Solar Oscillation Frequencies Research Articles

Time Variation of the Solar Tachocline

We have used solar oscillation frequencies and frequency splittings obtained over solar cycles 23 and 24 and the rising phase of solar cycle 25 to investigate whether the tachocline properties (the change in the rotation rate across the tachocline. i.e., the jump, the width, and the position) show any time variation. We confirm that the change in rotation rate across the tachocline changes substantially; however, the change does not show a simple correlation with solar cycle unlike, for instance, changes in mode frequencies. The change during the ascending phase of solar cycle 25 is almost a mirror image of the change during the descending part of solar cycle 24, tempting us to speculate that the tachocline has a much longer period than either the sunspot or the magnetic cycle. We also find that the position of the tachocline, defined as the midpoint of the change in rotation rate, showed significant changes during solar cycle 24. The width of the tachocline, on the other hand, has shown significant changes during solar cycle 23 but not later. The change in the tachocline becomes more visible if we look at the upper and lower extents of the tachocline, defined as (position ± width). We find that for epochs around solar maxima and minima, the extent decreases before increasing again—a few more years of data should clarify this trend. Our results reinforce the need to continue helioseismic monitoring of the Sun to understand solar activity and its evolution.

Latitudinal Dependence of Variations in the Frequencies of Solar Oscillations Above the Acoustic Cut-Off

At high frequencies beyond the acoustic cut-off, a peak-like structure is visible in the solar power spectrum. Known as the pseudo-modes, their frequencies have been shown to vary in anti-phase with solar magnetic activity. In this work, we determined temporal variations in these frequencies across the solar disc, with the aim of identifying any potential latitudinal dependence of pseudo-mode frequency shifts. We utilised nearly 22 years of spatially resolved GONG data for all azimuthal orders, m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\ extit{m}$\\end{document}, for harmonic degrees 0≤l≤200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$0\\leq l\\leq 200$\\end{document}, and determined shifts using the resampled periodogram method. Periodogram realisations were created from overlapping, successive 216 day-long segments in time, and cropped to 5600 – 6800 μHz. Cross-correlation functions were then repeatedly generated between these realisations to identify any variation in frequency and the uncertainty. We categorised each mode by its latitudinal sensitivity and used this categorisation to produce average frequency shifts for different latitude bands (15∘ and 5∘ in size) which were compared to magnetic proxies, the F10.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$F_{\\mathrm{10.7}}$\\end{document} index and GONG synoptic maps. Morphological differences in the pseudo-mode shifts between different latitudes were found, which were most pronounced during the rise to solar maximum where shifts reach their minimum values. At all latitudes, shift behaviour was strongly in anti-correlation with the activity proxy. Additionally, periodicities shorter than the 11-year cycle were observed. Wavelet analysis was used to identify a periodicity of four years at all latitudes.

Asphericity of the Base of the Solar Convection Zone

We have used solar oscillation frequencies and frequency splittings obtained over solar cycles 23 and 24 to investigate whether the base of the solar convection zone shows any departure from spherical symmetry. We used the even-order splitting coefficients, a 2–a 8, and estimated the contributions from each one separately. The average asphericity over the two solar cycles was determined using frequencies and splittings obtained with a 9216-day time series. We find that evidence of asphericity is, at best, marginal: the a 2 component is consistent with no asphericity, the a 4 and a 6 components yield results at a level a little greater than 1σ, while the a 8 component shows a signature below 1σ. The combined results indicate that the time average of the departure from the spherically symmetric position of the base of the convection zone is ≲0.0001R ⊙. We have also used helioseismic data obtained from time series of lengths of 360, 576, 1152, and 2304 days in order to examine the consistency of the results and evaluate whether there is any time variation. We find that the evidence for time variation is statistically marginal in all cases, except for the a 6 component, for which tests consistently yield p-values of less than 0.05.

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

ABSTRACT 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⊙.

