Basal heating in main-sequence stars and giants. Results from monochromatic acoustic wave models

We calculate time-dependent models of acoustically heated chromospheres for main-sequence stars between spectral type F0 V and M0 V and for two giants of spectral type K0 III and K5 III assuming monochromatic waves. The hydrodynamic equations are solved together with the radiative transfer and statistical equilibrium equations to investigate the propagation of acoustic waves into the chromospheric regions. The emergent radiation in Mg II h+k and Ca II H+K is calculated and compared with observations, We find good agreement, over nearly 2 orders of magnitude? between the time-averaged emission in these lines and the observed basal Bur emission, which had been suspected to be due to nonmagnetic (i.e., acoustic) heating operating in all late-type stars. The height dependence of the acoustic energy flux can be explained by the limiting strength property of the acoustic shocks and is consistent with that found in models of quiet solar regions. We also confirm the validity of the Ayres scaling law, which has originally been derived for semiempirical chromosphere models and is thus independent of assumptions about the chromospheric heating mechanism. Our results strongly support the idea that the "basal heating" of chromospheres of late-type stars as revealed by the frequency-integrated Mg II and Ca II line emission is fully attributable to the dissipation of acoustic wave energy.