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 with different levels of magnetic activity. The two components are a nonmagnetic component heated by acoustic waves and a magnetic component heated by longitudinal tube waves. The filling factor for the magnetic component is determined from an observational relationship between the measured magnetic area coverage and the stellar rotation period. We consider stellar rotation periods between 10 and 40 days. We investigate two different geometrical distributions of magnetic flux tubes: uniformly distributed tubes, and tubes arranged as a chromospheric network embedded in the nonmagnetic region. The chromosphere models are constructed by performing state-of-the-art calculations for the generation of acoustic and magnetic energy in stellar convection zones, the propagation and dissipation of this energy at the different atmospheric heights, and the formation of specific chromospheric emission lines that are then compared to the observational data. In all these steps, the two-component structure of stellar photospheres and chromospheres is fully taken into account. We find that heating and chromospheric emission is significantly increased in the magnetic component and is strongest in flux tubes that spread the least with height, expected to occur on rapidly rotating stars with high magnetic filling factors. For stars with very slow rotation, 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 stellar rotation rate deduced from our models is consistent with the relationship given by observations.