Linear Acoustic Waves in a Nonisothermal Atmosphere. II. Photospheric Resonator Model of Three-minute Umbral Oscillations

Abstract

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 upwardpropagating 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.

Doppler shift oscillations of a sunspot detected by CYRA and IRIS

“…So, the threeminute oscillation at the sunspot umbra could come from the upper photosphere or the temperature minimum region and then propagate to the chromosphere, supporting the interpretation that propagating waves above the sunspots originate from the lower solar atmosphere (De Moortel et al 2002;O'Shea et al 2002;Brynildsen et al 2004;Khomenko & Collados 2015;Krishna Prasad et al 2015). In other words, the three-minute oscillation can be regarded as the upwardly propagating slow magnetoacoustic waves (e.g., Su et al 2016;Chae et al 2019;Cho & Chae 2020;Feng et al 2020b). Finally, Chae et al (2017) found that the threeminute oscillation in the light bridge or umbral dots of a sunspot originates from the photosphere (see aslo Cho et al 2019), which is consistent with our results and further suggests that the CYRA data is reliable.…”

“…They are thought to be resonant modes of sunspot oscillations, with cavities that may be located at sunspot umbrae in the solar layers of sub-photospheres (Scheuer & Thomas 1981;Thomas 1984Thomas , 1985 or chromospheres (Uexkuell et al 1983;Gurman 1987;Khomenko & Collados 2015). The typical three-minute oscillation above the sunspot can be simultaneously detected from the photosphere through the chromosphere and transition region to the corona, supporting the interpretation of propagating waves at sunspots (De Moortel et al 2002;O'Shea et al 2002;Brynildsen et al 2004;Su et al 2016;Chae et al 2019), for instance trans-sunspot waves (Tziotziou et al 2006) or slow magnetoacoustic waves (Bloomfield et al 2007;Krishna Prasad et al 2015;Wang et al 2018;Cho et al 2019;Cho & Chae 2020).…”

“…Sunspot oscillations can be observed at various layers in solar atmosphere, and are often interpreted in terms of magnetohydrodynamic waves (e.g., Bogdan 2000;Chae & Goode 2015;Khomenko & Collados 2015;Jess et al 2016;Zhugzhda & Sych 2018;Chae et al 2019). The dominant period of sunspot oscillations in the low solar atmosphere (photosphere) is about five minutes (Beckers & Schultz 1972;Lites 1988;Wang et al 2020), which is believed to be related to the five-minute p-mode wave (Thomas 1985;Bogdan 2000;Solanki 2003;Yuan 2015).…”

Chromospheric resonances above sunspots and potential seismological applications

“…In the last years several works have pointed out the relevance of resonances in the umbral chromosphere (Botha et al 2011;Snow et al 2015;Felipe 2019) and photosphere (Chae et al 2019). Recently, Jess et al (2020a) claimed the presence of a resonant cavity above a sunspot based on the detection of a high-frequency power peak in He i 10830 Å observations.…”

Signatures of sunspot oscillations and the case for chromospheric resonances

“…They show an enhanced power and a shorter dominant period, from waves with an amplitude of a few hundred meters per second in the five-minute band at the photosphere, to amplitudes of several kilometers per second in the three-minute band at the chromosphere. Various models have been proposed to explain this behaviour [1][2][3] , including the presence of a chromospheric resonance cavity between the photosphere and the transition region [4][5][6][7][8] . Jess et al 9 claimed the detection of observational evidence supporting this model, obtained from the comparison of spectropolarimetric observations and numerical simulations.…”