On the Effect of Radiative Relaxation on the Flux of Mechanical-Wave Energy in the Solar Atmosphere

In estimating the flux of mechanical-wave energy in the solar photosphere from observations it is generally assumed that the energy is transported upwards at the group velocity. It is pointed out that because the associated fluctuations in temperature relax through exchange of radiation, meaning that there is some dissipation of wave energy, the energy velocity is not the group velocity. An expression for the energy velocity is deduced for the case of an underlying isothermal atmosphere. It seems likely that the energy velocity in the solar atmosphere is significantly lower than the group velocity except at high and very low frequencies.