We studied the temporal evolution of quasi-biennial oscillations (QBOs) using acoustic mode oscillation frequencies from the Global Oscillation Network Group. The data used here span over more than 25 yr, covering solar cycles 23 and 24 and the ascending phase of cycle 25. The analysis reveals that the QBO-like signals are present in both the cycles, but with different periods. The dominant QBO period in cycle 23 is found to be about 2 yr while it is about 3 yr in cycle 24. Furthermore, the quasi-biennial oscillatory signals are present only during the ascending and high-activity phases of cycle 23 and quickly weaken around 2005 during the declining phase. In comparison, the QBO signals are present throughout the cycle 24, starting from 2009 to 2017. We also explored the depth dependence in QBO signals and obtained a close agreement at all depths, except in the near-surface shear layer. A detailed analysis of the near-surface shear layer suggests that the source region of QBOs is probably within a few thousand kilometers just below the surface.
We looked for signatures of Quasi-Biennial Periodicity (QBP) over different phases of solar cycle by means of acoustic modes of oscillation. Low-degree p-mode frequencies are shown to be sensitive to changes in magnetic activity due to the global dynamo. Recently have been reported evidences in favor of two-year variations in p-mode frequencies. Long high-quality helioseismic data are provided by BiSON (Birmingham Solar Oscillation Network), GONG (Global Oscillation Network Group), GOLF (Global Oscillation at Low Frequency) and VIRGO (Variability of Solar IRradiance and Gravity Oscillation) in…
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 …
Spatio-temporal analysis of helioseismic quasi-biennial oscillations
Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick（华威大学物理与天体物理融合空间与天文研究中心）；Engineering Research Institute “Ventspils International Radio Astronomy Centre (VIRAC)”, Ventspils University of Applied Sciences（文茨皮尔斯应用科学大学文茨皮尔斯国际射电天文中心（VIRAC）工程研究所）
We investigated the solar cycle dependency 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 & 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 MgII index, for the last four solar cycles to study the associated QBO. The analyses were performed using Empirical Mode Decomposit…
Quasi-biennial oscillation (QBO) of solar magnetic activities is intrinsic to dynamo mechanism, but still far from fully understood. In this work, the phase and amplitude asymmetry of solar QBO of Halpha flare activity in the northern and southern hemispheres is studied by the ensemble empirical mode decomposition, the cross-correlation analysis, and the wavelet transform technique. The following results are found: (1) solar QBO of Halpha flare index in the two hemispheres has a complicated phase relationship, but does not show any systematic regularity; (2) the solar cycle mode of solar Halph…
Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline using the shallow water magnetohydrodynamic approximation. Our analysis shows that the combination of typical differential rotation and a toroidal magnetic field with a strength > 10^5 G triggers the instability of the m=1 magnetic Rossby wave harmonic with a period of 2 years. This harmonic is antisymmetric with respect to the equator and …
This study aims to provide further evidence for the potential influence of the global solar magnetic field on localised chromospheric jets, the macrospicules (MS). To find a connection between the long-term variation of properties of MS and other solar activity proxies, including e.g. the temporal variation of the frequency shift of solar global oscillations, sunspot area, etc., a database overarching seven years of observations was built up. This database contains 362 MS, based on observations at the 30.4 nm of the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SD…
Solar quasi-biennial oscillations with period range 0.6 to 4 years, are prominent in records of solar activity. Here we show that the 1.6 year quasi-biennial oscillation in solar activity has the exceptional feature of phase inversion between each solar cycle in the sequence of four solar cycles, 20 to 23. The hypothesis advanced is that this feature is due to synchronicity between solar activity and planetary alignment. An index of alignment between Earth and Mercury, Venus, Jupiter and Saturn is shown to have dominant peaks of alignment separated by 1.6 years in each solar cycle with, howeve…
In this work, we apply multichannel singular spectrum analysis (MSSA), a data-adaptive, multivariate, non-parametric technique that simultaneously exploits the spatial and temporal correlations of the input data to extract common modes of variability, to investigate the intermediate quasi-periodicities of the Fe XIV green coronal emission line at 530.3 nm for the period between 1944 and 2008. Our analysis reveals several significant mid-term periodicities in a range from about one to four years that are consistent with the so-called quasi-biennial oscillations (QBOs), which have been detected …
