High-frequency modes in solar-like stars

p-mode oscillations in solar-like stars are excited by the outer convection zone in these stars and reflected close to the surface. The p modes are trapped inside an acoustic cavity, but the modes only stay trapped up to a given frequency [known as the acoustic cut-off frequency  (ν_ac)  ] as modes with larger frequencies are generally not reflected at the surface. This means that modes with frequency larger than the acoustic cut-off frequency must be travelling waves. The high-frequency modes may provide information about the physics in the outer layers of the stars and the excitation source and are therefore highly interesting as it is the estimation of these two phenomena that cause some of the largest uncertainties when calculating stellar oscillations.
High-frequency modes have been detected in the Sun, in β Hydri and in α Cen A and α Cen B by smoothing the so-called echelle diagram and the large frequency separation as a function of frequency has been estimated. The large frequency separation has been compared with a simple model of the acoustic cavity which suggests that the reflectivity of the photosphere is larger at high frequency than predicted by standard models of the solar atmosphere and that the depth of the excitation source is larger than what has been estimated by other models and might depend on the order n and degree l of the modes.     

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.     

Multisite campaign on the open cluster M67 – II. Evidence for solar-like oscillations in red giant stars

Measuring solar-like oscillations in an ensemble of stars in a cluster, holds promise for testing stellar structure and evolution more stringently than just fitting parameters to single field stars. The most-ambitious attempt to pursue these prospects was by Gilliland et al. who targeted 11 turn-off stars in the open cluster M67 (NGC 2682), but the oscillation amplitudes were too small (<20 μmag) to obtain unambiguous detections. Like Gilliland et al. we also aim at detecting solar-like oscillations in M67, but we target red giant stars with expected amplitudes in the range 50–  500 μmag  and periods of 1 to 8 h. We analyse our recently published photometry measurements, obtained during a six-week multisite campaign using nine telescopes around the world. The observations are compared with simulations and with estimated properties of the stellar oscillations. Noise levels in the Fourier spectra as low as  27 μmag  are obtained for single sites, while the combined data reach  19 μmag  , making this the best photometric time series of an ensemble of red giant stars. These data enable us to make the first test of the scaling relations (used to estimate frequency and amplitude) with an homogeneous ensemble of stars. The detected excess power is consistent with the expected signal from stellar oscillations, both in terms of its frequency range and amplitude. However, our results are limited by apparent high levels of non-white noise, which cannot be clearly separated from the stellar signal.     

Stellar turbulence and mode physics

An overview of selected topical problems on modelling oscillation properties in solar-like stars is presented. High-quality oscillation data from both space-borne intensity observations and ground-based spectroscopic measurements provide first tests of the still-ill-understood superficial layers in distant stars. Emphasis will be given to modelling the pulsation dynamics of the stellar surface layers, the stochastic excitation processes and the associated dynamics of the turbulent fluxes of heat and momentum.     

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.     

Multisite campaign on the open cluster M67 – I. Observations and photometric reductions

We report on an ambitious multisite campaign aimed at detecting stellar variability, particularly solar-like oscillations, in the red giant stars in the open cluster M67 (NGC 2682). During the six-week observing run, which comprised 164 telescope nights, we used nine 0.6-m to 2.1-m class telescopes located around the world to obtain uninterrupted time series photometry. We outline here the data acquisition and reduction, with emphasis on the optimization of the signal-to-noise ratio of the low-amplitude (50–500 μmag) solar-like oscillations. This includes a new and efficient method for obtaining the linearity profile of the CCD response at ultrahigh precision (∼10 parts per million). The noise in the final time series is 0.50 mmag per minute integration for the best site, while the noise in the Fourier spectrum of all sites combined is 20 μmag. In addition to the red giant stars, this data set proves to be very valuable for studying high-amplitude variable stars such as eclipsing binaries, W UMa systems and δ Scuti stars.     

