Standing Mode of Compressional-Body Gravity Wave in the Solar Chromosphere.

Propagation features of the low4requency hydrodynamic waves under the influence of gravity are investigated in relation to the observed solar chromospheric oscillation It is shown that, in addition to the vertical acoustic mode investigated by Bahng and Schwarzschild, the compressional gravity-wave mode can yield a standing wave in the low chromosphere for a frequency and a horixontal wavelength near the observed values. The equations reduce to the form d2 /dz2 + f(w, k z) = 0, where is the Fourier coefficient in time and the horizontal distance of po'12 X (vertical displacement). The behavior of J(w, k z) for some given temperature profiles is investigated for various and k , and it is shown that the temperature minimum in the low chromosphere behaves like a "potential well" in quantum mechanics (if we remember that our reduced equation has the same form as the one-dimensional Schr6dinger equation) for the compressional gravity-wave mode with co and k around the observed values. The analysis of this eigenvalue problem indicates that the fundamental resonance value of 2ir/co is near the observed period of S minutes, if we take k corresponding to the observed lateral scale of the oscillation cell. The eigensolution corresponding to these parameters seems to explain fairly well the observed properties of the oscillation.