Helioseismology

The sun being the nearest star, seismic observations with high spatial resolution are possible, thus providing accurate measurement of frequencies of about half million modes of solar oscillations covering a wide range of degree. With these data helioseismology has enabled us to study the solar interior in sufficient detail to infer the large-scale structure and rotation of the solar interior. With the availability of high quality helioseismic data over a good fraction of a solar cycle it is also possible to study temporal variations in solar structure and dynamics. Some of these problems and recent results will be discussed.     

Perspectives on the interior of the Sun

The interior of the Sun is not directly accessible to observations. Nonetheless, it is possible to infer the physical conditions inside the Sun with the help of structure equations governing its equilibrium and with the powerful observational tools provided by the neutrino fluxes and oscillation frequencies. The helioseismic data show that the internal constitution of the Sun can be adequately represented by a standard solar model. It turns out that a cooler solar core is not a viable solution for the measured deficit of neutrino fluxes, and the resolution of the solar neutrino puzzle should be sought in the realm of particle physics.     

Inverting helioseismic data

Methods by which the observed frequencies of solar oscillations can be, and in some cases have been used to infer the internal structure of the Sun are discussed. Attention is confined to so-called inverse methods that identify and extract the information that is actually contained in the data. Because only a finite quantity of data can ever be acquired, the functions describing the interior stratification of the Sun can never be established completely without the acceptance of certain assumptions. Nevertheless, the assumptions that are required are simple to understand, and the results do not depend on the complicated and uncertain theory of stellar evolution which has traditionally been used to construct solar models. First results of the inversions have given us an estimate of the sound speed and the angular velocity throughout much of the solar interior. These estimates have already stimulated speculation which hopefully will encourage further theoretical and observational research that will improve our understanding of the Sun.     

太阳P模振动理论的研究

日震学是太阳物理的一个前沿分支学科,是根据太阳振动的观测来研究太阳的内部结构与运动的一种方法学。太阳５ｍｉｎ振动频率的理论计算和实测之间存在的显著偏差和振动模的激发问题一直是困扰日震学的两大难题,经过多年的研究仍然没有解决。然而太阳的表面层内绝热假设条件与真实情况有很大的偏差,我们认为绝大多数标准太阳模型的Ｐ模频率计算忽略了非绝热效应对频率的影响,忽略了振动的激发和衰减机制以及缺乏振动与对流湍流相互作用的知识。因此,我们必须发展非绝热理论来处理太阳５ｍｉｎ的振动问题     

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.     

Solar oscillations and the equation of state

Summary Accurate measurements of observed frequencies of solar oscillations are providing a wealth of data on the properties of the solar interior. The frequencies depend on solar structure, and on the properties of the plasma in the Sun. Here we consider in particular the dependence on the thermodynamic state. From an analysis of the equations of stellar structure, and the relevant aspects of the properties of the oscillations, we argue that in the convection zone one can isolate information about the equation of state which is relatively unaffected by other uncertainties in the physics of the solar interior. We review the different treatments that have been used to describe the thermodynamics of stellar plasmas. Through application of several of these to the computation of models of the solar envelope we demonstrate that the sensitivity of the observed frequencies is in fact sufficient to distinguish even quite subtle features of the physics of solar matter. This opens up the possibility of using the Sun as a laboratory for statistical mechanics, under conditions that are out of reach in a terrestrial laboratory.     

Helioseismology as a diagnostic of the solar interior

Helioseismology has given us a unique window into the solar interior. Helioseismic data have enabled us to study the internal structure and dynamics with unprecedented detail. This has also allowed us to use the Sun as a laboratory to study the basic properties of stellar matter. We describe how helioseismology is used to determine solar structure and what we have learned about the Sun so far. We also describe how knowledge of the solar structure can be used to constrain the physics inputs.     

