Two-component theoretical chromosphere models for K dwarfs of different magnetic activity: Exploring the CaII emission-stellar rotation relationship

We compute two-component theoretical chromosphere models for K2 V stars wit h different levels of magnetic activity. The two components are a nonmagnet ic component heated by acoustic waves and a magnetic component heated by lo ngitudinal tube waves. The filling factor for the magnetic component is det ermined from an observational relationship between the measured magnetic ar ea coverage and the stellar rotation period. We consider stellar rotation p eriods between 10 and 40 days. We investigate two different geometrical dis tributions of magnetic flux tubes: uniformly distributed tubes, and tubes a rranged as a chromospheric network embedded in the nonmagnetic region. The chromosphere models are constructed by performing state-of-the-art calculat ions for the generation of acoustic and magnetic energy in stellar convecti on zones, the propagation and dissipation of this energy at the different a tmospheric heights, and the formation of specific chromospheric emission li nes that are then compared to the observational data. In all these steps, t he two-component structure of stellar photospheres and chromospheres is ful ly taken into account. We find that heating and chromospheric emission is s ignificantly increased in the magnetic component and is strongest in flux t ubes that spread the least with height, expected to occur on rapidly rotati ng stars with high magnetic filling factors. For stars with very slow rotat ion, we are able to reproduce the basal pur limit of chromospheric emission previously identified with nonmagnetic regions. Most importantly, however, we find that the relationship between the Ca II H + K emission and the ste llar rotation rate deduced from our models is consistent with the relations hip given by observations.