Internal gravity waves in the solar atmosphere. II. Effects of radiative damping

Radiative damping of internal gravity waves in the solar atmosphere is considered in a linearized approximation with a height-dependent Newtonian cooling time. A linear fit is made to Stix damping times for the photosphere, and this linear relation is simply extended into the chromosphere. Initial energy fluxes of 108, 107, and 106 ergs cm-2 s-1 are assumed for monochromatic gravity waves with a wide range of frequencies and horizontal wavenumbers. It is found that damping has the least effect on waves with small values of the vertical wavenumber. For such waves energy fluxes of 105--106 ergs cm-2 s-1 can reach the temperature minimum from an initial flux of 107--108 ergs cm-2 s-1 in the low photosphere. The energy flux of these gravity waves at chromospheric heights appears to be limited by development of nonlinearities more than by radiative damping. Gravity waves have larger horizontal than vertical velocities; radiative damping causes the ratio of the velocities to increase and the velocity amplitudes to diminish with height from the low photosphere to the temperature minimum region. These waves may play an important role in the broadening and strengthening of photospheric spectral lines; like granulation flows, the center-to-limb variation and the height dependence of the velocities have the same sense as those deduced from observations. Phase lags between vertical velocity and the pressure, temperature, and density perturbations are strongly affected by the damping. Also altered are vertical wavelength, group velocity, and ray path. Amplitudes of the thermodynamic perturbations change relative to one another and to the velocity amplitudes. These effects are discussed both in terms of the comparison between adiabatic and damped gravity waves and in relation to the effects of waves on spectral lines