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.     

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.     

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     

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.     

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.     

On the choice of parameters in solar-structure inversion

The observed solar p-mode frequencies provide a powerful diagnostic of the internal structure of the Sun and permit us to test in considerable detail the physics used in the theory of stellar structure. Among the most commonly used techniques for inverting such helioseismic data are two implementations of the optimally localized averages (OLA) method, namely the subtractive optimally localized averages (SOLA) and multiplicative optimally localized averages (MOLA). Both are controlled by a number of parameters, the proper choice of which is very important for a reliable inference of the solar internal structure. Here we make a detailed analysis of the influence of each parameter on the solution and indicate how to arrive at an optimal set of parameters for a given data set.     

The future of solar physics

The future of solar physics is founded on the existing fundamental unsolved problems in stellar physics. Thus, for instance, the physics of stellar interiors has been called into serious question by the very low-measured neutrino flux. The ⁷¹Ga neutrino detection experiment is the next step in unravelling this mystery. If that experiment should find the expected neutrino flux from the basic p-p reaction in the Sun, then astrophysics is in a difficult situation, because the most likely explanation for the low neutrino flux found in the ³⁷Cl experiment would be an error in our calculation of the opacity or an error in our understanding of the elemental abundances in stellar interiors, with serious implications for present ideas on stellar structure and the age of the galaxy.The new methods of helioseismology, for probing the interior of the Sun, have already found the primordial rapid rotation of the central core. The forthcoming world-wide helioseismology observing network will permit fuller exploitation of the method, promising to provide the first direct sounding of the interior of a star, hitherto known to us only through theoretical inference and the discrepant neutrino emission.The activity of all stars involves much the same phenomena as make up the activity of the Sun. The effects are too complex, and too foreign to the familiar dynamics in the terrestrial laboratory, to be deciphered by theoretical effort alone. It has become clear through the observational and theoretical work of the past decade or two that much of the essential dynamics of the activity of the atmosphere takes place on scales of the order of 10² km. Thus, an essential step in developing the physics of stellar activity will be the Solar Optical Telescope (presently planned by NASA to be launched early in the next decade) to permit a microscopic examination of the surface of the Sun to study the source of the action. The activity and X-ray emission of other stars depend on much the same effects, so that the study is essential to determining the significance of the X-ray emission from other stars.This work was supported in part by the National Aeronautics and Space Administration under grant NGL-14-001-001.     

The Solar-Stellar Connection: Magneto-Acoustic Pulsations in 1.5M ⊙ – 2M ⊙ Peculiar A Stars

Stellar astronomers look on in envy at the wealth of data, the incredible spatial resolution, and the maturity of the theoretical understanding of the Sun. Yet the Sun is but one star, so stellar astronomy is of great interest to solar astronomers for its range of different conditions under which to test theoretical understanding gained from the study of the Sun. The rapidly oscillating peculiar A stars are of particular interest to solar astronomers. They have strong, global, dipolar magnetic fields with strengths in the range 1?–?25?kG, and they pulsate in high-overtone p modes similar to those in the Sun; thus they offer a unique opportunity to study the interaction of pulsation, convection, and strong magnetic fields, as is now done in the local helioseismology of sunspots. Some of them even pulsate in modes with frequencies above the acoustic cutoff frequency, in analogy with the highest frequency solar modes, but with mode lifetimes up to decades in the roAp stars, very unlike the short mode lifetimes of the Sun. They offer the most extreme cases of atomic diffusion, a small, but important ingredient of the standard solar model with wide application in stellar astrophysics. They are compositionally stratified and are observed and modelled as a function of atmospheric depth and thus can inform plans to expand helioseismic observations to have atmospheric depth resolution. Study of this unique class of pulsating stars follows the advanced state of studies of the Sun and offers more extreme conditions for the understanding of physics shared with the Sun.     

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.     

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.     

Present Observational Status of Solar-type stars

Observing stellar oscillations provides a powerful probe for studying stellarinteriors. The frequencies of these modes depend on the properties of the star and give strong constraints on stellar models and evolution theories. The five-minute oscillations in the Sun, induced by stochastic excitation of its convective zone, have provided a wealth of information about the solar interior and has led to significant revisions to solar models. Until recently, the Sun was the only star in which solar-like oscillations were clearly established and characterized. The most important difficulty lies in the extremely small amplitude of the acoustic modes. Thanks in great part to high precision ground based Doppler measurements, solar-like oscillations have been now clearly detected in a growing list of main sequence and subgiant stars (Procyon, Hyi, Her A, Cen A, Eri and Boo). In some of them, p-modes were identified and characterized. New results and prospects in this field are presented.     

Seismology of stellar envelopes: probing the outer layers of a star through the scattering of acoustic waves

The outer layers of Sun-like stars are regions of rapid spatial variation which modulate the p-mode frequencies by partially reflecting the constituent acoustic waves. With the accuracy that has been achieved by current solar observations, and that is expected from imminent stellar observations, this modulation can be observed from the spectra of the low-degree modes. We present a new and simple theoretical calculation to determine the leading terms in an asymptotic expansion of the outer phase of these modes, which is determined by the structure of the surface layers of the star. Our procedure is to compare the stellar envelope with a plane-parallel polytropic envelope, which we regard as a smooth reference background state. Then we can isolate a seismic signature of the acoustic phase and relate it to the stratification of the outer layers of the convection zone. One can thereby constrain theories of convection that are used to construct the convection zones of the Sun and Sun-like stars. The accuracy of the diagnostic is tested in the solar case by comparing the predicted outer phase with an exact numerical calculation.     

