Author name code: dappen ADS astronomy entries on 2022-09-14 author:"Dappen, Werner" ------------------------------------------------------------------------ Title: Ionization of heavy elements and the adiabatic exponent in the solar plasma Authors: Baturin, V. A.; Oreshina, A. V.; Däppen, W.; Ayukov, S. V.; Gorshkov, A. B.; Gryaznov, V. K.; Iosilevskiy, I. L. Bibcode: 2022A&A...660A.125B Altcode: 2022arXiv220209331B Context. The adiabatic exponent Γ1 is studied as a thermodynamic quantity in the partially ionized plasma of the solar convection zone.
Aims: The aim of this study is to understand the impact of heavy elements on the Γ1 profile. We calculated Γ1 with the SAHA-S equation of state for different chemical compositions of plasma, and we analyzed contributions of individual elements to Γ1. We attempted to determine the mass fractions of the heavy elements using our analysis of the Γ1 profile.
Methods: We studied the decrease in Γ1 due to the ionization of heavy elements in comparison with the value obtained for a pure hydrogen-helium plasma. These types of differences are denoted as "Z contributions", and we analyzed them for eight elements (C, N, O, Ne, Mg, S, Si, and Fe) as well as for a mixture of elements corresponding to the solar chemical composition. The contributions of the heavy elements are studied on an adiabat in the lower part of the convection zone, where the influence of hydrogen and helium to the Z contribution is minimal. The Z-contribution profiles are unique for each chemical element. We compared linear combinations of individual Z contributions with the exact Z contribution. Applying a least-squares technique to the decomposition of the full Z contribution to a basis of individual-element contributions, we obtained the mass fractions of the heavy elements.
Results: The Z contribution of heavy elements can be described by a linear combination of individual-element Z contributions with a high level of accuracy of 5 × 10−6. The inverse problem of estimating the mass fractions of heavy elements from a given Γ1 profile was considered for the example of solar-type mixtures. In ideal numerical simulations, the mass fractions of the most abundant elements could be determined with a relative accuracy better than a few tenths of a percent. In the presence of random or systematic errors in the Γ1 profile, abundance estimations become remarkably less accurate, especially due to unknown features of the equations of state. If the amplitude of the errors does not exceed 10−4, we can expect a determination of at least the oxygen abundance with a relative error of about 10%. Otherwise, the results of the method would not be reliable. Title: Better Physics for Modelling Stars and their Oscillations Authors: Trampedach, R.; Houdek, G.; Däppen, W. Bibcode: 2020svos.conf..317T Altcode: Our interpretation of stellar observations can only be as good as our stellar models and the strong constraints provided by asteroseismology demand very good models indeed. We have approached modelling improvements from three angles: Including effects of realistic 3D convection on the structure of stellar surface layers, including non-adiabatic effects of that convection on oscillations, and finally improving and modernising the equation of state for stellar plasmas. We present a review of our progress on all three fronts. Title: Interpolation of equation-of-state data Authors: Baturin, V. A.; Däppen, W.; Oreshina, A. V.; Ayukov, S. V.; Gorshkov, A. B. Bibcode: 2019A&A...626A.108B Altcode: 2019arXiv190508303B
Aims: We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation.
Methods: We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines.
Results: The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum lgP difference lies in the range from 10-9 to 10-4, and Γ1 difference varies from 10-9 to 10-3. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at T ∼ 1.5 × 103-105 K. The best precision is achieved at higher temperatures, T > 105 K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points. Title: Equation of state SAHA-S meets stellar evolution code CESAM2k Authors: Baturin, V. A.; Däppen, W.; Morel, P.; Oreshina, A. V.; Thévenin, F.; Gryaznov, V. K.; Iosilevskiy, I. L.; Starostin, A. N.; Fortov, V. E. Bibcode: 2017A&A...606A.129B Altcode: 2017arXiv170804937B Context. We present an example of an interpolation code of the SAHA-S equation of state that has been adapted for use in the stellar evolution code CESAM2k.
Aims: The aim is to provide the necessary data and numerical procedures for its implementation in a stellar code. A technical problem is the discrepancy between the sets of thermodynamic quantities provided by the SAHA-S equation of state and those necessary in the CESAM2k computations. Moreover, the independent variables in a practical equation of state (like SAHA-S) are temperature and density, whereas for modelling calculations the variables temperature and pressure are preferable. Specifically for the CESAM2k code, some additional quantities and their derivatives must be provided.
Methods: To provide the bridge between the equation of state and stellar modelling, we prepare auxiliary tables of the quantities that are demanded in CESAM2k. Then we use cubic spline interpolation to provide both smoothness and a good approximation of the necessary derivatives. Using the B-form of spline representation provides us with an efficient algorithm for three-dimensional interpolation.
Results: The table of B-spline coefficients provided can be directly used during stellar model calculations together with the module of cubic spline interpolation. This implementation of the SAHA-S equation of state in the CESAM2k stellar structure and evolution code has been tested on a solar model evolved to the present. A comparison with other equations of state is briefly discussed.
