Solar Oscillation Frequencies Research Articles

Influence of random magnetic field on solar global oscillations: The incompressible f-mode

The discrepancies between theoretically predicted and observed frequencies of solar global oscillations (e.g. p - and f -modes) have attracted major attention in the past decades. The f -mode is essentially a surface wave hence the mode frequencies are less likely to be influenced by the solar stratification. Most probably then the discrepancies are the result of some near surface mechanism(s) such as interactions with surface or sub-surface magnetic fields and flows. In the following we explore whether the small-scale photospheric magnetic fields, sometimes also called the magnetic carpet, may be part of the explanation for the apparent frequency paradox.

The Sun's Surface and Subsurface. Investigating Shape and Irradiance

Since the Sun's radiative output establishes the Earth's thermal environment, knowing the source and nature of its variability is essential for understanding and predicting the interactions in the Earth‐Sun system, among which are climate changes and the energy balance, photochemistry, and dynamics of the middle and upper atmosphere. The Sun's Surface and Subsurface brilliantly demonstrates how precise measurements of the Sun's properties, such as the solar diameter, oblateness, irradiance, and oscillation frequencies of normal modes provide insight into the structure and dynamics of the deep interior and the physical mechanisms of solar variability.This relatively compact book provides a comprehensive review of the basic principles, methodology, and tools for studying the solar variability. The main focus is on measurements and interpretation of the solar properties rather than on theory. It provides both an excellent introduction to the field and an exciting review of the recent advances in solar observations from the ground and space.

Bounds on the Magnetic Fields in the Radiative Zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound of ≲7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.

Global Parameter and Helioseismic Tests of Solar Variability Models

We construct models of the structure and evolution of the Sun which include variable magnetic fields and turbulence. The magnetic effects are (1) magnetic pressure, (2) magnetic energy, and (3) magnetic modulation to turbulence. The effects of turbulence are (1) turbulent pressure, (2) turbulent kinetic energy, and (3) turbulent inhibition of the radiative energy loss of a convective eddy, and (4) turbulent generation of magnetic fields. Using these ingredients we construct five types of solar variability models (including the standard solar model) with magnetic effects. These models are in part based on three-dimensional numerical simulations of the superadiabatic layers near the surface of the Sun. The models are tested with several sets of observational data, namely, the changes of (1) the total solar irradiance, (2) the photospheric temperature, (3) radius, (4) the position of the convection zone base, and (5) low- and medium-degree solar oscillation frequencies. We find that turbulence plays a major role in solar variability, and only a model that includes a magnetically modulated turbulent mechanism can agree with all the current available observational data. We find that because of the somewhat poor quality of all observations (other than the helioseismological ones), we need all data sets in order to restrict the range of models.

SUNSHINE, EARTHSHINE AND CLIMATE CHANGE I. ORIGIN OF, AND LIMITS ON SOLAR VARIABILITY

Changes in the earth's climate depend on changes in the net sunlight reaching us. The net depends on the sun's output and earth's reflectance, or albedo. Here we develop the limits on the changes in the sun's output in historical times based on the physics of the origin of solar cycle changes. Many have suggested that the sun's output could have been <TEX>$0.5\%$</TEX> less during the Maunder minimum, whereas the variation over the solar cycle is only about <TEX>$0.1\%$</TEX>. The frequencies of solar oscillations (f- and p-modes) evolve through the solar cycle, and provide the most exact measure of the cycle-dependent changes in the sun. But precisely what are they probing? The changes in the sun's output, structure and oscillation frequencies are driven by some combination of changes in the magnetic field, thermal structure and velocity field. It has been unclear what is the precise combination of the three. One way or another, this thorny issue rests on an understanding of the response of the solar structure to increased magnetic field, but this is complicated. Thus, we do not understand the origin of the sun's irradiance increase with increasing magnetic activity. Until recently, it seemed that an unphysically large magnetic field change was required to account for the frequency evolution during the cycle. However, the problem seems to have been solved (Dziembowski, Goode & Schou 2001) using f-mode data on size variations of the sun. From this and the work of Dziembowski & Goode (2003), we suggest that in historical times the sun couldn't be much dimmer than it is at activity minimum.

Helioseismic limit on heavy element abundance

Primary inversions of accurately measured solar oscillation frequencies coupled with the equations of thermal equilibrium and other input physics, enable us to infer the temperature and hydrogen abundance profiles inside the Sun. These profiles also help in setting constraints on the input physics as well as on heavy element abundance in the solar core. Using different treatments of plasma screening for nuclear reaction rates, limits on the cross-section of proton-proton nuclear reaction as a function of heavy element abundance in the solar core are obtained and an upper limit on heavy element abundance in the solar core is also derived from these results.

