We have calculated time dependent models of acoustically heated chromospheres for main sequence stars of spectral types F0 V to M4 V and for two giant stars of spectral types K0 III and K5 III.

The equations of hydrodynamics together with the equation of radiative transfer (RTE) are solved in order to investigate the propagation of acoustic waves into chromospheric regions. A new computational method has been developed which is able to solve the RTE on the very irregular depth grids resulting from the presence of shock discontinuities in the computational domain.

Molecular opacities of TiO and water vapor have been included to get realistic models for the coolest M-dwarfs.

The emergent radiation of the MgII h+k and CaII H+K lines has been calculated and compared with observations. We find good agreement of the time averaged emissions from both ions with the observed basal emissions which are thought to be due to a non-magnetic chromospheric heating mechanism operating in all late type stars. The height dependence of the acoustic heating can be explained by the limiting strength of the shocks and is consistent with the height dependence of heating observed for the quit sun.

Our results strongly support the idea that the basal non-magnetic heating mechanism for stellar chromospheres is due to the dissipation of acoustic wave energy.

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