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.     

On helioseismic tests of basic physics

An important goal of helioseismology is to provide information about the basic physics and parameters that determine the structure of the solar interior. Here we discuss the procedures applied in such analyses, using as an example attempts to obtain significant constraints on the value of Newton's gravitational constant G from helioseismology. The analysis is based on complete direct and inverse helioseismic analysis of a set of accurate observed acoustic frequencies. We confirm, as found by previous investigations based on different approaches, that the actual level of precision of the helioseismic inferences does not allow us to constrain G with a precision better than that which can be reached with direct experimental measurements. The conclusion emphasizes the importance in helioseismic inferences of considering not only the accuracy with which solar oscillations are measured, but also the effect of uncertainties in other aspects of the model computation and helioseismic analysis.     

The DynaMICCS perspective

The DynaMICCS mission is designed to probe and understand the dynamics of crucial regions of the Sun that determine solar variability, including the previously unexplored inner core, the radiative/convective zone interface layers, the photosphere/chromosphere layers and the low corona. The mission delivers data and knowledge that no other known mission provides for understanding space weather and space climate and for advancing stellar physics (internal dynamics) and fundamental physics (neutrino properties, atomic physics, gravitational moments...). The science objectives are achieved using Doppler and magnetic measurements of the solar surface, helioseismic and coronographic measurements, solar irradiance at different wavelengths and in-situ measurements of plasma/energetic particles/magnetic fields. The DynaMICCS payload uses an original concept studied by Thalès Alenia Space in the framework of the CNES call for formation flying missions: an external occultation of the solar light is obtained by putting an occulter spacecraft 150 m (or more) in front of a second spacecraft. The occulter spacecraft, a LEO platform of the mini sat class, e.g. PROTEUS, type carries the helioseismic and irradiance instruments and the formation flying technologies. The latter spacecraft of the same type carries a visible and infrared coronagraph for a unique observation of the solar corona and instrumentation for the study of the solar wind and imagers. This mission must guarantee long (one 11-year solar cycle) and continuous observations (duty cycle > 94%) of signals that can be very weak (the gravity mode detection supposes the measurement of velocity smaller than 1 mm/s). This assumes no interruption in observation and very stable thermal conditions. The preferred orbit therefore is the L1 orbit, which fits these requirements very well and is also an attractive environment for the spacecraft due to its low radiation and low perturbation (solar pressure) environment. This mission is secured by instrumental R and D activities during the present and coming years. Some prototypes of different instruments are already built (GOLFNG, SDM) and the performances will be checked before launch on the ground or in space through planned missions of CNES and PROBA ESA missions (PICARD, LYRA, maybe ASPIICS).     

90年代太阳模型和太阳震荡研究进展(I):太阳模型研究进展(英)

太阳模型的研究是了解太阳整体结构和性质的极为重要的手段。90年代以来太阳模型研究取得了进展。随着MHD及OPAL物态方程的引入,理论上的太阳振荡频率与观测值的差别已大为减小,而考虑湍流频谱分布的局域对流理论和三维流体动力学模拟结果可对太阳内部对流能量传输过程有更深刻的理解．以前所发现的理论模型与反演结果得到的初始氦丰度的差别已能由扩散过程加以解释,而太阳表面锂丰度亏损问题也可以由扩散过程或早期演化星风来加以解决,太阳中微子问题则似应由粒子物理而不是天体物理来解决。     

90年代太阳模型和太阳震荡研究进展(II):太阳振荡研究进展(英)

太阳振荡研究现已成为研究太阳内部性质的新手段,也成为检验太阳模型构造时输入物理参量的最重要工具。90年代以来理论与观测日震频率的差别已随输入物理参量及太阳振荡理论的改进而大为减小,可是现有的差别仍远大于观测误差。由日震反演可对太阳内部对流区、表面氦丰度及自转随纬度和径向的分布都有更多了解。太阳振荡的湍动随机激发及激发源的位置都已得到研究,不过现在问题还未完全解决。今后一方面要探测更多的振动方式,另一方面也需要解决不同观测者得到的结果存在系统差的问题,而最外层的非绝热现象及理论与观测存在差别仍是最关键的难题。     

Propagating Linear Waves in Convectively Unstable Stellar Models: A Perturbative Approach

Linear time-domain simulations of acoustic oscillations are unstable in the stellar convection zone. To overcome this problem it is customary to compute the oscillations of a stabilized background stellar model. The stabilization affects the result, however. Here we propose to use a perturbative approach (running the simulation twice) to approximately recover the acoustic wave field while preserving seismic reciprocity. To test the method we considered a 1D standard solar model. We found that the mode frequencies of the (unstable) standard solar model are well approximated by the perturbative approach within 1 μHz for low-degree modes with frequencies near 3 mHz. We also show that the perturbative approach is appropriate for correcting rotational-frequency kernels. Finally, we comment that the method can be generalized to wave propagation in 3D magnetized stellar interiors because the magnetic fields have stabilizing effects on convection.