Quasi-biennial oscillations (QBOs) are considered as a fundamental mode of solar magnetic activity at low latitudes ($\leq50^\circ$). However, the evolutionary aspect and the hemispheric distribution of solar QBOs at high latitudes ($\geq60^\circ$) are rarely studied. Here, a relatively novel time-frequency analysis technique, named the synchrosqueezed wavelet transform, is applied to extract the main components of the polar faculae in the northern and southern hemispheres for the time interval from August 1951 to December 1998. It is found as the following: (1) Apart from the 22-year Hale cyc…
Contex: Solar magnetic activity exhibits variations with periods between 1.5--4 years, the so-called quasi-biennial oscillations (QBOs), in addition to the well-known 11-year Schwabe cycles. Solar dynamo is thought to be the responsible mechanism for generation of the QBOs. Aims: In this work, we analyse sunspot areas to investigate the spatial and temporal behaviour of the QBO signal and study the responsible physical mechanisms using simulations from fully nonlinear mean-field flux-transport dynamos. Methods: We investigated the behaviour of the QBOs in the sunspot area data in full disk, an…
Quasi-biennial oscillation (QBO) is a well-known quasi-periodical variation with characteristic time 0.5-4 years in different solar, heliospheric and cosmic ray characteristics. In this paper a hypothesis is checked on the causes of the apparent lack of correlation between solar and heliospheric QBOs, then the possible mechanisms of QBO in the GCR intensity are discussed as well as the idea of the same nature of the step-like changes and Gnevyshev Gap effects in the GCR intensity. Our main conclusions are as follows: 1) In the first approximation the hypothesis is justified that the change in …
Jets, whatever small (e.g. spicules) or large (e.g. macrospicules) their size, may play a key role in momentum and energy transport from photosphere to chromosphere and at least to the low corona. Here, we investigate the properties of abundant, large-scale dynamic jets observable in the solar atmosphere: the macrospicules (MS). These jets are observationally more distinct phenomena than their little, and perhaps more ubiquitous, cousins, the spicules. Investigation of long-term variation of the properties of macrospicules may help to a better understanding of their underlying physics of gener…
Using a nonlinear mean-field solar dynamo model, we study relationships between the amplitude of the `extended' mode of migrating zonal flows (`torsional oscillations') and magnetic cycles, and investigate whether properties the torsional oscillations in subsurface layers and in the deep convection zone can provide information about the future solar cycles. We consider two types of dynamo models: models with regular variations of the alpha-effect, and models with stochastic fluctuations, simulating `long'- and 'short-memory' types of magnetic activity variations. It is found that torsional osc…
The last solar minimum was, by recent standards, unusually deep and long. We are now close to the maximum of the subsequent solar cycle, which is relatively weak. In this article we make comparisons between different global (unresolved) measures of the Sun's magnetic activity, to investigate how they are responding to this weak-activity epoch. We focus on helioseismic data, which are sensitive to conditions, including the characteristics of the magnetic field, in the solar interior. Also considered are measures of the magnetic field in the photosphere (sunspot number and sunspot area), the chr…
The solar-activity-cycle minimum observed between Cycles 23 and 24 is generally regarded as being unusually deep and long. That minimum is being followed by one of the smallest amplitude cycles in recent history. We perform an in-depth analysis of this minimum with helioseismology. We use Global Oscillation Network Group (GONG) data to demonstrate that the frequencies of helioseismic oscillations are a sensitive probe of the Sun's magnetic field: The frequencies of the helioseismic oscillations were found to be systematically lower in the minimum following Cycle 23 than in the minimum precedin…
Manifestations of the solar magnetic activity through periodicities of about 11 and 2 years are now clearly seen in all solar activity indices.In this paper, we add information about the mechanism driving the 2 year period by studying the time and latitudinal properties of acoustic modes that are sensitive probes of the subsurface layers. We use almost 17 years of high quality resolved data provided by the Global Oscillation Network Group (GONG) to investigate the solar cycle changes in p-mode frequencies for spherical degrees l from 0 to 120 and 1.6 mHz < nu < 3.5 mHz. For both periodic compo…
We apply the ring-diagram technique to high resolution Dopplergrams in order to estimate the variation in oscillation mode parameters between active and quiet regions. We demonstrate that the difference in mode parameters between two quiet regions can be as large as those between a pair of active and quiet region. This leads us to conclude that the results derived on the basis of a single quiet region could be biased.
