One of the basic problems in astrophysics is to identify the heating mechanisms of chromospheres and coronae. In the reviews by Narain & Ulmschneider (1990, 1996), Ulmschneider (1996), Ulmschneider & Musielak (2003) it is shown that there are a large number of different heating mechanisms that can be classified as acoustic mechanisms (where acoustic waves are dissipated by shocks) and magnetic mechanisms. The magnetic mechanisms can be subdivided into wave mechanisms (AC-mechanisms) where magnetohydrodynamic (MHD) wave energy is guided by the magnetic field and dissipated by shocks, and current mechanisms (DC-mechanisms) where the energy stored in the magnetic field is dissipated by reconnection.

Since the discovery in the 1970's that short period acoustic waves could be responsible for the heating of the solar chromosphere (Ulmschneider 1970) and that the presence of such waves is indicated from the theoretically computed frequency spectra of acoustic waves, generated in the turbulent convection zone (Stein 1968), our group in a series of publications has attempted to predict the acoustic wave generation and studied in detail the shock wave heating by short period acoustic waves (e.g. Ulmschneider et al. 1978, Schmitz, Ulmschneider & Kalkofen 1985, Ulmschneider, Muchmore & Kalkofen 1987, Rammacher & Ulmschneider 1992, 2003, Fawzy et al. 2002a, b, c). In a similar way we calculated the generation of magnetohydrodynamic (MHD) waves in magnetic flux tubes and generated theoretical chromosphere models for stars that are covered by various amounts of magnetic fields (Huang, Musielak & Ulmschneider 1995, Ulmschneider & Musielak 1998, Ulmschneider, Musielak & Fawzy 2001, Cuntz et al. 1999, Fawzy et al. 2002a, b, c).

The great difficulty in deciding whether acoustic waves, MHD-waves or reconnection are important heating mechanisms for stellar chromospheres is, that despite of the close proximity of the Sun it is currently not possible to reliably differentiate between magnetic heating in unresolved fields on the Sun and acoustic dissipation. This is because the spatial resolution of the solar surface is still insufficient for a reliable discrimination. Surprisingly it has turned out that by observing distant stars, which appear as mere point sources in the sky, it has become possible to progress significantly towards an answer to this question.

It is well known that models of the stellar interior can be computed by solving a system of 4 differential equations: the mass- and energy conservation equations (here the energy generation is by nuclear processes and by gravitational contraction), the hydrostatic equilibrium equation and an equation that describes the transport of energy from the stellar core through the stellar envelope by means of radiation and convection. These differential equations have to be augmented by equations describing material properties, the nuclear energy generation rate epsilon, the absorption coefficient for radiation kappa and some thermodynamic quantities as functions of temperature T and gas pressure p.

One finds that exactly 3 free parameters uniquely specify the structure and evolution of a star model: the surface-metallicity of the stellar gas Z_M, the stellar mass M_* and the evolutionary time t_E that has elapsed since the star began its hydrogen burning. The last two parameters can be replaced by two surface parameters, the effective temperature T_{eff} and surface gravity g. The fact that the stellar interior depends on only the 3 independent parameters Z_M, T_{eff} and g is also valid for stellar photospheres, the regions that lie directly below the chromospheres and emit most of the visible light.

Since chromospheres and coronae owe their existence to the stellar interior, they therefore ought to depend only on 3 parameters. This is valid for cases where magnetic fields are not important. However, as magnetic fields dominate most chromospheres and certainly the coronae there is a fourth independent parameter, the stellar rotation period P_{Rot} that has to be specified because the mechanism that generates stellar magnetic fields, the dynamo mechanism, works only when convection and rotation are both present in a star.

A powerful method to clarify the relative importance of chromospheric and coronal heating mechanisms, in addition to a detailed comparison study of the individual mechanisms is, to observe how the chromospheric emission varies when the values of Z_M, T_{eff}, g and P_{Rot} change among the stars.