Chromospheric activity in $\epsilon$ Eridani: results from theoretical wave studies

This work discusses theoretical models of chromospheric heating for \(\epsilon\) Eridani by shock waves. Self-consistent, nonlinear and time-dependent ab-initio numerical computations for the excitation of the atmosphere (i.e., arrays of flux tubes) are pursued based on waves generated in stellar convective zones. Based on previous studies the magnetic filling factor is estimated according to the stellar rotational period, although general models are described as well. The Ca II H+K fluxes are computed assuming partial redistribution (PRD). Time-dependent ionization notably affects the resulting Ca II fluxes, as expected. The emergent Ca II H+K fluxes are based on two-component models, consisting of a dominant magnetic component (as given by longitudinal tube waves) and a subordinate acoustic component. The Ca II fluxes as obtained are smaller by about a factor of 2 than those given by observations. Possible reasons for this discrepancy include (1) inherent limitations of our theoretical approach as it is based on 1-D rather than 3-D modelling and/or (2) the existence of additional heating processes in \(\epsilon\) Eridani (a young star) not included here.