How asteroseismology can constrain the global parameters of solar-like star models

In the previous years, p-mode oscillations (pressure oscillations stochastically excited by convection) have been detected in several solar-like stars thanks to the ground-based spectroscopic and space spectroscopic and photometric observations. We study the importance of seismic constraints on stellar modeling and the impact of their accuracy on reducing the uncertainties of global stellar parameters (i.e. mass, age, etc.). We use the Singular Value Decomposition (SVD) method to analyze the sensitivity of stellar models to seismic constraints. In this context, we construct a grid of evolutionary sequences for solar-like stars with varying age and mass. Around each model of this grid, we evaluate the partial derivatives with respect to a large set of free parameters: mass ?, age τ, mixing-length parameter α, initial helium abundance Y ₀, and initial metallicity Z/X ₀. Masses between 0.9 and 1.55 M _⊙ and central hydrogen abundances from Xc=0.7 to 0.05 have been considered in this study.     

Gaussian process modelling of asteroseismic data

The measured properties of stellar oscillations can provide powerful constraints on the internal structure and composition of stars. To begin this process, oscillation frequencies must be extracted from the observational data, typically time series of the star's brightness or radial velocity. In this paper, a probabilistic model is introduced for inferring the frequencies and amplitudes of stellar oscillation modes from data, assuming that there is some periodic character to the oscillations, but that they may not be exactly sinusoidal. Effectively, we fit damped oscillations to the time series, and hence the mode lifetime is also recovered. While this approach is computationally demanding for large time series (>1500 points), it should at least allow improved analysis of observations of solar-like oscillations in subgiant and red giant stars, as well as sparse observations of semiregular stars, where the number of points in the time series is often low. The method is demonstrated on simulated data and then applied to radial velocity measurements of the red giant star  ξ Hydrae  , yielding a mode lifetime between 0.41 and 2.65 d with 95 per cent posterior probability. The large frequency separation between modes is ambiguous, however we argue that the most plausible value is 6.3 μHz, based on the radial velocity data and the star's position in the Hertzsprung–Russell diagram.     

Semiclassical approximation for low-degree stellar p modes – I. The classical eigenfrequency equation

A new eigenfrequency equation for low-degree solar-like oscillations in stars is developed, based on the assumption of purely classical propagation in the stellar interior of acoustic waves modified by buoyancy and gravity . Compared with high-frequency asymptotic analysis, the eigenfrequency equation has a new functional form, with expansion in powers of ℓ(ℓ+1) instead of 1/ ω . Basic observable quantities, the 'large' and 'small' frequency separations , are interpreted as the dependence on frequency and refraction angle of a classical action integral for waves propagating close to the stellar diameter. The new eigenfrequency equation gives a significant improvement in accuracy over previous analyses when tested with solar p modes, suggesting this as an alternative and more powerful tool for applications in stellar seismology.     

The YNEV stellar evolution and oscillation code

We have developed a new stellar evolution and oscillation code YNEV,which calculates the structures and evolutions of stars,taking into account hydrogen and helium burning.A nonlocal turbulent convection theory and an updated overshoot mixing model are optional in this code.The YNEV code can evolve low-and intermediate-mass stars from the pre-main sequence to a thermally pulsing asymptotic branch giant or white dwarf.The YNEV oscillation code calculates the eigenfrequencies and eigenfunctions of the adiabatic oscillations for a given stellar structure.The input physics and numerical scheme adopted in the code are introduced.Examples of solar models,stellar evolutionary tracks of low-and intermediate-mass stars with different convection theories(i.e.mixing-length theory and nonlocal turbulent convection theory),and stellar oscillations are shown.     

Multi-wavelength observations of stellar flares

We present observational data on stellar flares from a range of wavelength regimes, many of which were obtained simultaneously. Physical parameters of these flares are derived and discussed in the frame-work of the general solar flare model. It is found that flares on dMe stars are solar-like, except in mean energy. The parameters of flares on RS CVn stars are more extreme, however, and may require new models for their interpretation.     

The phase function for stellar acoustic oscillations — IV. Solar-like stars

In recent years there has been some progress towards detecting solar-like oscillations in stars. The goal of this challenging project is to analyse frequency spectra similar to that observed for the Sun in integrated light. In this context it is important to investigate what can be learned about the structure and evolution of the stars from such future observations. Here we concentrate on the structure of the upper layers, as reflected in the phase function. We show that it is possible to obtain this function from low-degree p modes, at least for stars on the main sequence. We analyse its dependence on several uncertainties in the structure of the uppermost layers. We also investigate a filtered phase function, which has properties that depend on the layers around the second helium ionization zone.     

Asteroseismology: from dream to reality

With the resounding success of helioseismology in determining the interior structure and rotation of the Sun, and in providing unprecedented studies of the interaction of pulsation and magnetic fields in the solar atmosphere, astronomers have been delighted, after decades of disappointing attempts, with the recent discovery of solar-like oscillations in ξ Hya, β Hyi, α Cen A and B, η Boo, ν Ind, ζ Her, δ Eri, HD 20794, HD 160191, and others as this list is growing rapidly. There is now true seismology of some solar-like stars. Asteroseismology also studies stars with a wide variety of interior and surface conditions. For two decades asteroseismic techniques have been applied to many pulsating stars across the HR diagram. This review describes some recent developments for some selected classes of pulsating stars other than the solar-like oscillators.     

Excitation of solar-like oscillations: From PMS to MS stellar models

The amplitude of solar-like oscillations results from a balance between excitation and damping. As in the sun, the excitation is attributed to turbulent motions that stochastically excite thep modes in the uppermost part of the convective zone. We present here a model for the excitation mechanism. Comparisons between modeled amplitudes and helio and stellar seismic constraints are presented and the discrepancies discussed. Finally the possibility and the interest of detecting such stochastically excited modes in pre-main sequence stars are also discussed.     

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.     

X-ray Activity and Accretion in Young Stellar Objects

I discuss recent observational results on the X-ray properties of young stellar objects, based mostly on Chandra and XMM-Newton observations. The sensitive X-ray data on large, well characterized samples of T Tauri stars (and a number of protostars) allow to study in detail the dependence of magnetic activity on the bulk properties of the young objects and to draw important clues towards the origin of the X-ray emission. The absence of a relation between X-ray activity and rotation for T Tauri stars clearly suggests that their magnetic activity cannot be simply explained by the action of a scaled-up solar-like dynamo. I discuss alternative models for the generation of magnetic fields and also consider the long standing question whether the X-ray properties of the T Tauri stars are related to the presence/absence of circumstellar disks or active accretion.     

Starspots

Starspots are created by local magnetic fields on the surfaces of stars, just as sunspots. Their fields are strong enough to suppress the overturning convective motion and thus block or redirect the flow of energy from the stellar interior outwards to the surface and consequently appear as locally cool and therefore dark regions against an otherwise bright photosphere (Biermann in Astronomische Nachrichten 264:361, 1938; Z Astrophysik 25:135, 1948). As such, starspots are observable tracers of the yet unknown internal dynamo activity and allow a glimpse into the complex internal stellar magnetic field structure. Starspots also enable the precise measurement of stellar rotation which is among the key ingredients for the expected internal magnetic topology. But whether starspots are just blown-up sunspot analogs, we do not know yet. This article is an attempt to review our current knowledge of starspots. A comparison of a white-light image of the Sun (G2V, 5 Gyr) with a Doppler image of a young solar-like star (EK Draconis; G1.5V, age 100 Myr, rotation 10 × Ω _Sun) and with a mean-field dynamo simulation suggests that starspots can be of significantly different appearance and cannot be explained with a scaling of the solar model, even for a star of same mass and effective temperature. Starspots, their surface location and migration pattern, and their link with the stellar dynamo and its internal energy transport, may have far reaching impact also for our understanding of low-mass stellar evolution and formation. Emphasis is given in this review to their importance as activity tracers in particular in the light of more and more precise exoplanet detections around solar-like, and therefore likely spotted, host stars.     

