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 neutrino data and the 11-year solar activity cycle

Recent data on solar neutrino flux have been analysed and it is shown that there is a statistically significant variation of solar neutrino flux data with the solar activity cycle. Thus the observation suggests that the solar activity cycle is due to the pulsating characters of the nuclear energy generation in the interior of the Sun.     

Radius of the Sun in relation to solar activity

Radius of the Sun has been measured by many researchers using various techniques over more than three centuries, which demonstrated that the solar radius is not constant in time, but exhibits significant variations. As in cases of variations in most other observed features of the Sun, correlation has been saught between solar radius and sunspot numbers, the latter being recognized as the best index of solar activity. However, such studies have so far produced completely contradictory results, viz., both correlation and anticorrelation have been reported. The reason appears to be the data used, which is highly inhomogeneous. I report here a statistically significant relationship between solar radius and sunspot numbers in the sense that a larger diameter of the Sun is associated with higher levels of solar activity, when a homogenised data base covering observations over the last three centuries is used for solar radius.     

Solar interior structure and luminosity variations

The assumptions of standard solar evolution theory are mentioned briefly, and the principle conclusions drawn from them are described. The result is a rationalization of the present luminosity and radius of the Sun. Because there is some uncertainty about the interior composition of the Sun, a range of models is apparently acceptable.To decide which model is the most accurate, other more sensitive comparisons with observations must be made. Recent measurements of frequencies of dynamical oscillations are particularly valuable in this respect. The most accurate observations are of the five-minute oscillations, which suggest that the solar composition is not atypical of other stars of the same age as the Sun.The theory predicts that the solar luminosity has risen steadily from about 70% of its current value during the last 4.7 x 10⁹yr. Superposed on this there might have been variations on shorter timescales. Variations lasting about 10⁷yr and occurring at intervals of 10⁸yr have been suggested as being the cause of terrestrial ice ages. Moreover, there may be other variations, associated with instabilities arising from the coupling between the convection zone and the radiative interior, that occur on a timescale of 10⁵yr and which also have climatic consequences. These issues are quite uncertain.We do know that the Sun varies magnetically with a period of about 22 yr, and that this oscillation is modulated irregularly on a timescale of centuries. This appears to be a phenomenon associated with the convection zone and its immediate neighbourhood, though control from a more deeply-seated mechanism is not out of the question. There is a small luminosity variation associated with this cycle, and the way by which this might come about is discussed in terms of certain theories of the solar dynamo.Finally, there must be small surface flux variations associated with the dynamical oscillations mentioned above. Though the total luminosity variations are extremely small, the flux in any specific direction, and in particular that of the earth, may be measurable.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

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     

Intensity Distribution and Contrast of the Solar EUV Network

Intensity distributions of the EUV network and the cell interior in the solar atmosphere have been obtained in fourteen emission lines from Solar and Heliospheric Observatory (SOHO)/Coronal Diagnostic Spectrometer (CDS) observations. The formation temperature of the observed lines is in the range log T=4.90 – 6.06 (T in Kelvin), and hence they represent increasing heights in the solar atmosphere from the upper chromosphere and the transition region to the low corona. Intensity distributions of the cell interior have been found to be different in the quiet Sun and the coronal hole even at the lower transition region, which is at variance with some earlier results. The intensity contrast of the network with respect to the cell interior has been obtained for each line, and differences in the quiet Sun and the coronal hole have been examined. The network contrast, in general, is lower for the coronal hole as compared to the quiet Sun, but becomes equal to it in the upper transition region. The maximum contrast for both the regions is at about log T=5.3. Also obtained are the relative contributions of the network and the cell interior to the total intensity. The implications of the results for models of the transition region are briefly mentioned.     

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.     

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.     

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.     

