型，这是一颗活动相对较低的橙矮星。追求自洽、非线性和时间相关的从头算数值计算，包括波的产生、传播和消散。我们考虑在通量管阵列之间运行的纵波以及与非磁性恒星区域有关的声波。此外，还考虑了纵向波的通量增强，由横向管波提供。假设部分再分布以及时间相关电离 (TDI)，计算 Ca ii K 通量（多射线处理）。TDI 的自洽处理（尤其是氢气）极大地影响了大气温度和电子密度（尤其是在冲击之后）；它还影响出现的 Ca ii 通量。特别是，我们关注磁加热对恒星大气结构和出射 Ca ii 发射的影响，以及非线性的影响。我们的研究表明，较高的光球磁填充因子需要较大的 Ca ii 发射；然而，增加的初始波能量通量（例如与模式耦合相关）几乎没有区别。我们的理论结果与观察结果的比较将在即将发表的论文 II 中传达。G。与模式耦合相关）几乎没有区别。我们的理论结果与观察结果的比较将在即将发表的论文 II 中传达。G。与模式耦合相关）几乎没有区别。我们的理论结果与观察结果的比较将在即将发表的论文 II 中传达。