What We Have Learned from Helioseismology

The Sun's global oscillations, which are studied both in spatially unresolved ("Sun-as-a-star") and resolved observations of the solar disk, have enabled helioseismology to probe in detail the solar interior. I review first what is learned from the unresolved measurements, since this gives an idea of what we may in the not too distant future be able to learn about the interiors of other stars undergoing solar-type oscillations. I then look at the main results from resolved observations, which have begun to reveal the structure and dynamics of the interior of a star in exquisite detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

High-precision stellar abundances of the elements: methods and applications

Efficient spectrographs at large telescopes have made it possible to obtain high-resolution spectra of stars with high signal-to-noise ratio and advances in model atmosphere analyses have enabled estimates of high-precision differential abundances of the elements from these spectra, i.e. with errors in the range 0.01–0.03 dex for F, G, and K stars. Methods to determine such high-precision abundances together with precise values of effective temperatures and surface gravities from equivalent widths of spectral lines or by spectrum synthesis techniques are outlined, and effects on abundance determinations from using a 3D non-LTE analysis instead of a classical 1D LTE analysis are considered. The determination of high-precision stellar abundances of the elements has led to the discovery of unexpected phenomena and relations with important bearings on the astrophysics of galaxies, stars, and planets, i.e. (i) Existence of discrete stellar populations within each of the main Galactic components (disk, halo, and bulge) providing new constraints on models for the formation of the Milky Way. (ii) Differences in the relation between abundances and elemental condensation temperature for the Sun and solar twins suggesting dust-cleansing effects in proto-planetary disks and/or engulfment of planets by stars; (iii) Differences in chemical composition between binary star components and between members of open or globular clusters showing that star- and cluster-formation processes are more complicated than previously thought; (iv) Tight relations between some abundance ratios and age for solar-like stars providing new constraints on nucleosynthesis and Galactic chemical evolution models as well as the composition of terrestrial exoplanets. We conclude that if stellar abundances with precisions of 0.01–0.03 dex can be achieved in studies of more distant stars and stars on the giant and supergiant branches, many more interesting future applications, of great relevance to stellar and galaxy evolution, are probable. Hence, in planning abundance surveys, it is important to carefully balance the need for large samples of stars against the spectral resolution and signal-to-noise ratio needed to obtain high-precision abundances. Furthermore, it is an advantage to work differentially on stars with similar atmospheric parameters, because then a simple 1D LTE analysis of stellar spectra may be sufficient. However, when determining high-precision absolute abundances or differential abundance between stars having more widely different parameters, e.g. metal-poor stars compared to the Sun or giants to dwarfs, then 3D non-LTE effects must be taken into account.     

A Theoretical Probe for Excitation Mechanisms of Solar-like and Mira-like Oscillations of Stars

The linear stability analysis of the radial and non-radial oscillations for the evolutionary model of a star with the mass of 0.6∼3 M8 has been per- formed by using the nonlocal and time-dependent convection theory. The results show that the unstable low-temperature stars on the right side of the instabil- ity strip in the HR diagram can be divided into two groups. One is of the stars of solar-like oscillations, composed of the main-sequence dwarfs, subgiants, and the red giants with low- and intermediate-luminosity, which are unstable in the intermediate- and high-order (nr ≥ 12) p-modes, but stable in the low- order (nr ≤ 5) p-modes. Another is of the Mira-like stars, composed of the luminous red giants and AGB stars, which are just contrary to the solar-like stars, unstable in the low-order (nr ≤ 5) p-modes, but stable in the intermediate- and high-order (nr ≥ 12) p-modes. On the red edge of Cepheid (δ Scuti) insta- bility strip, the oscillations of solar-like and Mira-like stars can be explained uniformly by the coupling between convection and oscillations (CCO). For the low-temperature stars on the right side of the instability strip, the CCO is the dominant excitation and damping mechanism for the low- and intermediate-order p-modes, and the stochastic excitation of turbulence becomes important only for the high-order p-modes of solar-like oscillations.