Solar oscillations: Past,present, and future

Observation of global oscillations of the Sun constitutes a primitive seismology of the solar interior. The frequencies, if correctly identified with definite normal modes of vibration, provide a measure of the average velocity of sound in the interior and thereby of its composition and temperature. Fine structure in the frequencies of nonradial modes may provide information on their character (multiplicity) and on the rotation of the solar interior. Study of the amplitudes and phase fluctuations of the vibrations may clarify the excitation and damping of the vibrations.After a brief historical review emphasizing global velocity spectroscopy an account is given of the present status of the observations of global oscillations in the range of periods of 3 to 160 min.Finally the future capabilities of the observational techniques and their resultant potential is discussed.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

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 Hz, which is much larger than the observational accuracy.     

Solar internal rotation rate and the latitudinal variation of the tachocline

A new set of accurately measured frequencies of solar oscillations is used to infer the rotation rate inside the Sun, as a function of radial distance as well as latitude. We have adopted a regularized least-squares technique with iterative refinement for both 1.5D inversion, using the splitting coefficients, and 2D inversion using individual m splittings. The inferred rotation rate agrees well with earlier estimates showing a shear layer just below the surface and another one around the base of the convection zone. The tachocline or the transition layer where the rotation rate changes from differential rotation in the convection zone to an almost latitudinally independent rotation rate in the radiative interior is studied in detail. No compelling evidence for any latitudinal variation in the position and width of the tachocline is found, although it appears that the tachocline probably shifts to a slightly larger radial distance at higher latitudes and possibly also becomes thicker. However, these variations are within the estimated errors and more accurate data would be needed to make a definitive statement about latitudinal variations.     

Helioseismic imaging of sunspots at their antipodes

Recent work by Braun, Duvall, and LaBonte has shown that sunspots absorb helioseismic waves. We propose that sunspot absorption causes a seismic deficit that should be imaged at the antipode of the sunspot. If these images are observable, it should be possible to produce seismic maps of magnetic regions on the far side of the Sun. This possibility opens a broad range of synoptic and diagnostic applications. Diagnostic applications would include lifetimes of higher-frequency modes, and possibly rotation of the solar interior and detection of subsurface magnetic structure. We outline elements of the theory of seismic imaging and consider some applications. We propose the extention of acoustic holography to solar interior diagnostics in the context of antipodal imaging.Now at the Institute for Astronomy, University of Hawaii, Honolulu, HI 96822, U.S.A.     

Neutrino spin-flavor oscillations in solar environment

We study the phenomenon of neutrino spin-flavor oscillations due to solar magnetic fields. This allows us to examine how significantly the electron neutrinos produced in the solar interior undergo a resonant spin-flavor conversion. We construct analytical models for the solar magnetic field in all the three regions of the Sun. Neutrino spin-flavor oscillations in this magnetic field are examined by studying the level crossing phenomenon and comparing the two cases of zero and non-zero vacuum mixing respectively.Results from the Borexino experiment are used to place an upper limit on the magnetic field in the solar core. Related phenomena such as effects of matter on neutrino spin transitions and differences between Dirac and Majorana transitions in the solar magnetic fields are also discussed.     

Present problems of the solar interior

The standard model of solar evolution is reviewed and a number of problems highlighted. A fundamental question is whether there is any mixing of matter in the central regions, since such mixing could radically alter the model of the present Sun and modify our understanding of the evolution of other stars. Standard models of solar evolution become unstable to ³He driven global oscillations at an age of 3 × 10⁸ years and this may drive some mixing, even if this is not the case the finite amptitude limit of these oscillations is likely to produce modifications in the standard model. Convective overshooting at the bottom of the outer convective zone leads to an increased depth of this zone and small changes in the interior. It is pointed out that the young Sun had a ¹²C driven convective core whose extent and duration depends on the extent of overshooting. Such a core is likely to produce a magnetic field which will affect the internal dynamics. The internal rotation of the Sun remains an enigma and absence of knowledge of any internal magnetic field makes it difficult to study the problem. Rotationally driven instabilities are ineffective in the central chemically inhomogenous regions but may contribute to the inward diffusion of lithium from the convective zone. These and other problems are considered, but few solutions are proposed.     

