Changes in the sensitivity of solar p-mode frequency shifts to activity over three solar cycles

Low-degree solar p-mode observations from the long-lived Birmingham Solar Oscillations Network (BiSON) stretch back further than any other single helioseismic data set. Results from BiSON have suggested that the response of the mode frequency to solar activity levels may be different in different cycles. In order to check whether such changes can also be seen at higher degrees, we compare the response of medium-degree solar p-modes to activity levels across three solar cycles using data from Big Bear Solar Observatory (BBSO), Global Oscillation Network Group (GONG), Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI), by examining the shifts in the mode frequencies and their sensitivity to solar activity levels. We compare these shifts and sensitivities with those from radial modes from BiSON. We find that the medium-degree data show small but significant systematic differences between the cycles, with solar cycle 24 showing a frequency shift about 10 per cent larger than cycle 23 for the same change in activity as determined by the 10.7 cm radio flux. This may support the idea that there have been changes in the magnetic properties of the shallow subsurface layers of the Sun that have the strongest influence on the frequency shifts.Comment: 6 pages, 3 figures, accepted by MNRAS 3rd July 201

A new efficient method for determining weighted power spectra: detection of low-frequency solar p-modes by analysis of BiSON data

We present a new and highly efficient algorithm for computing a power spectrum made from evenly spaced data which combines the noise-reducing advantages of the weighted fit with the computational advantages of the Fast Fourier Transform (FFT). We apply this method to a 10-year data set of the solar p-mode oscillations obtained by the Birmingham Solar Oscillations Network (BiSON) and thereby uncover three new low-frequency modes. These are the l=2, n=5 and n=7 modes and the l=3, n=7 mode. In the case of the l=2, n=5 modes, this is believed to be the first such identification of this mode in the literature. The statistical weights needed for the method are derived from a combination of the real data and a sophisticated simulation of the instrument performance. Variations in the weights are due mainly to the differences in the noise characteristics of the various BiSON instruments, the change in those characteristics over time and the changing line-of-sight velocity between the stations and the Sun. It should be noted that a weighted data set will have a more time-dependent signal than an unweighted set and that, consequently, its frequency spectrum will be more susceptible to aliasing.Comment: 11 pages, 7 Figures, accepted for publication in MNRAS, Figure 6 had to be reduced in size to upload and so may be difficult to view on screen in .ps versio

A Multi-Instrument Investigation of the Frequency Stability of Oscillations Above the Acoustic Cut-Off Frequency with Solar Activity

Below the acoustic cut-off frequency, oscillations are trapped within the solar interior and become resonant. However, signatures of oscillations persist above the acoustic cut-off frequency, and these travelling waves are known as pseudomodes. Acoustic oscillation frequencies are known to be correlated with the solar cycle, but the pseudomode frequencies are predicted to vary in anti-phase. We have studied the variation in pseudomode frequencies with time systematically through the solar cycle. We analyzed Sun-as-a-star data from Variability of Solar Irradiance and Gravity Oscillations (VIRGO), and Global Oscillations at Low Frequencies (GOLF), as well as the decomposed data from Global Oscillation Network (GONG) for harmonic degrees $0\le l \le 200$. The data cover over two solar cycles (1996--2021, depending on instrument). We split them into overlapping 100-day long segments and focused on two frequency ranges, namely $5600$--$6800\,\rm\mu Hz$ and $5600$--$7800\,\rm\mu Hz$. The frequency shifts between segments were then obtained by fitting the cross-correlation function between the segments' periodograms. For VIRGO and GOLF, we found no significant variation of pseudomode frequencies with solar activity. However, in agreement with previous studies, we found that the pseudomode frequency variations are in anti-phase with the solar cycle for GONG data. Furthermore, the pseudomode frequency shifts showed a double-peak feature at their maximum, which corresponds to solar activity minimum, and is not seen in solar activity proxies. An, as yet unexplained, pseudo-periodicity in the amplitude of the variation with harmonic degree $l$ is also observed in the GONG data

Low-degree multi-spectral p-mode fitting

We combine unresolved-Sun velocity and intensity observations at multiple wavelengths from the Helioseismic and Magnetic Imager and Atmospheric Imaging Array onboard the Solar Dynamics Observatory to investigate the possibility of multi-spectral mode-frequency estimation at low spherical harmonic degree. We test a simple multi-spectral algorithm using a common line width and frequency for each mode and a separate amplitude, background and asymmetry parameter, and compare the results with those from fits to the individual spectra. The preliminary results suggest that this approach may provide a more stable fit than using the observables separately