We report on a signature of chromospheric downflows in two emerging-flux regions detected by time-distance helioseismology analysis. We use both chromospheric intensity oscillation data in the Ca II H line and photospheric Dopplergrams in the Fe I 557.6nm line obtained by Hinode/SOT for our analyses. By cross-correlating the Ca II oscillation signals, we have detected a travel-time anomaly in the plage regions; outward travel times are shorter than inward travel times by 0.5-1 minute. However, such an anomaly is absent in the Fe I data. These results can be interpreted as evidence of downflows…
Helioseismic holography is an imaging technique used to study heterogeneities and flows in the solar interior from observations of solar oscillations at the surface. Holograms contain noise due to the stochastic nature of solar oscillations. We provide a theoretical framework for modeling signal and noise in Porter-Bojarski helioseismic holography. The wave equation may be recast into a Helmholtz-like equation, so as to connect with the acoustics literature and define the holography Green's function in a meaningful way. Sources of wave excitation are assumed to be stationary, horizontally homo…
As the amount of asteroseismic data available continues to grow, the inability to accurately model observed oscillation frequencies is becoming a critical problem for interpreting these frequencies. A major component of this problem is the modeling of the near-surface layers. Our aim is to develop a method to estimate the effect of the near-surface layers on oscillation frequencies. In the proposed method we numerically estimate eigenfunctions in 3D hydrodynamic simulations. We match those to the eigenfunctions calculated from the classic equations applied to the horizontal averages of the str…
We present a new and up-to-date analysis of the solar low-degree $p$-mode parameter shifts from the Birmingham Solar-Oscillations Network (BiSON) over the past 22 years, up to the end of 2014. We aim to demonstrate that they are not dominated by changes in the asymmetry of the resonant peak profiles of the modes and that the previously published results on the solar-cycle variations of mode parameters are reliable. We compare the results obtained using a conventional maximum likelihood estimation algorithm and a new one based on the Markov Chain Monte Carlo (MCMC) technique, both taking into a…
The solar-cyle variation of acoustic mode frequencies has a frequency dependence related to the inverse mode inertia. The discrepancy between model predictions and measured oscillation frequencies for solar and solar-type stellar acoustic modes includes a significant frequency-dependent term known as the surface term that is also related to the inverse mode inertia. We parametrize both the surface term and the frequency variations for low-degree solar data from Birmingham Solar-Oscillations Network (BiSON) and medium-degree data from the Global Oscillations Network Group (GONG) using the mode …
At intermediate and high degree $l$, solar p- and f modes can be considered as surface waves. Using variational principle, we derive an integral expression for the group velocities of the surface waves in terms of adiabatic eigenfunctions of normal modes, and address the benefits of using group-velocity measurements as a supplementary diagnostic tool in solar seismology. The principal advantage of using group velocities, when compared with direct analysis of the oscillation frequencies, comes from their smaller sensitivity to the uncertainties in the near-photospheric layers. We address some n…
We studied the presence and spatiotemporal evolution of the quasi-biennial oscillations (QBOs) in the rotation rate residuals at target depths of 0.90$R_{\odot}$, 0.95$R_{\odot}$, and 0.99$R_{\odot}$ and at low (0 -- 30$^{\circ}$), mid (30 -- 50$^{\circ}$), and high (50 -- 70$^{\circ}$) latitudinal bands. To achieve these objectives we used data from the Michelson Doppler Imager (MDI) on {\it the Solar and Heliospheric Observatory} ({\it SOHO}) and the Helioseismic and Magnetic Imager (HMI) on the {\it Solar Dynamics Observatory} ({\it SDO}), covering solar cycles 23 and 24, respectively. The …
Solar torsional oscillations are migrating bands of slower- and faster-than-average rotation, which are strongly related to the Sun's magnetic cycle. We perform a long-term study (16 yr) of hemispherical asymmetry in solar torsional oscillation velocity using helioseismic data for the first time. We study the north-south asymmetry in the velocity using the zonal flow velocities obtained by ring diagram analysis of the Global Oscillation Network Group (GONG) Doppler images. We find significant hemispherical asymmetry in the torsional oscillation velocity and explore its variation with respect t…
We present an analysis of the variability of the solar oscillation spectrum during solar cycle 23 and its extended minimum. We use simultaneous observations of the low-degree solar p modes collected by the space-based, Sun-as-a-star GOLF (radial velocity) and VIRGO (intensity) instruments, and by the ground-based, multi-site network GONG. We investigate in particular the response of the p-mode eigenfrequencies to the observed peculiar deep solar minimum of surface activity of 2007-2009 as compared with the previous solar cycle 23. We study the different temporal variations of the p-mode freque…
Normal-mode coupling is a technique applied to probe the solar interior using surface observations of oscillations. The technique, which is straightforward to implement, makes more use of the seismic information in the wavefield than other comparable local imaging techniques and therefore has the potential to significantly improve current capabilities. Here, we examine supergranulation power spectra using mode-coupling analyses of intermediate-to-high-degree modes by invoking a Cartesian-geometric description of wave propagation under the assumption that the localized patches are much smaller …
The Sun is a variable star whose magnetic activity varies most perceptibly on a timescale of approximately 11 years. However, significant variation is also observed on much shorter timescales. We observe a quasi-biennial (2 year) signal in the natural oscillation frequencies of the Sun. The oscillation frequencies are sensitive probes of the solar interior and so by studying them we can gain information about conditions beneath the solar surface. Our results point strongly to the 2 year signal being distinct and separate from, but nevertheless susceptible to the influence of, the main 11 year …
In addition to the well-known 11-year solar cycle, the Sun's magnetic activity also shows significant variation on shorter time scales, e.g. between one and two years. We observe a quasi-biennial (2-year) signal in the solar p-mode oscillation frequencies, which are sensitive probes of the solar interior. The signal is visible in Sun-as-a-star data observed by different instruments and here we describe the results obtained using BiSON, GOLF, and VIRGO data. Our results imply that the 2-year signal is susceptible to the influence of the main 11-year solar cycle. However, the source of the signa…
Normal modes of oscillation of the Sun are useful probes of the solar interior. In this work, we use the even-order splitting coefficients to study the evolution of magnetic fields in the convection zone over solar cycle 23, assuming that the frequency splitting is only due to rotation and a large scale magnetic field. We find that the data are best fit by a combination of a poloidal field and a double-peaked near-surface toroidal field. The toroidal fields are centered at r=0.999R_solar and r=0.996R_solar and are confined to the near-surface layers. The poloidal field is a dipole field. The p…
The pattern of migrating zonal flow bands associated with the solar cycle, known as the torsional oscillation, has been monitored with continuous global helioseismic observations by the Global Oscillations Network Group, together with those made by the Michelson Doppler Imager onboard the Solar and Heliosepheric Observatory and its successor the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, since 1995, giving us nearly two full solar cycles of observations. We report that the flows now show traces of the mid-latitude acceleration that is expected to become the main e…
The parameters of the p-mode oscillations vary with solar activity. Such temporal variations provide insights for the study of the structural and dynamical changes occurring in the Sun's interior throughout the solar cycle. We present here a complete picture of the temporal variations of the global p-mode parameters (excitation, damping, frequency, peak asymmetry, and rotational splitting) over the entire solar cycle 23 and the beginning of cycle 24 as observed by the space-based, Sun-as-a-star helioseismic GOLF and VIRGO instruments onboard SoHO.
We examine the role of small-scale transients in the formation and evolution of solar coronal plumes. We study the dynamics of plume footpoints seen in the vicinity of a coronal hole using the Atmospheric Imaging Assembly (AIA) images, the Helioseismic and Magnetic Imager (HMI) magnetogram on board the Solar Dynamics Observatory (SDO) and spectroscopic data from the Interface Region Imaging Spectrograph (IRIS). Quasi-periodic brightenings are observed in the base of the plumes and are associated with magnetic flux changes. With the high spectral and spatial resolution of IRIS, we identify the …
The frequency, $ν_{\rm max}$, at which the envelope of pulsation power peaks for solar-like oscillators is an important quantity in asteroseismology. We measure $ν_{\rm max}$ for the Sun using 25 years of Sun-as-a-Star Doppler velocity observations with the Birmingham Solar-Oscillations Network (BiSON), by fitting a simple model to binned power spectra of the data. We also apply the fit to Sun-as-a-Star Doppler velocity data from GONG and GOLF, and photometry data from VIRGO/SPM on the ESA/NASA SOHO spacecraft. We discover a weak but nevertheless significant positive correlation of the solar $…
While the {\it Helioseismic and Magnetic Imager} (HMI) onboard the {\it Solar Dynamics Observatory} (SDO) provides Doppler velocity [$V$], continuum intensity [$I_C$], and line-depth [$Ld$] observations, each of which is sensitive to the five-minute acoustic spectrum, the {\it Atmospheric Imaging Array} (AIA) also observes at wavelengths -- specifically the 1600 and 1700 Angstrom bands -- that are partly formed in the upper photosphere and have good sensitivity to acoustic modes. In this article we consider the characteristics of the spatio--temporal Fourier spectra in AIA and HMI observables …
The integrated brightness of the Sun shows variability on time-scales from minutes to decades. This variability is mainly caused by pressure mode oscillations, by granulation and by dark spots and bright faculae on the surface of the Sun. By analyzing the frequency spectrum of the integrated brightness we can obtain greater knowledge about these phenomena. It is shown how the frequency spectrum of the integrated brightness of the Sun in the frequency range from 0.1 to 3.2 mHz shows clear signs of both granulation, faculae and p-mode oscillations and that the measured characteristic time-scales…
The helioseismic Global Oscillation at Low Frequency (GOLF) and the Variability of solar Irradiance and Gravity Oscillations (VIRGO) instruments onboard SoHO, have been observing the Sun continuously for the last 14 years. In this preliminary work, we characterize the acoustic modes over the entire p-mode range in both, Doppler velocity and luminosity, with a special care for the low-frequency modes taking advantage of the stability and the high duty cycle of space observations.
Oscillatory Phase and Acoustic Travel-Time Inconsistencies Measured between SDO/HMI and GONG Dopplergrams
Stanford University（斯坦福大学）；Indian Institute of Astrophysics（印度天体物理研究所）；National Solar Observatory（国家太阳观测台）；National Research University TIIAME（塔什干国立研究技术大学）
Using data from the Helioseismic Magnetic Imager, we report on the amplitudes and phase relations of oscillations in quiet-Sun, plage, umbra and the polarity inversion line (PIL) of an active region NOAA$\#$11158. We employ Fourier, wavelet and cross correlation spectra analysis. Waves with 5-minute periods are observed in umbra, PIL and plage with common phase values of $ϕ(v,I)=\fracπ{2}$, $ϕ(v,B_{los})=-\fracπ{2}$. In addition, $ϕ(I,B_{los})=π$ in plage are observed. These phase values are consistent with slow standing or fast standing surface sausage wave modes. The line width variations, a…
Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycle. Here we report the statistical analysis of grouped solar flare (GSF) and sunspot number (SN) during the time interval from January 1965 to March 2009. We find that, 1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity, the quasi-biennial oscillation (QBO), and the eleven-year Schwabe cycle (ESC), but the specific values are not absolutely identical; 2) the ESC si…
Solar activity has significantly changed over the last two Schwabe cycles. After a long and deep minimum at the end of Cycle 23, the weaker activity of Cycle 24 contrasts with the previous cycles. In this work, the response of the solar acoustic oscillations to solar activity is used in order to provide insights on the structural and magnetic changes in the sub-surface layers of the Sun during this on-going unusual period of low activity. We analyze 18 years of continuous observations of the solar acoustic oscillations collected by the Sun-as-a-star GOLF instrument onboard the SoHO spacecraft.…
The Birmingham Solar-Oscillations Network (BiSON) has collected helioseismic data over three solar cycles. We use these data to determine how the internal properties of the Sun during this minimum differ from the previous two minima. The cycle 24 data show oscillatory differences with respect to the other two sets, indicating relatively localized changes in the solar interior. Analysis of MDI data from Cycle 23 and Cycle 24 also show significant signs of differences.
Coronal bright points (BPs) are small-scale luminous features seen in the solar corona. Quasi-periodic brightenings are frequently observed in the BPs and are generally linked with underneath magnetic flux changes. We study the dynamics of a BP seen in the coronal hole using the Atmospheric Imaging Assembly (AIA) images, the Helioseismic and Magnetic Imager (HMI) magnetogram on board the Solar Dynamics Observatory (SDO) and spectroscopic data from the newly launched Interface Region Imaging Spectrograph (IRIS). The detailed analysis shows that the BP evolves throughout our observing period alo…
Numerous analyses suggest the existence of various quasi-periodicities in solar activity. The power spectrum of solar activity recorded in sunspot data is dominated by the $\sim$11-year quasi-periodicity, known as the Schwabe cycle. In the mid-term range (1 month -- 11 years) a pronounced variability known as a quasi-biennial oscillation (QBO) is widely discussed. In the shorter time scale a pronounced peak, corresponding to the synodic solar rotation period ($\sim$ 27 days) is observed. Here we revisited the mid-term solar variability in terms of statistical dynamic of fully turbulent systems…
The Sun's magnetic field varies in multiple time scales. Observations show that the minimum between cycles 24 and 25 was the second consecutive minimum which was deeper and wider than several earlier minima. Since the active regions observed at the Sun's surface are manifestations of the magnetic field generated in the interior, it is crucial to investigate/understand the dynamics below the surface. In this context, we report, by probing the solar interior with helioseismic techniques applied to long-term oscillations data from the Global Oscillation Network Group (GONG), that the seismic mini…
We present a study of multi-wavelength observations, of a C 2.3 solar flare in Active Region NOAA 12353, observed on 2015 May 23, which reveal new properties of acoustic waves in the flaring region. The space-, and ground-based data measured by the HELioseismological Large Regions Interferometric Device, operating at the Vacuum Tower Telescope, the Atmospheric Imaging Assembly, and Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory, were used in this paper. First, using power spectra of solar oscillations, we identified the dominant frequencies and their location at seven …
Sunspots are known to be strong absorbers of solar oscillation modal power. The most convincing way to demonstrate this is done via Fourier-Hankel decomposition (FHD), where the local oscillation field is separated into in- and outgoing waves, showing the reduction in power. Due to the Helioseismic and Magnetic Imager's high-cadence Doppler measurements, power absorption can be investigated at frequencies beyond the acoustic cutoff frequency. We perform an FHD on five sunspot regions and two quiet-Sun control regions and study the resulting absorption spectra $α_\ell(ν)$, specifically at frequ…
Although there are now some tentative signs that the start of cycle 24 has begun there is still considerable interest in the somewhat unusual behaviour of the current solar minimum and the apparent delay in the true start of the next cycle. While this behaviour is easily tracked by observing the change in surface activity a question can also be asked about what is happening beneath the surface where the magnetic activity ultimately originates? In order to try to answer this question we can look at the behaviour of the frequencies of the Sun's natural seismic modes of oscillation - the p modes.…
Sub-surface structural changes associated with successive 11-yr solar activity cycles have been progressively more confined near the surface: new helioseismic results on Cycles 22 -- 25 from BiSON
University of Birmingham（伯明翰大学）；Yale University（耶鲁大学）