Certain problems of solar and heliospheric physics in the light of novel satellite data

Recent satellite data have given a better insight into the possible nature of extremely strong disturbances on the Sun and in the heliosphere by relating them to processes in the solar interior. The energy, momentum, and mass transfer on various spatiotemporal scales are organized in the Sun into a hierarchy of coupled nonlinear processes. Confirmation has been given to the fact that coronal mass ejections and solar flares are not linked causally but merely reflect the existence of two channels of free-energy dissipation in the solar atmosphere in the form of plasma motion and plasma emission; their relative role can be described by a corresponding nondimensional parameter. Information on the global asymmetry of the solar emission and active processes has been gained. A great diversity in the geometry of eruptive events (not necessarily associated with magnetic reconnection) has been revealed. In our opinion, the basic unresolved problems in the investigation of solar activity dictate the necessity of carrying out more accurate, absolutely calibrated measurements of the whitelight solar emission at appropriately high spatiotemporal resolutions. The development of direct and indirect techniques of measuring the electric fields and currents with the aim of reconstructing the solar and heliospheric current system remains a challenging task.     

Magnetic convection

In this paper the process of magnetic convection is studied. It is shown that outside of a radius of about 2 × 10⁵ km, magnetic fields in the Sun may be buoyant. Outside this limit strong field regions tend to rise at the expense of weak field regions which tend to sink. Magnetic convection may be important in magnetic stars and even in the solar interior. A recent calculation of the angular velocity of the Sun provides a period of rotation for the solar core of from 0.5 to 5 days. This calculation requires that the magnetic field extract angular momentum from the solar interior. Magnetic convection thus seems to be required, if this calculation is correct. Furthermore, magnetic convection may transfer heat and thereby possibly change the internal temperature structure of the Sun from what would be expected solely by radiation transfer.     

利用GPS探测电离层异常中的高斯过程处理方法

平静状态下电离层总电子含量（TEC）随时间的变化通常可以视为平稳随机过程。然而，太阳或地球的突发事件（如太阳耀斑、地磁场的扰动）会引起电离层的扰动，破坏该平稳过程，从而引起其统计参数的变化。依据平稳随机过程——高斯过程的相关性质，利用其自协方差函数和TEC时间系列，构建了独立同标准正态分布的观测样本，并利用X^2假设检验的方法来探测电离层异常现象。此外，还利用了2000年7月14日太阳耀斑期间我国国际IGS跟踪站武汉GPS跟踪站的数据，进行了实例分析。结果表明，该方法可以有效地探测电离层异常现象。     

Why Study the Sun?

In this presentation we briefly describe the Sun through large number of illustrations and pictures of the Sun taken from early times to the present day space missions. The importance of the study of the Sun is emphasized as it is the nearest star which presents unparallelled views of surface details and numerous phenomena. Our Sun offers a unique celestial laboratory where a large variety of phenomena take place, ranging in temporal domain from a few milliseconds to several decades, in spatial domain from a few hundred kilometers to thousands of kilometers, and in the temperature domain from a few thousand degrees to several million degrees. Its mass motion ranges from thousandths to thousands of kilometers per second. Such an object provides us with a unique laboratory to study the state of matter in the Universe. The existing solar ground-based and space missions have already revealed several mysteries of the outer environment of our Sun and much more is going to come in the near future from planned new sophisticated ground-based solar telescopes and Space missions. The new technique of helioseismology has unravelled many secrets of the solar interior and has put the Standard Solar Model (SSM) on firm footing. The long-standing problem of solar neutrinos has been recently sorted out, and even the ‘back side’ view of the Sun can be seen using the technique of holographic helioseismology.     

A new way to measure the departure from thermodynamic equilibrium in stellar atmospheres

A new way to measure the departure from thermodynamic equilibrium is proposed based on the departure factor which evaluates the deviation from a Boltzmann level distribution, used by Short and Hauschildt (2005) and others. The way is based on an explicit relationship describing the departure factor as a function of line to continuum source, dynamic temperature and line photon frequency, under three assumptions that the scattering can be neglected, the background continuum can be treated as a Planck function, and finally the complete redistribution can be true. It has the advantage that the departure can be very conveniently evaluated from the spectral analysis with only the radiative transfer involved. Some physical insights are recovered for some extreme cases.Some example calculations of the departure are presented for the quiet Sun, faint solar flare and strong solar flare for the generally used solar chromospheric lines: Hα, Hβ,CaII H, K and triplet. It is revealed that in the case of solar flares, the departure is less than thermodynamic equilibrium along the larger depth range than in the quiet sun due to chromospheric condensation. It becomes hard to distinguish the departures for the different lines of the same atom or ion. It is expected that this investigation can be constructive for studying stellar atmospheres in cases where the three assumptions are close to reality.     

