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We have used a time-dependent hydrodynamics code to follow the propagation of acoustic waves from the photosphere of an M dwarf star upwards into the chromosphere and corona. An important qualitative difference between M dwarfs and stars such as the Sun is that the acoustic spectrum in M dwarfs is believed to peak at periods close to the acoustic cut-off $P_A$: as a result of this, the waves can more effectively penetrate into the corona, rather than being essentially entirely dissipated in the chromosphere. In our code, radiative losses in the photosphere, chromosphere, and corona are computed using Rosseland mean opacities, MgII $k$ and Ly-$\alpha$ emission, and optically thin emissivities respectively. Our results indicate that acoustic heating can maintain a corona in an M dwarf with a temperature of order 0.7-1 million K and a surface X-ray flux $F_X$ up to $(1-1.5) \times 10^5$ ergs cm$^{-2}$ sec$^{-1}$. We find that it is not possible for acoustic waves to generate larger $F_X$ values: when we attempt to raise the $F_X$ values by supplying more input flux at the photosphere, the effect is to push the transition region to greater heights, thereby reducing the emission measure of the X-ray plasma. Preliminary results from a ROSAT study of a nearly complete sample of dK/dM stars out to several parsecs (J. Schmitt and T. Fleming, 1993, priv. comm.) indicate that most inactive dwarfs have log $F_X$ no larger than 5.1-5.2, and temperature no hotter than about 1 million K. In view of the good correspondence between our calculations and these data, we suggest that such inactive stars may be candidates for acoustically maintained coronae.
\vskip0.2truein \noindent This work has been supported by NASA Grant NAGW-2456.