Conclusions: The choice of a regular net of mesh points for specific primary quantities in the SAHA-S equation of state, together with accurate and consistently smooth tabulated values, provides an effective algorithm of interpolation in modelling calculations. The proposed module of interpolation procedures can be easily adopted in other evolution codes. Title: Dynamic Screening in Solar and Stellar Nuclear Reactions Authors: Däppen, W.; Mussack, K. Bibcode: 2012CoPP...52..149D Altcode: No abstract at ADS Title: Microphysics of Stellar Interiors Authors: Däppen, Werner Bibcode: 2011iasa.confE...5D Altcode: No abstract at ADS Title: High-Precision Equation-of-State Formalisms for Solar and Stellar Modeling Authors: Däppen, Werner Bibcode: 2011CoPP...51..328D Altcode: No abstract at ADS Title: Dynamic Screening Correction for Solar p-p Reaction Rates Authors: Mussack, Katie; Däppen, Werner Bibcode: 2011ApJ...729...96M Altcode: 2011arXiv1102.5073M The solar abundance controversy inspires renewed investigations of the basic physics used to develop solar models. Here we examine the correction to the proton-proton reaction rate due to dynamic screening effects. Starting with the dynamic screening energy from the molecular-dynamic simulations of Mao et al., we compute a reaction-rate correction for dynamic screening. We find that, contrary to static screening theory, this dynamic screening does not significantly change the reaction rate from that of the bare Coulomb potential. Title: Dynamic screening in solar and stellar nuclear reactions Authors: Mussack, Katie; Däppen, Werner Bibcode: 2010Ap&SS.328..153M Altcode: 2010Ap&SS.tmp....8M; 2009arXiv0909.2646M In the hot, dense plasma of solar and stellar interiors, the Coulomb interaction is screened by the surrounding plasma. Although the standard Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. In particular, Shaviv and Shaviv apply the techniques of molecular dynamics to the conditions in the solar core in order to numerically determine the dynamic screening effect. By directly calculating the motion of ions and electrons due to Coulomb interactions, they compute the effect of screening without the mean-field assumption inherent in the Salpeter approximation. Here we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of stellar nuclear reaction rates. Title: Emulating the OPAL equation of state Authors: Lin, Hsiao-Hsuan; Däppen, Werner Bibcode: 2010Ap&SS.328..175L Altcode: 2010Ap&SS.tmp...27L The equation of state for the structure of the Sun and stars has to be precise to allow comparisons with observations, i.e., helioseismic inversions of thermodynamic quantities. Among the two of the most popular formalisms are (1) the OPAL equation of state developed at Livermore and (2) the Mihalas-Hummer-Däppen (MHD) equation of state. While OPAL has a solid theoretical foundation, and matches the observational data better, the MHD formalism is more intuitive, easy to realize, and has the possibility of adjustable parameters. Furthermore, it an open-source product in contrast to the proprietary OPAL. Recently a version of MHD has been obtained by including the so-called “Plank-Larkin partition function” and by adding scattering-state terms. The resulting formalism matches OPAL rather well. Here, we report on the next logical step, the implementation of this MHD upgrade into the simple and popular CEFF equation of state. Such an implementation will make it a flexible and convenient tool, allowing an approximative on-line implementation of OPAL in solar and stellar models. Title: Accurate and versatile equations of state for the Sun and Sun-like stars Authors: Däppen, Werner Bibcode: 2010Ap&SS.328..139D Altcode: 2010Ap&SS.tmp...37D For models of the Sun and Sun-like stars, a high-quality equation of state is crucial. In addition, helioseismic and asteroseismic observations also put constraints on the physical formalisms. Thus, they effectively turn the Sun and the stars into laboratories for dense plasmas. Currently, the main astrophysical beneficiary of a good equation of state is the determination of the chemical composition. Here, seismic data have supplemented spectroscopic information. Recently, there has been theoretical progress in the equation of state, thanks to renewed rigorous and phenomenological approaches. Title: The solar-interior equation of state with the path-integral formalism. I. Domain of validity Authors: Perez, A.; Mussack, K.; Däppen, W.; Mao, D. Bibcode: 2009A&A...505..735P Altcode: Aims: This is the first paper in a series that deals with solar-physics applications of the equation-of-state formalism based on the formulation of the so-called “Feynman-Kac (FK) representation”. Here, the FK equation of state is presented and adapted for solar applications. Its domain of validity is assessed. The practical application to the Sun will be dealt with in Paper II. Paper III will extend the current FK formalism to a higher order.
Methods: A recent rigorous quantum-statistical formalism for Coulomb systems is used to compute the thermodynamical quantities for solar modeling, taking into account the necessary requirements on smoothness and accuracy. The FK formalism being a virial expansion, it suffers from the well-known deficiency that it is limited to nearly full ionization. This point is elaborated in detail, and the quantitative criterion for the domain of validity of the FK equation of state is established.
Results: Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This includes the inner region of the Sun out to about .98 of the solar radius. Despite this limitation, in the parts of the Sun where it is applicable, the FK equation of state has the power to be more accurate than the equations of state currently used in solar modeling. The FK approach is especially suited to study physical effects such as Coulomb screening, bound states, the onset of recombination of fully ionized species, as well as diffraction and exchange effects.
Conclusions: Despite technical difficulties in its application, there are unique features in the FK approach that promise to turn it into the most exact of the available formalisms, provided FK is restricted to the deeper layers of the Sun where more than 90% of helium is ionized. The localizing power of helioseismology allows a test of the FK equation of state. Such a test will be beneficial both for better solar models and for tighter solar constraints of the equation of state. Title: Dynamic Screening in Solar Plasma Authors: Mao, Dan; Mussack, Katie; Däppen, Werner Bibcode: 2009ApJ...701.1204M Altcode: 2009arXiv0906.3406M In the hot, dense plasma of solar and stellar interiors, Coulomb potentials are screened, resulting in increased nuclear reaction rates. Although Salpeter's approximation for static screening is widely accepted and used in stellar modeling, the question of screening in nuclear reactions has been revisited. In particular, the issue of dynamic effects has been raised by Shaviv and Shaviv who apply the techniques of molecular dynamics to the conditions in the Sun's core in order to numerically determine the effect of screening. By directly calculating the motion of ions and electrons due to Coulomb interactions, the simulations are used to compute the effect of screening without the mean field assumption inherent in Salpeter's approximation. In this paper, we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included when stellar nuclear reaction rates are computed. Title: A smooth equation of state for solar and stellar abundance determinations Authors: Däppen, Werner; Mao, Dan Bibcode: 2009JPhA...42u4006D Altcode: The modulation of the equation of state by the chemical composition leads to a natural method to determine the helium and heavy-element abundance in the sun and stars. For solar helium this has indeed become the only reliable method. However, one has to keep in mind that the result is only as good as the quality of the equation of state. So far, there are only theoretical formalisms, but no experiments, for the relevant physical conditions. It is obvious that sharp theoretical tools in the form of smooth thermodynamic (and opacity) quantities are crucial for the interpretation of the astrophysical data, both for abundance determinations and improvements of the theory. An emulator of the OPAL equation of state was developed, by which the OPAL equation of state can be applied directly in stellar models, without recourse to pre-computed tables. Title: Rigorous and Phenomenological Equations of State Authors: Däppen, Werner; Mao, Dan Bibcode: 2008IAUS..252...27D Altcode: For solar and stellar modeling, a high-quality equation of state is crucial. But the inverse is also true: the astrophysical data (helioseismic today, asteroseismic tomorrow) put constraints on the physical formalisms, making the Sun and the stars laboratories for plasma physics. One of the main astrophysical benefits from a good equation of state is an improved abundance determination. Recent theoretical progress in the equation of state has involved both rigorous and phenomenological approaches, giving the user a considerable choice. Title: Seismic Abundance Determination in the Sun and in Stars Authors: Däppen, Werner Bibcode: 2007AIPC..948..179D Altcode: The modulation of the equation of state by the chemical composition leads to a natural helio- and asteroseismic method to determine the helium and heavy-element abundance. The idea was first proposed by Douglas Gough, who suggested to exploit the thermodynamic signature of each element. For solar helium this became indeed the only reliable method. Its result (0.24-0.25 in mass fraction) turned out to be substantial lower than the calibrated values for age-zero solar models (0.27-0.28), a discrepancy which drew renewed attention to the importance of the effect of gravitational settling of helium and heavier elements. One has to keep in mind that the result is only as good as the quality of the equation of state, and so far, there are only theoretical formalisms, but no experiments, for the relevant physical conditions. Astrophysical constraints on the quality of the equation of state, however, might come from the solar heavy-element abundance determination. For the heavy elements there are spectroscopic measurements (recently somewhat clouded in doubt though). These measurements can be used to constrain the equation of state. As a consequence, the seismic element determinations become part of a larger project, making the Sun and stars laboratories to study thermodynamic properties of Coulomb systems under conditions not (yet) achieved on Earth. In this enterprise, asteroseismology will play an important parallel role, where the lack of solar-quality data will be more than compensated by the possibility to study stars of significantly different element abundances. Title: Evaluation of Molecular-Dynamics Simulations for the Study of Hot Dense Coulomb Systems Authors: Mussack, Katie; Mao, Dan; Däppen, Werner Bibcode: 2007AIPC..948..207M Altcode: In the plasma of solar and stellar interiors, Coulomb potentials are screened, resulting in increased nuclear reaction rates. Though Salpeter's approximation for static screening is widely accepted and used in stellar modelling, the question of screening in nuclear reactions has recently been revisited. In particular the issue of dynamic effects has been raised by Shaviv and Shaviv who apply the techniques of molecular dynamics to the conditions in the Sun's core in order to numerically determine the effect of screening. By directly calculating the motion of ions and electrons due to Coulomb interactions, they are able to compute the effect of screening without the mean field assumption inherent in Salpeter's approximation. However, Shaviv and Shaviv's work includes a variety of assumptions that must be evaluated before their results can be accepted. We carried out a pilot study of a small system under conditions similar to the solar core in order to examine the assumptions and approximations in Shaviv and Shaviv's numerical simulations. Our work confirms Shaviv and Shaviv's conclusion that instead of relying on the static approximation, dynamic effects must also be considered. Title: The Solar-Interior Equation of State with the Path-Integral Formalism I. Domain of Validity Authors: Perez, Asher; Mussack, Katie; Dappen, Werner; Mao, Dan Bibcode: 2007arXiv0705.0547P Altcode: This is the first paper in a series that deals with solar-physics applications of the equation-of-state formalism based on the formulation of the so-called "Feynman-Kac (FK) representation". Here, the FK equation of state is presented and adapted for solar applications. Its domain of validity is assessed. The practical application to the Sun will be dealt with in Paper II. Paper III will extend the current FK formalism to a higher order. Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This incudes the inner region of the Sun out to about .98 of the solar radius. Despite this limitation, in the parts of the Sun where it is applicable, the FK equation of state has the power to be more accurate than the equations of state currently used in solar modeling. The FK approach is especially suited to study physical effects such as Coulomb screening, bound states, the onset of recombination of fully ionized species, as well as diffraction and exchange effects. The localizing power of helioseismology allows a test of the FK equation of state. Such a test will be beneficial both for better solar models and for tighter solar constraints of the equation of state. Title: Helioseismology and Plasma Physics Authors: Däppen, W. Bibcode: 2007ASPC..370....3D Altcode: Helioseismology has become a very successful diagnosis of the equation of state. Although the gas in the solar interior is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismological measurements puts strong constraints on the nonideal part of the equation of state. For solar and stellar modeling, a high-quality equation of state is crucial. But the inverse is also true: the observational data put constraints on the physical formalisms, thus making the Sun and the stars laboratories for plasma physics. The main diagnostic methods are discussed. Title: Molecular-dynamics simulations of hot dense Coulomb systems Authors: Mussack, K.; Mao, D.; Däppen, W. Bibcode: 2006ESASP.624E..20M Altcode: 2006soho...18E..20M No abstract at ADS Title: A Synoptic Comparison of the Mihalas-Hummer-Däppen and OPAL Equations of State Authors: Trampedach, R.; Däppen, W.; Baturin, V. A. Bibcode: 2006ApJ...646..560T Altcode: 2006astro.ph..4352T A detailed comparison is carried out between two popular equations of state (EOSs), the Mihalas-Hummer-Däppen (MHD) and OPAL equations of state, which have found widespread use in solar and stellar modeling during the past two decades. They are parts of two independent efforts to recalculate stellar opacities: the international Opacity Project (OP) and the Livermore-based OPAL project. We examine the difference between the two EOSs in a broad sense, over the whole applicable ϱ-T range, and for three different chemical mixtures. Such a global comparison highlights both their differences and their similarities. We find that omitting a questionable hard-sphere correction, τ, to the Coulomb interaction in the MHD formulation, greatly improves the agreement between the MHD and OPAL EOSs. We also find signs of differences that could stem from quantum effects not yet included in the MHD EOS, and differences in the ionization zones that are probably caused by differences in the mechanisms for pressure ionization. Our analysis not only gives a clearer perception of the limitations of each EOS for astrophysical applications, but also serves as guidance for future work on the physical issues behind the differences. The outcome should be an improvement of both EOSs. Title: The equation of state for the solar interior Authors: Däppen, Werner Bibcode: 2006JPhA...39.4441D Altcode: Helioseismology has become a very successful diagnosis of the equation of state. Although the gas in the solar interior is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismological measurements puts strong constraints on the nonideal part of the equation of state. For solar and stellar modelling, a high-quality equation of state is crucial. But the inverse is also true: the astrophysical data (helioseismic today, asteroseismic tomorrow) can put constraints on the physical formalisms, thus making the Sun and the stars laboratories for plasma physics. Title: The Chemical Composition and Equation of State of the Sun Inferred from Seismic Models through an Inversion Procedure Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2005ApJ...623..556L Altcode: The remarkable quality of present helioseismic data provides the possibility to investigate the microscopic physics of the solar interior. An inversion procedure to reveal the equation of state and chemical composition in the Sun has been developed. The method is based on using the discrepancy in the adiabatic gradient γ1≡(∂lnP/∂lnρ)s (s being the specific entropy) to infer the discrepancies in the equation of state and in the chemical composition between the Sun and solar models. Adequate accuracy and stability of the procedure have been demonstrated. Our inverted δγ1/γ1 between the Sun and model S of Christensen-Dalsgaard et al. is consistent with the earlier result obtained by Basu et al. We also found that the inverted δγ1/γ1 between the Sun and an envelope model implemented with the so-called CEFF equation of state (Christensen-Dalsgaard & Däppen) basically shows two dips. The dips are located at 0.975 and 0.988 Rsolar. Both dips cannot be eliminated merely by tuning the helium abundance over a reasonable range; hence, it appears that the dips are a manifestation of inappropriate approximations used in the equation of state of the underlying models. Title: Equation-of-State and Phase-Transition in Models of Ordinary Astrophysical Matter Authors: Celebonovic, Vladan; Gough, Douglas; Däppen, Werner Bibcode: 2004AIPC..731.....C Altcode: No abstract at ADS Title: Development of Molecular-Dynamics Tools to Study Hot Dense Coulomb Systems Authors: Mao, D.; Mussack, K.; Däppen, W. Bibcode: 2004ESASP.559..560M Altcode: 2004soho...14..560M No abstract at ADS Title: The chemical composition and equation of state of the Sun inferred from seismic models through an inversion procedure Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2004AIPC..731..230L Altcode: The present helioseismic data, with their remarkable precision, provide the possibility to investigate the microscopic physics of the solar interior. In this study, we are specifically interested in the chemical composition and equation of state (EOS). Since these properties are not directly measurable, we chose the adiabatic gradient, γ1 ≡ ∂lnP/∂lnρ|s, as the probe to examine these properties. Specifically, we infer the discrepancies in the chemical composition and EOS by the discrepancy in γ1, i.e., δγ1/γ1, between two solar structures.

Even though the heavy elements only constitute less than 2% of the solar material, our inversion results showed that the variation in the relative abundances among heavy elements would result in discernible features in δγ1/γ1. Title: The Chemical Composition and Equation of State of the Sun Inferred from Seismic Models Through AN Inversion Procedure Authors: Däppen, W.; Lin, C. -H. Bibcode: 2004ESASP.559..400D Altcode: 2004soho...14..400D No abstract at ADS Title: Phenomenological and Rigorous Equations of State for Solar and Stellar Modeling Authors: Dappen, W. Bibcode: 2004ESASP.559..261D Altcode: 2004soho...14..261D No abstract at ADS Title: Equations of state for solar and stellar modeling Authors: Däppen, Werner Bibcode: 2004AIPC..731....3D Altcode: Helioseismology has become the most successful diagnosis of the equation of state for the plasma of stellar interiors. Although in the solar interior the plasma is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismological observations puts nevertheless strong constraints on the nonideal part of the equation of state. For solar and stellar modeling, a high-quality equation of state is crucial. But the inverse is also true: the astrophysical data put constraints on the physical formalisms, making the Sun and the stars novel laboratories for plasma physics. Title: Isolating the effects of chemical composition in the equation of state Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2004AIPC..731..219L Altcode: The effects of different chemical compositions and of different equation-of-state formalisms on a solar structure are often mixed. The reason being that the chemical composition in modern, sophisticated equations of state cannot be easily adjusted. Therefore, most of related studies simply consider the combined effect of the two, rather than individual effect. The actual error in the formalism of the equation of state is thus inevitably obscured.

The aim of this paper is to examine and isolate the effects of varying chemical compositions, in hope to help to extract the effects purely from the formalism of equation of state.

We present a strategy and the results of examining the effects of the ionization of individual element. Title: Emulating the Opal Equation of State Authors: Liang, A.; Däppen, W. Bibcode: 2004ESASP.559..548L Altcode: 2004soho...14..548L No abstract at ADS Title: Equation of State for the Internal Structure of Solar-Type Stars Authors: Baturin, V. A.; Däppen, W. Bibcode: 2003ARep...47..685B Altcode: The physical basis for thermodynamical modeling of plasma under the conditions typical of moderate-mass stars is considered. We apply the method of thermodynamic potentials to introduce chemical and physical plasma models that represent basic, modern descriptions of a nondegenerate, weakly nonideal plasma. Ionization of an ideal multicomponent plasma at low temperatures is used as a basic approximation for the solar convection zone and in the corresponding chemical picture. The effects of Coulomb free-free and bound-free electron interactions are classified according to their appearance in the solar interior. Modeling internal stellar structure requires a formalism with nonideal ionization at high densities (frequently called pressure ionization). Perspectives for describing such ionization are considered in the framework of several models. Title: Helioseismic constraints on the chemical composition and the equation of state Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2003ESASP.517..337L Altcode: 2003soho...12..337L The intrinsic γ1 difference is defined as the discrepancy in the adiabatic exponent γ1, resulting from the discrepancies in the equation of state and the chemical composition. The other part of the γ1 difference, "induced" by the discrepancy in the internal structure (i.e., pressure, density or temperature) is excluded. Our examination of solar models revealed that the discrepancy in the heavy-element composition and the discrepancy in the equation of state result in different and independent features in the functional form of the intrinsic γ1 difference. Therefore, the two discrepancies can be distinguished by looking for the features that do not change when only either the equation of state or the chemcical composition is being varied. The possibility of such a strategy was already discussed in an earlier study (Gong, Däppen and Nayfonov 2001), although only theoretically. Our inversion tests demonstrate the potential of its realization. In this paper, we present our initial inversion results between the Sun and various solar models and discuss the strengths and limits of our inversion code. Title: Modifications of the equation of state to achieve desired changes in thermodynamic quantities Authors: Liang, Aihua; Däppen, Werner Bibcode: 2003ESASP.517..333L Altcode: 2003soho...12..333L Various helioseismological applications are subject to the uncertainty in the equation of state. A typical example is the helioseismic determination of the helium abundance in the convection zone. Only confidence in the quality of the equation of state will lead to a reliable result. There are several methods to improve the quality, depending on the type of the equation of state. Some equations of state are rather fundamental, but become very complicated for realistic astrophysical matter. An example is the OPAL equation of state developed at Livermore. Other equations of state are more intuitive and less rigorous, but easier in their practical realization. An example is the Mihalas-Hummer-Däppen (MHD) equation of state. It makes sense therefore to try to modify the physical parameters in MHD, such that it can emulate OPAL. The result will be a flexible tool for stellar modelers. We report on preliminary work in this direction, based on a systematic study of the response of the thermodynamic quantities to several classes of modifications of the occupation probabilities, as well as different truncations of the internal partition functions. We have also re-visited the issue of the so-called Planck-Larkin partition function (PLPF). Title: Investigating inversion uncertainties resulting from mode selections Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2003ESASP.517..341L Altcode: 2003soho...12..341L The quality of an inversion depends on many factors. In addition to the well known ones, such as the target function, the surface term and the suppression parameters, different inversion codes utilizing different matrix inversion algorithms could also bring in an additional uncertainty. Therefore, it is important to assess the uncertainty and the stability of an inversion code prior using it to obtain any reliable result. The examination of our inversion code suggested the following: low-degree low-order modes are essential for an accurate inversion; when the quantity being inverted contains narrow features near the surface, the inversions using different mode sets would be inconsistent. In this paper, we show some representative results, in order to invite stimulating discussions and insightful suggestions. Title: Solar constraints on the equation of state Authors: Däppen, Werner Bibcode: 2003safd.book..179D Altcode: Helioseismology has become a very successful diagnosis of the equation of state of the plasma of the solar interior. Although the gas in the solar interior is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismological measurements puts strong constraints on the nonideal part of the equation of state. The helioseismic verification of major nonideal effects in the equation of state of solar matter has become well established. The dominant contribution is the Coulomb pressure, conventionally described in the Debye-Hückel approximation. However, in the last years, the increased precision of the helioseismic diagnosis has brought significant observational progress beyond the Debye-Hückel approximation. The helioseismic detection of a signature of relativistic electrons was a striking example. Very recently, effects of the excited states of the atoms and ions of heavy elements were discovered, which have a promising potential both for statistical mechanics and solar physics, in particular, the helioseismic determination of the heavy-elemental abundance. Title: The plasma-solid transition: Some implications in astrophysics Authors: Celebonovic, V.; Dappen, W. Bibcode: 2002SerAJ.165...23C Altcode: 2002astro.ph..6009C Using a criterion proposed by Salpeter and standard solid-state physics, we have determined the Debye temperature of a solid in equilibrium with the electron gas surrounding it. The results obtained can have astrophysical applications in the determination of parameters of interstellar and interplanetary clouds. Title: Effects of Heavy Elements and Excited States in the Equation of State of the Solar Interior Authors: Gong, Zhigang; Däppen, Werner; Nayfonov, Alan Bibcode: 2001ApJ...563..419G Altcode: 2001astro.ph..8307G Although 98% of the solar material consists of hydrogen and helium, the remaining chemical elements contribute in a discernible way to the thermodynamic quantities. An adequate treatment of the heavy elements and their excited states is important for solar models that are subject to the stringent requirements of helioseismology. The contribution of various heavy elements in a set of thermodynamic quantities has been examined. Characteristic features that can trace individual heavy elements in the adiabatic exponent γ1=(∂lnp/∂lnϱ)s (s being specific entropy), and hence in the adiabatic sound speed, were searched. It has emerged that prominent signatures of individual elements exist and that these effects are greatest in the ionization zones, typically located near the bottom of the convection zone. The main result is that part of the features found here depend strongly on both the given species (atom or ion) and its detailed internal partition function, whereas other features only depend on the presence of the species itself, not on details such as the internal partition function. The latter features are obviously well suited for a helioseismic abundance determination, while the former features present a unique opportunity to use the Sun as a laboratory to test the validity of physical theories of partial ionization in a relatively dense and hot plasma. This domain of plasma physics has so far no competition from terrestrial laboratories. Another, quite general, finding of this work is that the inclusion of a relatively large number of heavy elements has a tendency to smear out individual features. This affects both the features that determine the abundance of elements and the ones that identify physical effects. This property alleviates the task of solar modelers because it helps to construct a good working equation of state that is relatively free of the uncertainties from basic physics. By the same token, it makes more difficult the reverse task, which is constraining physical theories with the help of solar data. Title: Changes in convective properties over the solar cycle: effect on p-mode damping rates Authors: Houdek, G.; Chaplin, W. J.; Appourchaux, T.; Christensen-Dalsgaard, J.; Däppen, W.; Elsworth, Y.; Gough, D. O.; Isaak, G. R.; New, R.; Rabello-Soares, M. C. Bibcode: 2001MNRAS.327..483H Altcode: Measurements of both solar irradiance and p-mode oscillation frequencies indicate that the structure of the Sun changes with the solar cycle. Balmforth, Gough & Merryfield investigated the effect of symmetrical thermal disturbances on the solar structure and the resulting pulsation frequency changes. They concluded that thermal perturbations alone cannot account for the variations in both irradiance and p-mode frequencies, and that the presence of a magnetic field affecting acoustical propagation is the most likely explanation of the frequency change, in the manner suggested earlier by Gough & Thompson and by Goldreich et al. Numerical simulations of Boussinesq convection in a magnetic field have shown that at high Rayleigh number the magnetic field can modify the preferred horizontal length scale of the convective flow. Here, we investigate the effect of changing the horizontal length scale of convective eddies on the linewidths of the acoustic resonant mode peaks observed in helioseismic power spectra. The turbulent fluxes in these model computations are obtained from a time-dependent, non-local generalization of the mixing-length formalism. The modelled variations are compared with p-mode linewidth changes revealed by the analysis of helioseismic data collected by the Birmingham Solar-Oscillations Network (BiSON); these low-degree (low-l) observations cover the complete falling phase of solar activity cycle 22. The results are also discussed in the light of observations of solar-cycle variations of the horizontal size of granules and with results from 2D simulations by Steffen of convective granules. Title: Generalized Fermi-Dirac functions and derivatives: properties and evaluation Authors: Gong, Z.; Zejda, L.; Däppen, W.; Aparicio, J. M. Bibcode: 2001CoPhC.136..294G Altcode: 2001astro.ph..2329G The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac functions have been found. An effective numerical method to evaluate the derivatives of the generalized Fermi-Dirac functions up to third order with respect to both degeneracy and temperature is then proposed, following Aparicio [Ap.J.S.S. 117 (1998) 627]. A Fortran program based on this method, together with a sample test case, is provided. Accuracy and domain of reliability of some other, popularly used analytic approximations of the generalized Fermi-Dirac functions for extreme conditions are investigated and compared with our results. Title: The plasma-solid transition Authors: Celebonovic, V.; Dappen, W. Bibcode: 2001astro.ph..2284C Altcode: Using a criterion proposed by Salpeter and standard solid-state physics,we have determined conditions for the occurence of the plasma-solid transition.Possible astrophysical applications are discussed. Title: Inversion for the adiabatic gradient γ1 to examine equation-of-state effects Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2001ESASP.464..527L Altcode: 2001soho...10..527L The inversion method SOLA (subtractive optimally localized averages) has been successfully applied to study various properties of the solar interior. The focus of the present work is on the microscopic properties of solar matter. The following topics are prime targets of our investigation: (I) ionization of helium and heavy-elements in the deeper parts of the convection zone; (II) the discrepancy in the results of the helioseismic helium abundance determination from different inversion procedures; (III) the possibility of a remainder of not fully ionized helium in the solar core. For the diagnosis of the equation of state, an inversion for the adiabatic gradient γ1 = (∂ln p/∂ln ρ)s (s being specific entropy), and not sound speed, is the most appropriate. This is because the adiabatic gradient is mainly a function of the microscopic physics (ionization reaction; Coulomb pressure correction; pressure ionization; etc.) rather than the macroscopic structure of the model. We are adopting the inversion technique of Basu, Däppen & Nayfonov (1999) and modify it for our purposes. Preliminary results are presented in this paper. Title: MHD Equation of State with Relativistic Electrons Authors: Gong, Zhigang; Däppen, Werner; Zejda, Ladislav Bibcode: 2001ApJ...546.1178G Altcode: The Mihalas-Däppen-Hummer (MHD) equation of state does not include the effect of relativistic partially degenerate electrons, although nonrelativistic partial degeneracy is taken into account. The discovery of a relativistic correction in helioseismology forces us to perform an appropriate upgrade of the MHD equation of state. We have adopted the method of J. M. Aparicio to evaluate the relativistic Fermi-Dirac functions. Our calculations confirm the validity of the approximation used, which works well for the weakly relativistic electrons under solar-center conditions. However, our results will also provide reliable thermodynamic quantities in the stronger relativistic regime as found in more massive stars. Since a particular feature of the original MHD papers was an explicit list of the adopted free energy and its first- and second-order analytical derivatives, we give the corresponding relativistic quantities in the Appendix. Title: Extracting the excitation function on solar oscillations by means of deconvolution Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2001ESASP.464..649L Altcode: 2001soho...10..649L Acoustic oscillations normally are excited by continuous convective motion. Because of the turbulent nature of convection, the low-degree modes generated by convection should be uncorrelated. However, in earlier studies (e.g., Baudin, Gabriel, Gibert, Palle & Regulo (1996), Foglizzo (1998)), a possible correlation between different modes was noticed in the IPHIR data. It was suspected that there might have been occasional solar activities as excitation sources during this period of time. However, the existence of this kind of excitation mechanism was not directly shown. The goal of this study is to reconstruct the forcing function that causes the excitation. In typical observations of solar oscillations, the sampling time (around 1 minute) is insufficient to resolve the excitation resulting from continuous convection. Thus, only infrequent excitation caused by irregular events can be revealed. Therefore, this method can become a tool to investigate infrequent solar events. The testing results from artificial signals have been reported in our previous paper (Lin & Däppen, 2000). Here, we present our current status of the application to four sets of real signals: SOI/MDI, VIRGO, GOLF and IPHIR. Title: Solar Interior: Equation of State and Opacity Authors: Däppen, W. Bibcode: 2000eaa..bookE2002D Altcode: In stellar models, the equation of state and opacity are, together with nuclear reaction rates, the fundamental material properties. The structure of a star is a result of (i) a balance of forces, (ii) a balance between the energy loss at the stellar surface and energy generation in the core and (iii) stationary energy transport between the core and the surface (see SOLAR INTERIOR: STANDARD MODEL... Title: Stellar Interiors: Thermodynamics Authors: Däppen, W. Bibcode: 2000eaa..bookE2122D Altcode: Material properties and stellar models... Title: Seismology of the solar envelope: sound-speed gradient in the convection zone and its diagnosis of the equation of state Authors: Baturin, V. A.; Däppen, W.; Gough, D. O.; Vorontsov, S. V. Bibcode: 2000MNRAS.316...71B Altcode: We report the results of an asymptotic inversion of solar oscillation data for the gradient of the sound speed in the convection zone. This gradient reveals details of the non-ideal Coulomb interactions between particles, including pressure ionization. A simplified physical model is used to track down the effect of various physical assumptions in the sound-speed derivative. The model contains a calibration for the size of the H and He atoms and the He+ ion. We find that, for the pressure-ionization regions of hydrogen and helium, such a model matches the data better than any of the currently available parameter-free theories. Title: The plasma-solid transition:two simple examples Authors: Celebonovic, V.; Dappen, W. Bibcode: 2000astro.ph..7337C Altcode: Using a simple criterion proposed by Kirzhnitz,we have discussed the plasma-solid transition in two simple model cases: the Fermi-Dirac and Bose Einstein gas.Some possibilities of astrophysical applications of our results are also indicated. Title: Investigating the excitation of acoustic modes using homomorphic deconvolution Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 2000SoPh..193..357L Altcode: Properties of the convection zone are encrypted in the behavior of acoustic modes (p modes) and also in the excitation mechanism. The goal of this study is to reconstruct the pattern of the excitation (e.g., the rate and strength of the excitation) from an observed signal. The method, homomorphic deconvolution, has been tested on several sets of artificial signals. The preliminary results presented here are promising. Further rigorous tests and the eventual application to a real signal will be carried out in the near future. Title: The Sun as an Equation-of-State Laboratory Authors: Däppen, Werner; Nayfonov, Alan Bibcode: 2000ApJS..127..287D Altcode: Thanks to helioseismology, the equation of state of the plasma of the solar interior can be diagnosed. Although the gas in the solar interior is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismic measurements puts strong constraints on the nonideal part of the equation of state. The helioseismic verification of major nonideal effects in the equation of state of solar matter has become well established. The dominant contribution is the Coulomb pressure, conventionally described in the Debye-Hückel approximation. However, recently the increased precision of the helioseismic diagnosis has brought significant observational progress beyond the Debye-Hückel approximation. This is illustrated with the subtle effect of excited states in bound systems, in particular hydrogen. Title: Astrophysical Equation of State and Opacity Authors: Däppen, W.; Guzik, J. A. Bibcode: 2000ASIC..544..177D Altcode: 2000vsea.conf..177D No abstract at ADS Title: Atoms and Molecules Authors: Däppen, Werner Bibcode: 2000asqu.book...27D Altcode: No abstract at ADS Title: An Introduction to Helioseismology Authors: Christensen-Dalsgaard, J.; Däppen, W.; Dziembowski, W. A.; Guzik, J. A. Bibcode: 2000ASIC..544...59C Altcode: 2000vsea.conf...59C No abstract at ADS Title: Upgrading the MHD Equation of State to Include Relativistic Electrons Authors: Gong, Z.; Däppen, W. Bibcode: 2000ASPC..203..388G Altcode: 2000ilss.conf..388G; 2000IAUCo.176..388G So far, the effect of relativistic electrons has not been included in the Mihalas-Däppen-Hummer (Hummer & Mihalas 1988; Mihalas, Däppen, & Hummer 1988; Däppen et al. 1988; hereinafter MHD) equation of state, although degeneracy was taken into account. Following the findings about the detectability of the relativistic effect in helioseismological data of the solar center (Elliot & Kosovichev 1998; hereinafter EK98), we have upgraded the MHD equation of state to include relativistic degenerate electrons. Our numerical calculation confirms the result of EK98. Title: The MHD Equation of State with Post-Holtsmark Microfield Distributions Authors: Nayfonov, Alan; Däppen, Werner; Hummer, David G.; Mihalas, Dimitri Bibcode: 1999ApJ...526..451N Altcode: 1999astro.ph..1360N The Mihalas-Hummer-Däppen (MHD) equation of state is a part of the Opacity Project (OP), where it mainly provides ionization equilibria and level populations of a large number of astrophysically relevant species. Its basic concept is the idea of perturbed atomic and ionic states. At high densities, when many-body effects become dominant, the concept of perturbed atoms loses its sense. For that reason, the MHD equation of state was originally restricted to the plasma of stellar envelopes, that is, to relatively moderate densities, which should not exceed ρ<10-2 g cm-3. However, helioseismological analysis has demonstrated that this restriction is much too conservative. The principal feature of the original Hummer & Mihalas paper is an expression for the destruction probability of a bound state (ground state or excited) of a species (atomic or ionic), linked to the mean electric microfield of the plasma. Hummer & Mihalas assumed, for convenience, a simplified form of the Holtsmark microfield for randomly distributed ions. An improved MHD equation of state (Q-MHD) is introduced. It is based on a more realistic microfield distribution that includes plasma correlations. Comparison with an alternative post-Holtsmark formalism (APEX) is made, and good agreement is shown. There is a clear signature of the choice of the microfield distribution in the adiabatic index γ1, which makes it accessible to present-day helioseismological analysis. However, since these thermodynamic effects of the microfield distribution are quite small, it also follows that the approximations chosen in the original MHD equation of state were reasonable. A particular feature of the original MHD papers was an explicit list of the adopted free energy and its first- and second-order analytical derivatives. The corresponding Q-MHD quantities are given in the Appendix. Title: Helioseismic Analysis of the Hydrogen Partition Function in the Solar Interior Authors: Basu, Sarbani; Däppen, Werner; Nayfonov, Alan Bibcode: 1999ApJ...518..985B Altcode: 1998astro.ph.10132B The difference in the adiabatic gradient γ1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called intrinsic difference in γ1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Däppen (MHD) equation of state and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Däppen). The effect stems from an internal partition function of hydrogen, as is used in the MHD equation of state. Although it is a pure hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium abundance of the solar convection zone. Title: A Comment on ``On Density-dependent and Temperature-dependent Ground-State and Continuum Effects in the Equation of State for Stellar Interiors'' Authors: Kraeft, Wolf-Dietrich; Arndt, Stefan; Däppen, Werner; Nayfonov, Alan Bibcode: 1999ApJ...516..369K Altcode: Misunderstandings have occurred regarding the conclusions of the paper ``On Density-dependent and Temperature-dependent Ground-State and Continuum Effects in the Equation of State for Stellar Interiors'' by S. Arndt, W. Däppen, & A. Nayfonov (1998, ApJ, 498, 349). On occasion, its results have been interpreted as if it showed basic flaws in the general theory of dynamical screening. The aim of this comment is to emphasize the context in which the conclusions of the paper must be understood in order to avoid misinterpretations. Title: Grids of stellar models. VIII. From 0.4 to 1.0 {Msun} at Z=0.020 and Z=0.001, with the MHD equation of state Authors: Charbonnel, C.; Däppen, W.; Schaerer, D.; Bernasconi, P. A.; Maeder, A.; Meynet, G.; Mowlavi, N. Bibcode: 1999A&AS..135..405C Altcode: 1998astro.ph.10416C We present stellar evolutionary models covering the mass range from 0.4 to 1 Msun calculated for metallicities Z=0.020 and 0.001 with the MHD equation of state \cite[(Hummer & Mihalas 1988;] \cite[Mihalas et al. 1988;] \cite[Däppen et al. 1988).] A parallel calculation using the OPAL \cite[(Rogers et al. 1996)] equation of state has been made to demonstrate the adequacy of the MHD equation of state in the range of 1.0 to 0.8 Msun (the lower end of the OPAL tables). Below, down to 0.4 Msun, we have justified the use of the MHD equation of state by theoretical arguments and the findings of \cite[Chabrier & Baraffe (1997).] We use the radiative opacities by \cite[Iglesias & Rogers (1996),] completed with the atomic and molecular opacities by \cite[Alexander & Fergusson (1994).] We follow the evolution from the Hayashi fully convective configuration up to the red giant tip for the most massive stars, and up to an age of 20 Gyr for the less massive ones. We compare our solar-metallicity models with recent models computed by other groups and with observations. The present stellar models complete the set of grids computed with the same up-to-date input physics by the Geneva group (Z=0.020 and 0.001, \cite[Schaller et al. 1992;] \cite[Bernasconi 1996,] and \cite[Charbonnel et al. 1996;] Z=0.008, \cite[Schaerer et al. 1992;] Z=0.004, \cite[Charbonnel et al. 1993;] Z=0.040, \cite[Schaerer et al. 1993;] Z=0.10, \cite[Mowlavi et al. 1998;] enhanced mass loss rate evolutionary tracks, \cite[Meynet et al. 1994).] Data available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html Title: Investigate the Noise of Low-l P Modes Authors: Lin, Chia-Hsien; Däppen, Werner Bibcode: 1999soho....9E..70L Altcode: Turbulence and granulation in the convective region of the Sun are believed to be responsible for the excitation of the oscillation signal (i.e., the p modes); however, they are also the source of unwanted noise and the cause of a non-stationary signal. In other words, the noise in the solar data is entangled with the oscillation signal. To reduce the noise, it may be that the usual noise reduction methods for additive or multiplicative noise are not effective. The object of this study is first, to investigate the specific properties of the noise and its entanglement, and second, to separate the noise from the oscillation. Title: Research on the solar model and oscillation in 1990s (II): progress in research on the solar oscillations. Authors: Gong, Zhigang; Yuan, Yongquan; Li, Yan; Däppen, W.; Peng, Meixian Bibcode: 1998PABei..16..305G Altcode: Helioseismology has become a new tool for the study of the solar interior as well as one of the most important devices to determine the quality of the input physics that enters the solar models. The discrepancy between theoretical and observational frequencies has drastically decreased in the 1990s due to modified input physics and improved stellar oscillation theory. However, the discrepancy is still bigger than the observational error. From frequency inversion studies the authors know more about the solar convection zone, the surface helium abundance and rotational velocity distribution as a function of depth and latitude. The stochastic excitation mechanism by turbulence and the location of the excitation sources are well studied, but not completely understood. Title: Research on the solar model and oscillation in 1990s (I): progress in solar models. Authors: Gong, Zhigang; Yuan, Yongquan; Däppen, W.; Li, Yan; Peng, Meixian Bibcode: 1998PABei..16..287G Altcode: The study of solar models is the most important way to understand the global structure and properties of the Sun. Developments in solar modelling in the 1990s are reviewed. The use of the MHD and OPAL equations of states and of the OPAL opacity has moved the theoretical solar oscillation frequencies much closer to the observed values. The introduction of turbulent spectrum in the local convection theory and the 3D hydrodynamic simulation convection models have increased the knowledge of convective energy transportation, as well as its influence on the global Sun. The difference of surface helium abundance between models and inversion results has been filled by diffusion effects. Surface lithium may be depleted by turbulent diffusion or big mass loss. An astrophysical solution for the solar neutrino fluxes looks unlikely. A higher probability exists for a solution from particle physics. Title: VizieR Online Data Catalog: Grids of stellar models. VIII. (Charbonnel+ 1999) Authors: Charbonnel, C.; Dappen, W.; Schaerer, D.; Bernasconi, P. A.; Maeder, A.; Meynet, G.; Mowlavi, N. Bibcode: 1998yCat..41350405C Altcode: We present stellar evolutionary models covering the mass range from 0.4 to 1M⊙ calculated for metallicities Z=0.020 and 0.001 with the MHD equation of state (Hummer & Mihalas, 1988ApJ...331..794H, Mihalas et al., 1988ApJ...331..815M, Daeppen et al., 1988ApJ...332..261D). A parallel calculation using the OPAL (Rogers et al., 1996ApJ...456..902R) equation of state has been made to demonstrate the adequacy of the MHD equation of state in the range of 1.0 to 0.8M⊙ (the lower end of the OPAL tables). Below, down to 0.4M⊙, we have justified the use of the MHD equation of state by theoretical arguments and the findings of Chabrier & Baraffe (1997A&A...327.1039C). We use the radiative opacities by Iglesias & Rogers (1996ApJ...464..943I), completed with the atomic and molecular opacities by Alexander & Fergusson (1994ApJ...437..879A). We follow the evolution from the Hayashi fully convective configuration up to the redgiant tip for the most massive stars, and up to an age of 20Gyr for the less massive ones. We compare our solar-metallicity models with recent models computed by other groups and with observations.

