No abstract

No abstract

We review the mechanisms which have been proposed for the heating of stellar chromospheres and coronae. These consist of heating by acoustic waves, by slow and fast mhd waves, by body and surface Alfv6n waves, by current or magnetic field dissipation, by microflare heating and by heating due to bulk flows and magnetic flux emergence. Some relevant observational evidence has also been discussed.

We compute two-component theoretical chromosphere models for K2 V stars with di †erent 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 Ðlling 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 di †erent geometrical distributions of magnetic Ñux 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 di †erent atmospheric heights, and the formation of speciÐc 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 Ðnd that heating and chromospheric emission is signiÐ-cantly increased in the magnetic component and is strongest in Ñux tubes that spread the least with height, expected to occur on rapidly rotating stars with high magnetic Ðlling factors. For stars with very slow rotation, we are able to reproduce the basal Ñux limit of chromospheric emission previously identiÐed with nonmagnetic regions. Most importantly, however, we Ðnd 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.

We examine the propagation of kink and longitudinal waves in the solar magnetic network. Previously, we investigated the excitation of network oscillations in vertical magnetic flux tubes through buffeting by granules and found that footpoint motions of the tubes can generate sufficient wave energy for chromospheric heating. We assumed that the kink and longitudinal waves are decoupled and linear. We overcome these limitations by treating the nonlinear MHD equations for coupled kink and longitudinal waves in a thin flux tube. For the parameters we have chosen, the thin tube approximation is valid up to the layers of formation of the emission features in the H and K lines of Ca ii, at a height of about 1 Mm. By solving the nonlinear, timedependent MHD equations we are able to study the onset of wave coupling, which occurs when the Mach number of the kink waves is of the order of 0.3. We also investigate the transfer of energy from the kink to the longitudinal waves, which is important for the dissipation of the wave energy in shocks. We find that kink waves excited by footpoint motions of a flux tube generate longitudinal modes by mode coupling. For subsonic velocities, the amplitude of a longitudinal wave increases as the square of the amplitude of the transverse wave, and for amplitudes near Mach number unity, the coupling saturates and becomes linear when the energy is nearly evenly divided between the two modes.