太阳剩余磁场研究进展

太阳剩余磁场是指形成于太阳主序星阶段之前，深藏在太阳辐射核内部的原始磁场。由于太阳内部高电导率和准静态等因素，其剩余磁场耗散相当缓慢，而得以保留至今。太阳剩余磁场的存在不仅能够解释太阳活动的很多不对称性现象，如南北不对称性、活动经度与活动穴、低纬度冕洞和Maunder极小期等，还能通过改变自激发发电机模型的边值条件而影响整个太阳表面磁场的分布与演化。从观测结果和理论模型两方面评述了太阳剩余磁场的研究成果及最新进展，并简单讨论了进一步努力的方向。     

Stochastic Seismic Emission from Acoustic Glories and the Quiet Sun

Helioseismic images of multipolar active regions show enhanced seismic emission in 5-mHz oscillations in a halo surrounding the active region called the `acoustic glory'. The acoustic glories contain elements that sustain an average seismic emission 50% greater than similar elements in the quiet Sun. The most intense seismic emitters tend to form strings in non-magnetic regions, sometimes marking the borders of weak magnetic regions and the separation between weak magnetic regions of opposite polarity. This study compares the temporal character of seismic emission from acoustic glories with that from the quiet Sun. The power distribution of quiet-Sun seismic emission far from solar activity is exponential, as for random Gaussian noise, and therefore not perceivably episodic. The distribution of seismic power emanating from the most intense elements that comprise the acoustic glories is exponential out to approximately 4 times the average power emitted by the quiet Sun. Above this threshold the latter distribution shows significant saturation, suggesting the operation of a hydromechanical non-linearity that sets limits on the acoustic power generated by the convection zone. This could give us considerable insight into the physical mechanism of seismic emission from the near subphotosphere.     

Physics of solar-like oscillations

The physics of solar and stellar oscillations determines their observable properties: frequencies, amplitudes, lifetimes, line asymmetries and phase relations. In the solar case these quantities have been measured, often with high precision, and much has been learned about the properties of the solar interior, and the properties of the oscillations. With recent advances in observational techniques, such seismic investigations are now being extended to solar-like oscillations in distant stars. I provide a brief overview of the basic properties of stellar oscillations, and of the information about stellar properties that may be inferred from them, concentrating mostly on the low-degree modes for which information may be expected for distant stars. In addition, I consider the current state of investigations of solar-like oscillations in other stars, and the prospects for an improved understanding of the physics of such oscillations.     

Helioseismic Holography of Active-Region Subphotospheres – (Invited Review)

The development of solar acoustic holography has opened a major new diagnostic avenue in local helioseismology. It has revealed `acoustic moats' surrounding sunspots, `acoustic glories' surrounding complex active regions, and `acoustic condensations' suggesting the existence of significant seismic anomalies up to 20 Mm beneath active-region photospheres. Phase-sensitive seismic holography is now yielding high-resolution maps of sound travel-time anomalies caused by magnetic forces in the immediate subphotosphere, apparent thermal enhancements in acoustic moats, and Doppler signatures of subsurface flows. It has given us the first seismic images of a solar flare, and has uncovered a remarkable anomaly in the statistical distribution of seismic emission from acoustic glories. Seismic holography will probably give us the means for early detection of large active regions on the far-surface of the Sun, and possibly of deep subsurface activity as well. This powerful diagnostic now promises a new insight into the hydromechanical and thermal environments of the solar interior in the local perspective.     

Non-radial oscillations in an axisymmetric MHD incompressible fluid

It is well known from Helioseismology that the Sun exhibits oscillations on a global scale, most of which are non-radial in nature. These oscillations help us to get a clear picture of the internal structure of the Sun as has been demonstrated by the theoretical and observational (such as GONG) studies. In this study we formulate the linearised equations of motion for non-radial oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalarsU, V, P andT, respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation. The perturbed quantitiesU *, V *, P *, T * are written in terms of orthogonal polynomials. A special case of the above formulation and its stability is discussed.     

Internal rotation of the Sun as inferred from GONG observations

Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary.