An asteroseismic signature of helium ionization

We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent γ is a superposition of two decaying periodic functions of frequency ν, with 'frequencies' that are approximately twice the acoustic depths of the centres of the He  i and He  ii ionization regions. That variation is probably best exhibited in the second frequency difference  Δ₂ν _{n ,  l} ≡ν _{n −1,  l} − 2ν _{n ,  l} +ν _{n +1,  l}   . We show how an analytic approximation to the variation of γ leads to a simple representation of this oscillatory contribution to Δ₂ν which can be used to characterize the γ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize γ, not merely to find a formula for Δ₂ν that reproduces the data.     

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.     

Sounding stellar cycles with Kepler – I. Strategy for selecting targets

The long-term monitoring and high photometric precision of the Kepler satellite will provide a unique opportunity to sound the stellar cycles of many solar-type stars using asteroseismology. This can be achieved by studying periodic changes in the amplitudes and frequencies of the oscillation modes observed in these stars. By comparing these measurements with conventional ground-based chromospheric activity indices, we can improve our understanding of the relationship between chromospheric changes and those taking place deep in the interior throughout the stellar activity cycle. In addition, asteroseismic measurements of the convection zone depth and differential rotation may help us determine whether stellar cycles are driven at the top or at the base of the convection zone. In this paper, we analyse the precision that will be possible using Kepler to measure stellar cycles, convection zone depths and differential rotation. Based on this analysis, we describe a strategy for selecting specific targets to be observed by the Kepler Asteroseismic Investigation for the full length of the mission, to optimize their suitability for probing stellar cycles in a wide variety of solar-type stars.     

Evolution of temperature in granule and intergranular space

The temporal evolution of temperature in a dissolving granule and in an adjacent intergranular space is presented. The semi‐empirical evolutionary models have been calculated using an inversion method applied to 4‐min time series of Stokes I spectral line profiles. The models are presented in the form of the functional dependence of temperature T(log τ₅, t) on optical depth τ₅ at 500 nm and time t. The observed disappearance of the granule is accompanied with overall cooling of the granular photosphere. Temperature changes greater than 100 K have been found in deeper (log τ₅ ≥ 0) and upper layers (log τ₅ ≤ –2) whereas the intermediate layers are thermally stable. The intergranular space, which is 2 arcsec off the granule, keeps the temperature structure of the layers from log τ₅ = 0.5 to log τ₅ = –2 without global evolutionary changes except short‐term and spatially confined heating. Finally, the significant temperature changes in the upper layers (log τ₅ ≤ 2.5) observed during the time interval of 4 min are found to be typical for the granular and intergranular photosphere.     

X-ray and extreme-ultraviolet emission from the coronae of Capella

The primary objective of this work is the analysis and interpretation of coronal observations of Capella obtained in 1999 September with the High Energy Transmission Grating Spectrometer on the Chandra X-ray Observatory and the Extreme Ultraviolet Explorer ( EUVE ). He-like lines of O (O  vii ) are used to derive a density of 1.7×10¹⁰ cm⁻³ for the coronae of the binary, consistent with the upper limits derived from Fe  xxi , Ne  ix and Mg  xi line ratios. Previous estimates of the electron density based on Fe  xxi should be considered as upper limits. We construct emission measure distributions and compare the theoretical and observed spectra to conclude that the coronal material has a temperature distribution that peaks around 4–6 MK , implying that the coronae of Capella were significantly cooler than in the previous years. In addition, we present an extended line list with over 100 features in the 5–24 Å wavelength range, and find that the X-ray spectrum is very similar to that of a solar flare observed with SMM . The observed to theoretical Fe  xvii 15.012-Å line intensity reveals that opacity has no significant effect on the line flux. We derive an upper limit to the optical depth, which we combine with the electron density to derive an upper limit of 3000 km for the size of the Fe  xvii emitting region. In the same context, we use the Si  iv transition region lines of Capella from HST /Goddard High-Resolution Spectrometer observations to show that opacity can be significant at T =10⁵ K , and derive a path-length of ≈75 km for the transition region. Both the coronal and transition region observations are consistent with very small emitting regions, which could be explained by small loops over the stellar surfaces.     

Granulation and waves

A summary of the most recent observational results on the solar granulation phenomenon is given and its physical interpretation with respect to theoretical and numerical models is briefly discussed. Special attention is paid to unsolved questions concerning the relation between convective motions and related solar features.     

3‐D hydrodynamic simulations of the solar chromosphere

We present first results of three‐dimensional numerical simulations of the non‐magnetic solar chromosphere, computed with the radiation hydrodynamics code CO⁵BOLD. Acoustic waves which are excited at the top of the convection zone propagate upwards into the chromosphere where the waves steepen into shocks. The interaction of the waves leads to the formation of complex structures which evolve on short time scales. Consequently, the model chromosphere is highly dynamical, inhomogeneous, and thermally bifurcated.     

Signature of differential rotation in solar disk‐integrated chromospheric line emission

UARS SOLSTICE data have been subjected to Fourier and wavelet analyses in order to search for the signature of the solar rotation law in the disk‐integrated irradiance of UV lines. Lyman‐α, Mg II, and Ca II data show a different behaviour. In the SOLSTICE data there are significant temporal variations of the rotation rate of the UV tracers over 5—6 years. Often several distinct rotation periods appear almost simultaneously. Beside the basic period around 27 days there are signals at 32—35 days corresponding to the rotation rate at very high latitudes. For more than 5 years during another period of the solar cycle the rotational behaviour is quite different; there is an indication of differential rotation of active regions in these Ca II ground‐based data. The data contain a wealth of information about the solar differential rotation, but it proves difficult to disentangle the effects of the different emitting sources.     

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.     

Heating of the solar and stellar coronae: a review

Despite great advances in observations and modelling, the problem of solar and stellar heating still remains one of the most challenging problems of space physics. To find a definite answer to what sort of mechanisms act to heat the plasma to a few million degrees requires a collaborative effort of small scales observations, large capacity numerical modelling and complicated theoretical approaches. A unique theory should incorporate aspects such as the generation of energy, its transport and dissipation. Up to now, the first two problems are rather clarified. However, the modality of transfer of magnetic or kinetic energy into heat is a question still awaiting for an answer. In the present paper we review the various popular heating mechanisms put forward in the existing extensive literature. The heating processes are, somewhat arbitrarily, classified as hydrodynamic, magnetohydrodynamic or kinetic based on the characteristics of the model medium. These mechanisms are further divided based on the time scales of the ultimate dissipation involved (i.e. AC and DC heating, turbulent heating). In particular, special attention is paid to discuss shock dissipation, mode coupling, resonant absorption, phase mixing, and, reconnection. Finally, we briefly review the various heating mechanisms proposed to heat other stars. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation and meridional flow in the solar convection zone and beneath

The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a Λ‐effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations (∂Ω/∂r < 0 and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significant for the solar dynamo. The depth of the meridional flow penetration into the radiative zone is proportional to ν^0.5_core, where ν_core is the viscosity beneath the convection zone. The penetration is very small if the tachocline is laminar. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The use of frequency-separation ratios for asteroseismology

The systematic patterns of separations between frequencies of modes of different degree and order are a characteristic of p-mode oscillations of stars. The frequency separations depend on the internal structure of the star and so measuring them in the observed oscillation spectra of variable stars gives valuable diagnostics of the interior of a star. Roxburgh & Vorontsov proposed using the ratio of the so-called small frequency separation to the large frequency separation as a diagnostic of the stellar interior, and demonstrated that this ratio was less sensitive than the individual frequency separations themselves to uncertain details of the near-surface structure. Here we derive kernels relating the frequency separation ratio to structure, and show why the ratio is relatively insensitive to the near-surface structure in terms of the very small amplitude of the kernels in the near-surface layers. We also investigate the behaviour of the separation ratio for stars of different masses and ages, and demonstrate the usefulness of the ratio in the so-called asteroseismic Hertzsprung–Russell diagram.