2021MNRAS.502.5075F

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.