Temporal Variation of Solar Wind in Controlling Solar Wind‐Magnetosphere‐Ionosphere Energy Budget

AbstractPeriodic oscillations associated with Alfven waves with periods ranging from several tens of minutes to several hours are commonly seen in the solar wind. It is not yet known how the solar wind oscillation frequency, and thus its temporal variation, regulates the energy flow through the coupled solar wind‐magnetosphere‐ionosphere‐thermosphere system. Utilizing the Coupled Magnetosphere‐Ionosphere‐Thermosphere Model driven by solar wind and interplanetary magnetic field (IMF), we have analyzed the magnetosphere‐ionosphere‐thermosphere system response to IMF Bz oscillations with periods of 10, 30, and 60 min from the perspective of energy budget. Our results indicate that the energy flow from the solar wind to geospace depends on the IMF Bz oscillation frequency. The energy coupling efficiency, defined as the ratio of the globally integrated joule heating to Akasofu's Epsilon function, is higher for lower frequency IMF Bz oscillations. Joule heating in the upper atmosphere depends not only on directly driven processes due to solar wind variability but also on the intrinsic dynamics of the magnetosphere (i.e., loading‐unloading process). This work highlights the critical role of solar wind and IMF temporal variation and the inductive inertia and resistance of coupled magnetosphere‐ionosphere system in controlling the energy transfer in the coupled solar wind‐geospace system, which has not been explored before.

Solar-Cycle variation in the photospheric mean velocity flows: GONG observations

AbstractThe solar oscillation frequencies have shown variation over the solar activity cycle, which is believed to be the indicator of the structural and magnetic changes taking place in the Sun. The ground-based network of six identical solar telescopes in the Global Oscillation Network Group (GONG) program has been nearly-continuously observing the Sun since the last quarter of the year 1995 for Doppler imaging of the solar-disk aimed to study the oscillations and velocity flows on the surface of the Sun. In this work, we study the variations in the solar disk-integrated mean velocity flows on the solar surface as observed with the GONG over the complete Solar Cycle 23 and ongoing Cycle 24. The correlation analysis of these solar photospheric mean velocity flows relative to the various solar activity indicators is also discussed.

Search for possible solar influences in Ra-226 decays

Measurements of Ra-226 activity from eight HPGe gamma ray detectors at the NC State University PULSTAR Reactor were analyzed for evidence of periodic variations, with particular attention to annual variations. All measurements were made using the same reference source, and data sets were of varying length taken over the time period from September 1996 through August 2014. Clear evidence of annual variations was observed in data from four of the detectors. Short time periodograms from the data sets suggest temporal variability of both the amplitude and frequency of these variations. The annual variations in two of the data sets show peak values near the first of February, while surprisingly, the annual variations in the other two are roughly out of phase with the first two. Three of the four detectors exhibited annual variations over approximately the same time period. A joint statistic constructed by combining spectra from these three shows peaks approximating the frequencies of solar r-mode oscillations with νR=11.74cpy, m=1, and l=3, 5, 6. The fact that similar variations were not present in all detectors covering similar time periods rules out variations in activity as the cause, and points to differing sensitivities to unspecified environmental parameters instead. In addition to seasonal variations, the modulation of environmental parameters by solar processes remains a possible explanation of periodogram features, but without requiring new physics.

Variations of the Position of Perturbation Layer of Solar Frequency Shifts

The variation of solar p-mode oscillation frequency with the solar magnetic activity is called the frequency shift, which is considered to be caused by a perturbation in a thin layer near the solar surface. A method for predicting the frequency shift by the magnetic activity index and the solar model had been developed previously. In this method, the frequency shift depends on the intensity of magnetic activity and the position of the perturbing source. The intensity of magnetic activity is considered to be proportional to the magnetic activity index. And the position of the perturbing source was assumed to be fixed previously. This paper has studied the variation of the position of perturbing source. By using the observed p-mode oscillation frequency and Ca II index of the Sun, it is found that the position of perturbing source may be varied with the solar magnetic activity. In the solar maximum year, the position of perturbing source is deeper, but it is shallower in the solar minimum year.

