ACOUSTIC-WAVE PROPAGATION IN THE SOLAR ATMOSPHERE .1. REDISCUSSION OFTHE LINEARIZED THEORY INCLUDING NONSTATIONARY SOLUTIONS

The normal dispersion analysis for linear adiabatic wave propagation i n stratified atmospheres adopts a real frequency and solves for the co mplex vertical wavenumber. We show that an exponentially stratified at mosphere does not have any spatially bounded normal modes for real fre quencies. The usual treatment involves a representation where the imag inary part of the vertical wavenumber yields a rho(-1/2) dependence of the velocity amplitude which diverges as \z\ --> infinity. This solut ion includes a cutoff frequency below which acoustic modes cannot prop agate. The standard dispersion analysis is a local representation of t he wave behavior in both space and time but which is assumed to repres ent the motion throughout -infinity < t < infinity and 0 < z < infinit y. However, any solution which has a purely sinusoidal time dependence extends through this full domain and is divergent due to the rho(-1/2 ) dependence. We show that a proper description is in terms of a near field of a boundary piston which is driven arbitrarily as a function o f space and time. The atmosphere which responds to this piston is a se mi-infinite layer which has an initially constant sound speed but whic h has the usual gravitational stratification. In a restricted domain o f space and time above this boundary, the wavelike behavior of the med ium may be described by frequencies and vertical wavenumbers which are both complex. When both parameters are allowed to have imaginary comp onents, a new range of solutions is found for which there is virtually no cutoff frequency. We show that vertical energy propagation can tak e place through the solar atmosphere as a result of oscillations below the nominal cutoff frequency. Previously, the largest amplitude oscil lations which generally have low frequencies were dropped from the cal culation of energy flux because their frequencies are below the cutoff frequency. This new family of near-held waves permits these modes to carry energy vertically outward and raises the possibility that the la rgest amplitude 5 minute oscillations play a substantial role in the t ransport of acoustic energy to the chromosphere.