Solar cycle variations of large frequency separations of acoustic modes: Implications for asteroseismology

We have studied solar cycle changes in the large frequency separations that can be observed in Birmingham Solar Oscillations Network (BiSON) data. The large frequency separation is often one of the first outputs from asteroseismic studies because it can help constrain stellar properties like mass and radius. We have used three methods for estimating the large separations: use of individual p-mode frequencies, computation of the autocorrelation of frequency-power spectra, and computation of the power spectrum of the power spectrum. The values of the large separations obtained by the different methods are offset from each other and have differing sensitivities to the realization noise. A simple model was used to predict solar cycle variations in the large separations, indicating that the variations are due to the well-known solar cycle changes to mode frequency. However, this model is only valid over a restricted frequency range. We discuss the implications of these results for asteroseismology.Comment: 9 pages, 11 figures, accepted for publication in MNRAS, references updated, corrections following proof

Quasi-Biennial variations in helioseismic frequencies: Can the source of the variation be localized?

We investigate the spherical harmonic degree (l) dependence of the "seismic" quasi-biennial oscillation (QBO) observed in low-degree solar p-mode frequencies, using Sun-as-a-star Birmingham Solar Oscillations Network (BiSON) data. The amplitude of the seismic QBO is modulated by the 11-yr solar cycle, with the amplitude of the signal being largest at solar maximum. The amplitude of the signal is noticeably larger for the l=2 and 3 modes than for the l=0 and 1 modes. The seismic QBO shows some frequency dependence but this dependence is not as strong as observed in the 11-yr solar cycle. These results are consistent with the seismic QBO having its origins in shallow layers of the interior (one possibility being the bottom of the shear layer extending 5per cent below the solar surface). Under this scenario the magnetic flux responsible for the seismic QBO is brought to the surface (where its influence on the p modes is stronger) by buoyant flux from the 11-yr cycle, the strong component of which is observed at predominantly low-latitudes. As the l=2 and 3 modes are much more sensitive to equatorial latitudes than the l=0 and 1 modes the influence of the 11-yr cycle on the seismic QBO is more visible in l=2 and 3 mode frequencies. Our results imply that close to solar maximum the main influence of the seismic QBO occurs at low latitudes (<45 degrees), which is where the strong component of the 11-yr solar cycle resides. To isolate the latitudinal dependence of the seismic QBO from the 11-yr solar cycle we must consider epochs when the 11-yr solar cycle is weak. However, away from solar maximum, the amplitude of the seismic QBO is weak making the latitudinal dependence hard to constrain.Comment: 10 pages, 6 figures, accepted for publication in MNRA

Cycle dependence of a quasi-biennial variability in the solar interior

We investigated the solar cycle dependence on the presence and periodicity of the Quasi-Biennial Oscillation (QBO). Using helioseismic techniques, we used solar oscillation frequencies from the Global Oscillations Network Group (GONG), Michelson Doppler Imager (MDI), and Helioseismic and Magnetic Imager (HMI) in the intermediate-degree range to investigate the frequency shifts over Cycles 23 and 24. We also examined two solar activity proxies, the F10.7 index and the Mg ii index, for the last four solar cycles to study the associated QBO. The analyses were performed using Empirical Mode Decomposition (EMD) and the Fast Fourier Transform (FFT). We found that the EMD analysis method is susceptible to detecting statistically significant Intrinsic Mode Functions (IMFs) with periodicities that are overtones of the length of the data set under examination. Statistically significant periodicities, which were not due to overtones, were detected in the QBO range. We see a reduced presence of the QBO in Cycle 24 compared to Cycle 23. The presence of the QBO was not sensitive to the depth to which the p-mode travelled, nor the average frequency of the p-mode. The analysis further suggested that the magnetic field responsible for producing the QBO in frequency shifts of p-modes is anchored above approximately 0.95 R⊙

The Sun's interior structure and dynamics, and the solar cycle

The Sun's internal structure and dynamics can be studied with helioseismology, which uses the Sun's natural acoustic oscillations to build up a profile of the solar interior. We discuss how solar acoustic oscillations are affected by the Sun's magnetic field. Careful observations of these effects can be inverted to determine the variations in the structure and dynamics of the Sun's interior as the solar cycle progresses. Observed variations in the structure and dynamics can then be used to inform models of the solar dynamo, which are crucial to our understanding of how the Sun's magnetic field is generated and maintained.Comment: Accepted for publication in Space Science Reviews, 28 pages, 15 figures. Acknowledgements update