Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D₂ and Hα lines

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 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

The variation of relative magnetic helicity around major flares

We have investigated the variation of magnetic helicity over a span of several days around the times of 11 X-class flares which occurred in seven active regions (NOAA 9672, 10030, 10314, 10486, 10564, 10696, and 10720) using the magnetograms taken by the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO). As a major result we found that each of these major flares was preceded by a significant helicity accumulation over a long period (0.5 to a few days). Another finding is that the helicity accumulates at a nearly constant rate and then becomes nearly constant before the flares. This led us to distinguish the helicity variation into two phases: a phase of monotonically increasing helicity and the following phase of relatively constant helicity. As expected, the amount of helicity accumulated shows a modest correlation with time-integrated soft X-ray flux during flares. However, the average helicity change rate in the first phase shows even stronger correlation with the time-integrated soft X-ray flux. We discuss the physical implications of this result and the possibility that this characteristic helicity variation pattern can be used as an early warning sign for solar eruptions

Substructure of Quiet Sun Bright Points

Since photospheric bright points (BPs) were first observed, there has been a question as to how are they structured. Are they just single flux tubes or a bundle of the flux-tubes? Surface photometry of the quiet Sun (QS) has achieved resolution close to 0.1" with the New Solar Telescope at Big Bear Solar Observatory. This resolution allowed us to detect a richer spectrum of BPs in the QS. The smallest BPs we observed with TiO 705.68 nm were 0.13", and we were able to resolve individual components in some of the BPs clusters and ribbons observed in the QS, showing that they are composed of the individual BPs. Average size of observed BPs was 0.22".Comment: 4 pages, 3 figures, presented as poster at IAU Symposium 273, 201