Seismic tests for solar models with tachocline mixing

We have computed accurate 1-D solar models including both a macroscopic mixing process in the solar tachocline as well as up-to-date microscopic physical ingredients. Using sound speed and density profiles inferred through primary inversion of the solar oscillation frequencies coupled with the equation of thermal equilibrium, we have extracted the temperature and hydrogen abundance profiles. These inferred quantities place strong constraints on our theoretical models in terms of the extent and strength of our macroscopic mixing, on the photospheric heavy elements abundance, on the nuclear reaction rates such as $S_{11}$ and $S_{34}$ and on the efficiency of the microscopic diffusion. We find a good overall agreement between the seismic Sun and our models if we introduce a macroscopic mixing in the tachocline and allow for variation within their uncertainties of the main physical ingredients. From our study we deduce that the solar hydrogen abundance at the solar age is $X_{\rm inv}=0.732\pm 0.001$ and that based on the $^9$Be photospheric depletion, the maximum extent of mixing in the tachocline is 5% of the solar radius. The nuclear reaction rate for the fundamental $pp$ reaction is found to be $S_{11}(0)=4.06\pm 0.07$ $10^{-25}$ MeV barns, i.e., 1.5% higher than the present theoretical determination. The predicted solar neutrino fluxes are discussed in the light of the new SNO/SuperKamiokande results.

Inclusion of Turbulence in Solar Modeling

The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, until now there has not been any well-tested efficient method to incorporate turbulence into solar modeling. We present here two methods to include turbulence in solar modeling within the framework of the mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer of the sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two variables: the turbulent kinetic energy per unit mass, and the effective ratio of specific heats due to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g. pressure and temperature). We investigate the effects of both treatments of turbulence on the structure variables, the adiabatic sound speed, the structure of the highly superadiabatic layer, and the p-mode frequencies. We find that the second method reproduces the SAL structure obtained in 3D simulations, and produces a p-mode frequency correction an order of magnitude better than the first method.

Seismic view of the solar interior

The interior of the Sun is not directly observable to us. Nevertheless, it is possible to infer the physical conditions prevailing in the solar interior with the help of theoretical models coupled with observational input provided by measured frequencies of solar oscillations. The frequencies of these solar oscillations depend on the internal structure and dynamics of the Sun and from the knowledge of these frequencies it is possible to infer the internal structure as well as the large scale flows inside the Sun, in the same way as the observations of seismic waves on the surface of Earth help us in the study of its interior. With the accumulation of seismic data over the last six years it has also become possible to study temporal variations in the solar interior. Some of these seismic inferences would be described.

Changes in Solar Oscillation Frequencies during the Current Activity Maximum: Analysis and Interpretation

AbstractWe describe systematic changes in the centroid frequencies and the splitting coefficients as found using data from MDI on board SOHO, covering cycle 23. The data allow us to construct a seismic map of the evolving solar activity - covering all latitudes. At lower latitudes, the temporal evolution closely tracks that of butterfly diagram. The additional information from higher latitudes in the map is of a significant activity in the polar region, peaking at activity minimum in 1996. The most plausible source of solar oscillation frequency changes over the solar cycle is the evolution of the radial component of the small-scale magnetic field. The amplitude of the required mean field changes is ∼ 100 G at the photosphere, and increasing going inward.

Influence of a uniform coronal magnetic field on solar p modes: coupling to slow resonant MHD waves

The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfven resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations.

Ring Diagram Analysis of the Characteristics of Solar Oscillation Modes in Active Regions

The presence of intense magnetic fields in and around sunspots is expected to modify solar structure and oscillation frequencies. Applying the ring diagram technique to data from the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, we analyze the characteristics of high-degree f- and p-modes near active regions and compare them with the characteristics of the modes in quiet regions. As expected from earlier results, the f- and p-mode frequencies of high-degree modes are found to be significantly larger in magnetically active regions. In addition, we find that the power in both f- and p-modes is lower in active regions while the widths of the peaks are larger, indicating smaller lifetimes. We also find that the oscillation modes are more asymmetric in active regions than those in quiet regions, indicating that modes in active regions are excited closer to the surface. While the increase in mode frequency is monotonic in frequency, all other characteristics show more complex frequency dependences.