Development of a Code to Analyze the Solar White-Light Images from the Kodaikanal Observatory: Detection of Sunspots,Computation of Heliographic Coordinates and Area

Sunspots are the most conspicuous aspects of the Sun. They have a lower temperature, as compared to the surrounding photosphere; hence, sunspots appear as dark regions on a brighter background. Sunspots cyclically appear and disappear with a 11-year periodicity and are associated with a strong magnetic field ( ～10³ G) structure. Sunspots consist of a dark umbra, surrounded by a lighter penumbra. Study of umbra–penumbra area ratio can be used to give a rough idea as to how the convective energy of the Sun is transported from the interior, as the sunspot’s thermal structure is related to this convective medium.An algorithm to extract sunspots from the white-light solar images obtained from the Kodaikanal Observatory is proposed. This algorithm computes the radius and center of the solar disk uniquely and removes the limb darkening from the image. It also separates the umbra and computes the position as well as the area of the sunspots. The estimated results are compared with the Debrecen photoheliographic results. It is shown that both area and position measurements are in quite good agreement.     

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.     

About the rotation of the solar radiative interior

In the modern era of helioseismology we have a wealth of high-quality data available, e.g., more than 6 years of data collected by the various instruments on board the SOHO mission, and an even more extensive ground-based set of observations covering a full solar cycle. Thanks to this effort a detailed picture of the internal rotation of the Sun has been constructed. In this paper we present some of the actions that should be done to improve our knowledge of the inner rotation profile discussed during the workshop organized at Saclay on June 2003 on this topic. In particular we will concentrate on the extraction of the rotational frequency splittings of low- and medium-degree modes and their influence on the rotation of deeper layers. Furthermore, for the first time a full set of individual |m|-component rotational splittings is computed for modes ℓ≤4 and 1<ν<2 mHz, opening new studies on the latitudinal dependence of the rotation rate in the radiative interior. It will also be shown that these splittings have the footprints of the differential rotation of the convective zone which can be extremely useful to study the differential rotation of other stars where only these low-degree modes will be available.     

Global solar dynamo models: Simulations and predictions

Flux-transport type solar dynamos have achieved considerable success in correctly simulating many solar cycle features, and are now being used for prediction of solar cycle timing and amplitude. We first define flux-transport dynamos and demonstrate how they work. The essential added ingredient in this class of models is meridional circulation, which governs the dynamo period and also plays a crucial role in determining the Sun’s memory about its past magnetic fields. We show that flux-transport dynamo models can explain many key features of solar cycles. Then we show that a predictive tool can be built from this class of dynamo that can be used to predict mean solar cycle features by assimilating magnetic field data from previous cycles.     

Low‐frequency heliographic observations of the quiet Sun corona

We present new results of heliographic observations of quiet‐Sun radio emission fulfilled by the UTR‐2 radio telescope. The solar corona investigations have been made close to the last solar minimum (Cycle 23) in the late August and early September of 2010 by means of the two‐dimensional heliograph within 16.5–33 MHz. Moreover, the UTR‐2 radio telescope was used also as an 1‐D heliograph for one‐dimensional scanning of the Sun at the beginning of September 2010 as well as in short‐time observational campaigns in April and August of 2012. The average values of integral flux density of the undisturbed Sun continuum emission at different frequencies have been found. Using the data, we have determined the spectral index of quiet‐Sun radio emission in the range 16.5–200 MHz. It is equal to –2.1±0.1. The brightness distribution maps of outer solar corona at frequencies 20.0 MHz and 26.0 MHz have been obtained. The angular sizes of radio Sun were estimated. It is found that the solar corona at these frequencies is stretched‐out along equatorial direction. The coefficient of corona ellipticity varies slightly during above period. Its mean magnitudes are equal to ≈ 0.75 and ≈ 0.73 at 20.0 MHz and 26.0 MHz, respectively. The presented results for continuum emission of solar corona conform with being ones at higher frequencies. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)