Frequency shifts of resonant modes of the Sun due to near-surface convective scattering

AbstractMeasurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the “surface term.” The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary 3D flows, can be reduced to an effective “quiet-Sun” wave equation with altered sound speed, Brünt–Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

Sound speed and oscillation frequencies for solar models evolved with Los Alamos ATOMIC opacities

AbstractLos Alamos National Laboratory has calculated a new generation of radiative opacities (OPLIB data using the ATOMIC code) for elements with atomic number Z = 1-30 with improved physics input, updated atomic data, and finer temperature grid to replace the Los Alamos LEDCOP opacities released in the year 2000. We calculate the evolution of standard solar models including these new opacities, and compare with models evolved using the Lawrence Livermore National Laboratory OPAL opacities (Iglesias & Rogers 1996). We use the solar abundance mixture of Asplund et al. 2009. The Los Alamos ATOMIC opacities (Colgan et al. 2013a, 2013b, 2015) have steeper opacity derivatives than those of OPAL for temperatures and densities of the solar interior radiative zone. We compare the calculated nonadiabatic solar oscillation frequencies and solar interior sound speed to observed frequencies and helioseismic inferences. The calculated sound-speed profiles are similar for models evolved using either the updated Iben evolution code (see Guzik & Mussack 2010), or the MESA evolution code (Paxton et al. 2015). The LANL ATOMIC opacities partially mitigate the ‘solar abundance problem’.

Helioseismic measurements in the solar envelope using group velocities of surface waves

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 numerical examples where group velocities are used to reveal inconsistencies between the solar models and the seismic data. Further, we implement the group-velocity measurements to the calibration of the specific entropy, helium abundance Y and heavy-element abundance Z in the adiabatically-stratified part of the solar convective envelope, using different recent versions of the equation of state. The results are in close agreement with our earlier measurements based on more sophisticated analysis of the solar oscillation frequencies (Vorontsov et al. 2013, MNRAS 430, 1636). These results bring further support to the downward revision of the solar heavy-element abundances in recent spectroscopic measurements.

Variation of solar oscillation frequencies in solar cycle 23 and their relation to sunspot area and number(Corrigendum)

Variation of solar oscillation frequencies in solar cycle 23 and their relation to sunspot area and number<i>(Corrigendum)</i>

Solar oscillations in cycle 24 ascending

Solar oscillation frequencies are known to follow the trend of solar cycle and show a strong correlation with various activity indices. However, the extended minimum between cycles 23 and 24 has raised several questions on the correlation between frequencies and solar activity where frequencies with different mode sets sensed different minima. In this paper, we analyze intermediate-degree mode frequencies as the Sun emerges from the unusually long period of minimal magnetic activity to study their behaviour with activity indices and compare results with the corresponding phase of cycle 23. We show that a model based on the rising phase of cycle 23 is a good predictor for behaviour in the rising phase of cycle 24.

Variation of solar oscillation frequencies in solar cycle 23 and their relation to sunspot area and number

Aims. Studying the long term evolution of the solar acoustic oscillations is necessary for understanding how the large-scale solar dynamo operates. In particular, an understanding of the solar cycle variation in the frequencies of solar oscillations can provide a powerful diagnostic tool for constraining various dynamo models. In this work, we report the temporal evolution of solar oscillations for the solar cycle 23, and correlate with solar magnetic activity indices.Methods. We use solar oscillation frequencies obtained from the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, correlate them with the sunspot number provided by the international sunspot number, R I , and compare them with the sunspot number calculated with the Sunspot Tracking And Recognition Algorithm (STARA).Results. We find that the mean frequency shifts correlate very well with the sunspot numbers obtained from two different datasets. We also find a hysteresis-type behaviour for the STARA sunspot area and mean magnetic field strength for the different phases of the solar cycle. The increase in solar oscillation frequencies precedes slightly the increase in total sunspot area and the mean magnetic field strength for the solar cycle 23. We briefly discuss the cyclic behaviour in the context of p-mode frequencies.