STANDARD AND NON-STANDARD SOLAR MODELS

We summarize the physical input and assumptions commonly adopted in modern standard solar models that also produce good agreement with solar oscillation frequencies. We discuss two motivations for considering non-standard models: the solar neutrino problem and surface lithium abundance problem. We begin to explore the potential for mixed core models to solve the neutrino problem, and compare the structure, neutrino flux, and oscillation frequency predictions for several models in which the inner 25% of the radius is homogenized, taking into account the effects of non-local equilibrium abundances of 3He. The results for the neutrino flux and helioseismic predictions are far from satisfactory, but such models have the potential to reduce the predicted 7Be/8B neutrino flux ratio, and further studies are warranted. Finally, we discuss how much the neutrino problem can be alleviated in the framework of the standard solar model by using reaction rates, abundances and neutrino capture cross-sections at the limits of their uncertainties, while still satisfying the constraints of helioseismology.

Solar Metal Abundance Inferred from Helioseismology

In our previous work (Takata &amp; Shibahashi 1998), we constructed a solar model called the seismic solar model, which has the consistent profile of sound speed as well as the consistent depth of the convection zone with helioseismology. The profile of the heavy element abundance, however, had to be assumed to be constant for feasibility. Here we try to constrain the distribution of the heavy element abundance as well by the solar oscillation frequencies, adopting all of the basic equations which govern the solar structure.

Helioseismic search for magnetic field in the solar interior

The observed splittings of solar oscillation frequencies can be utilized to study possible large-scale magnetic fields present in the solar interior. Using the GONG data on frequency splittings an attempt is made to infer the strength of magnetic fields inside the Sun.

Signatures of the Rise of Cycle 23

During the rise of Cycle 23, we have found a sizable, systematic evolution of the Solar and Heliospheric Observatory/Michelson Doppler Imager solar oscillation frequencies implying significant changes in the spherically symmetric structure of the Sun's outer layers as well as in its asphericity up to a P18 Legendre distortion. We conducted a search for corresponding asymmetries in Ca II K data from Big Bear Solar Observatory. We found tight temporal and angular correlations of the respective asphericities up through P10. This result emphasizes the role of the magnetic field in producing the frequency changes. We carried out inversions of the frequency differences and the splitting coefficients assuming that the source of the evolving changes is a varying stochastic magnetic field. With respect to the most recent activity minimum, we detected a significant perturbation in the spherical part at a depth of 25-100 Mm, which may be interpreted as being a result of a magnetic perturbation, B2, of about (60KG)2 and/or a relative temperature perturbation of about 1.2 × 10-4. Larger, although less statistically significant, perturbations of the interior structure were found in the aspherical distortion.

Effect of Asymmetry in Peak Profiles on Solar Oscillation Frequencies

Most helioseismic analyses are based on solar oscillations frequencies obtained by fitting symmetric peak profiles to the power spectra. However, it has now been demonstrated that the peaks are not symmetric. In this work we study the effects of asymmetry of the peak profiles on the solar oscillations frequencies of p-modes for low and intermediate degrees. We also investigate how the resulting shift in frequencies affects helioseismic inferences.

Solar p and g modes in a model with a convection layer above a sub-adiabatic interior

We study high-order acoustic modes which reside in the outer layers of the solar interior. Magnetic field effects are not taken into account in this paper as we wish first to filter out how the modal frequencies depend on physical characteristics of a particular model structure of the Sun. In particular, we are interested in how the modal frequencies of solar global oscillations depend on the thickness of the convection layer and on the temperature gradient of the solar interior below. The model we use consists of three planar layers: an isothermal atmosphere, while the convection layer and the interior have temperature gradients that are adiabatic and sub-adiabatic, respectively. The presence of a convection layer with a finite thickness brings in additional modes while the variations in temperature gradient of the interior cause shifts in eigenfrequencies that are more pronounced for the p modes than for the g modes. These shifts can easily be of the order of several hundreds of μHz, which is much larger than the observational accuracy.

Helioseismic Search for Magnetic Field in the Solar Interior

AbstractThe observed splittings of solar oscillation frequencies can be utilized to study possible large-scale magnetic fields present in the solar interior. Using the GONG data on frequency splittings an attempt is made to infer the strength of magnetic fields inside the Sun.

CP-violation in neutrino oscillations

We study in a quantitative way CP-violating effects in neutrino oscillation experiments in the light of current and future data. Different scenarios with three and four neutrinos are worked out in detail including matter effects in long baseline experiments and it is shown that in some cases CP-violating effects could affect the analysis of a possible measurement. In particular in the three neutrino case we find that the effects can be larger than expected, at least in long-baseline νμ→νe. Moreover, measuring these effects could give useful information on the solar oscillation frequency. In four neutrino scenarios large effects are possible both in the νμ→ντ and νμ→νe channels of long-baseline experiments, whereas short-baseline experiments are affected only marginally.