Linear Acoustic Waves in a Nonisothermal Atmosphere. II. Photospheric Resonator Model of Three-minute Umbral Oscillations
The velocity oscillations observed in the chromosphere of sunspot umbrae resemble a resonance in that their power spectra are sharply peaked around a period of about three minutes. In order to describe the resonance that leads to the observed 3-minute oscillations, we propose the photospheric resonator model of acoustic waves in the solar atmosphere. The acoustic waves are driven by the motion of a piston at the lower boundary, and propagate in a nonisothermal atmosphere that consists of the lower layer (photosphere), where temperature rapidly decreases with height, and the upper layer (chromosphere), where temperature slowly increases with height. We have obtained the following results: (1) The lower layer (photosphere) acts as a leaky resonator of acoustic waves. The bottom end is established by the piston, and the top end by the reflection at the interface between the two layers. (2) The temperature minimum region partially reflects and partially transmits acoustic waves of frequencies around the acoustic cutoff frequency at the temperature minimum. (3) The resonance occurs in the photospheric layer at one frequency around this cutoff frequency. (4) The waves escaping the photospheric layer appear as upward-propagating waves in the chromosphere. The power spectrum of the velocity oscillation observed in the chromosphere can be fairly well reproduced by this model. The photospheric resonator model was compared with the chromospheric resonator model and the propagating wave model.