HOW PECULIAR WAS THE RECENT EXTENDED MINIMUM: A HINT TOWARD DOUBLE MINIMA

In this paper, we address the controversy regarding the recent extended solar minimum as seen in helioseismic low- and intermediate-degree mode frequencies: studies from different instruments identify different epochs of seismic minima. Here we use mode frequencies from a network of six identical instruments, the Global Oscillation Network Group, continuously collecting data for more than 15 years, to investigate the epoch of minimum in solar oscillation frequencies prior to the beginning of solar cycle 24. We include both low- and intermediate-degree modes in the l range of 0-120 and frequency range of 2.0-3.5 mHz. In this analysis, we demonstrate that there were indeed two minima in oscillation frequencies, depending upon the degree of modes, or more precisely the lower turning point radius of the propagating wave. We also analyze frequencies as a function of latitude to identify the beginning of solar cycle 24. We observe two minima at high latitudes and a single minimum at mid/low latitudes. This scenario is in contrast to cycle 23 where the epoch of seismic minimum did not change with latitude or depth. Our results also hint at a possible role of the relic magnetic field in modifying the oscillation frequencies of modes sampling deeper layers.

Are short-term variations in solar oscillation frequencies the signature of a second solar dynamo?

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 signal appears to be separate from that of the 11-year cycle. We speculate as to whether it might be the signature of a second dynamo, located in the region of near-surface rotational shear.

Temporal changes in the frequencies of the solar p-mode oscillations during solar cycle 23

AbstractWe present a study of the temporal changes in the sensitivities of the frequencies of the solar p-mode oscillations to corresponding changes in the levels of solar activity during Solar Cycle 23. From MDI and GONG++ full-disk Dopplergram three-day time series obtained between 1996 and 2008 we have computed a total of 221 sets of m-averaged power spectra for spherical harmonic degrees ranging up to 1000. We have then fit these 284 sets of m-averaged power spectra using our WMLTP fitting code and both symmetric Lorentzian profiles for the peaks as well as the asymmetric profile of Nigam and Kosovichev to obtain 568 tables of p-mode parameters. We then inter-compared these 568 tables, and we performed linear regression analyses of the differences in p-mode frequencies, widths, amplitudes, and asymmetries as functions of the differences in as many as ten different solar activity indices. From the linear regression analyses that we performed on the frequency difference data sets, we have discovered a new signature of the frequency shifts of the p-modes. Specifically, we have discovered that the temporal shifts of the solar oscillation frequencies are positively correlated with the changes in solar activity below a limiting frequency. They then become anti-correlated with the changes in activity for a range of frequencies before once again becoming positively-correlated with the activity changes at very high frequencies. We have also discovered that the two frequencies where the sensitivities of the temporal frequency shifts change sign also change in phase with the average level of solar activity.

Solar Cycle Related Changes at the Base of the Convection Zone

The frequencies of solar oscillations are known to change with solar activity. We use principal component analysis to examine these changes with high precision. In addition to the well-documented changes in solar normal mode oscillations with activity as a function of frequency, which originate in the surface layers of the Sun, we find a small but statistically significant change in frequencies with an origin at and below the base of the convection zone. We find that at r = (0.712+ 0.0097−0.0029) R☉, the change in sound speed is δ c2/c2 = (7.23 ± 2.08) × 10−5 between high and low activity. This change is very tightly correlated with solar activity. In addition, we use the splitting coefficients to examine the latitudinal structure of these changes. We find changes in sound speed correlated with surface activity for r≳ 0.9 R☉.

Testing Reynolds stress model in solar interior

AbstractThe Reynolds stress model (RSM) for turbulent convection motion is compared to the MLT in solar model. The free parameters involved in the RSM are also tested with the aid of helioseismology. It is found that, the structure of solar convection zone is differ from the MLT when using the RSM, especially for the Reynolds correlations and the temperature gradient. Both the local and non-local RSM can improve the calculated solar p-mode oscillation frequencies with the appropriate choice of the parameters' value.

Modeling Solar Oscillation Power Spectra. I. Adaptive Response Function for Doppler Velocity Measurements

Improving the accuracy and resolution of helioseismic inversions calls for more accurate modeling of the observational p-mode power spectra from which the solar oscillation frequencies are traditionally measured. We present a new technique of calculating the response function (leakage matrix) for Doppler velocity measurements that is based largely on an analytical description of the relevant instrumental and physical effects. The computational efficiency of the new approach allows us to implement the response function in an adaptive manner: i.e., the compensation for instrumental or optical distortions of unknown magnitude can be performed as a part of the spectral fitting procedure.