(21 data files). Title: On Density-dependent and Temperature-dependent Ground-State and Continuum Effects in the Equation of State for Stellar Interiors Authors: Arndt, Stefan; Däppen, Werner; Nayfonov, Alan Bibcode: 1998ApJ...498..349A Altcode: 1999astro.ph..1169K We examine the consequence of shifts in bound-state energies, as well as the position of the continuum for thermodynamic quantities. Two independent methods from different branches of physics are brought together. A simple free-energy model is used to examine the thermodynamic consequences of the results of quantum statistical calculations of two-particle properties in a plasma using the Green's function technique. A comparison with data inferred from helioseismology shows that our interdisciplinary procedure works very well for lower level approximations, such as the static screening in the effective two-particle wave equation. However, in the case of dynamic screening in the wave equation, the resulting thermodynamic quantities are inconsistent with observations. This could result from the inability of our method to compute the thermodynamic quantities or from the inappropriate treatment of the ion contribution to the electronic self-energy corresponding to the dielectric function used in random phase approximation. In any case, the results superbly demonstrate the power of helioseismology to test models of basic plasma physics. Title: Microphysics: Equation of State Authors: Däppen, Werner Bibcode: 1998SSRv...85...49D Altcode: The equation of state is one of the three fundamental ingredients used to construct stellar models. The plasma of the interiors of stars such as the Sun is only slightly non-ideal. However, the extraordinary accuracy of the helioseismological data requires refined equations of state. It turned out to be necessary to include a Coulomb correction, commonly evaluated in the Debye-Hückel approximation. Higher-order non-ideal effects have implications as well, both for plasma physics and for solar physics. As a typical example, the recently studied thermodynamic consequence of excited states in compound particles is discussed. This effect is of considerable relevance in the helioseismic determination of the helium abundance in the solar convection zone. Title: The Signature of the Internal Partition Function in Thermodynamical Quantities of the Solar Interior Authors: Nayfonov, Alan; Däppen, Werner Bibcode: 1998ApJ...499..489N Altcode: The extraordinary accuracy of available helioseismological data presents an opportunity to study nonideal plasma effects of the solar interior beyond the leading-order Coulomb correction term. The effect of different internal partition functions on a complete set of thermodynamical quantities is examined, and it is found that there is a clear signature of the excited states well within reach of present helioseismic inversion techniques. Title: Helioseismic Signature of the Presence of Excited States in the Adiabatic Exponent Authors: Basu, Sarbani; Däppen, Werner; Nayfonov, Alan Bibcode: 1998ESASP.418..435B Altcode: 1998soho....6..435B Recently, Nayfonov & Däppen (1998) have examined the signature of the internal partition function in the equation of state. That study has revealed interesting features about excited states and their treatment in the equation of state. The MHD equation of state with its specific, density-dependent occupation probabilities is causing a characteristic ``wiggle'' in the thermodynamic quantities. The wiggle is absent both in ground-state-only equations of state and in the OPAL equation of state, which is based on the temperature-dependent Planck-Larkin partition function. It seems that this effect of excited states has already been observed in the Sun. Very recently, solar oscillation frequencies were inverted for the adiabatic gradient γ1 in the 20% uppermost layers. The results have revealed that above 0.98 solar radii, MHD seems to give a more accurate description of the Sun than OPAL. The quantitative reason appears to be the presence of the excited-states wiggle in the solar data. Below the wiggle region, the study confirmed older findings, which give preference to the OPAL equation of state. Although the wiggle is located in the He II ionization zone, it is a pure hydrogen effect. If confirmed it would have a significant bearing on the helioseismic helium-abundance determination in the solar convection zone. Specifically, it could make the value based on the MHD equation of state (Y = 0.246) more likely than the currently preferred one (Y = 0.249), which is based on OPAL (Basu & Antia, 1995). Title: Solar p-mode Frequencies With Updated Atomic Opacities Authors: Gong, Z.; Dappen, W.; Li, Y. Bibcode: 1998ASPC..135..266G Altcode: 1998hcsp.conf..266G Significant differences in solar models have been found recently, by using OPAL and OP opacity, respectively. In this work we'll study its effect on solar oscillation frequencies, so as to figure out which set of opacity can fit the present sun more reasonably. Title: Solar p-Mode Frequencies with OPAL and OP Opacities Authors: Gong, Zhigang; Dappen, Werner; Li, Yan Bibcode: 1998ASPC..154..761G Altcode: 1998csss...10..761G The effect of the OPAL-92 and OP opacity on the frequencies of solar p-modes are studied. It is found that although no one can fit the observational data, the difference of OPAL model and observation frequencies have almost the same slope for different modes, which is more likely to come from the non-adiabatic effect in the outer envelope of the Sun, while the OP results have various slopes for different modes, which is difficult to analyze. Thus, the OPAL opacity is favored in solar model. The difference between a grey atmosphere and the Harvard-Smithsonian solar atmosphere model is small. Title: The Influence of Low-Temperature Opacity on Solar Models and p-Mode Frequencies Authors: Gong, Z. G.; Däppen, W. Bibcode: 1998ESASP.418..465G Altcode: 1998soho....6..465G The opacity is one of the leading input physics quantities that may influence the structure and p-mode frequencies of the sun. Although the most important opacity contribution on a solar model is the atomic and ionic contribution in the interior, the influence of the outside low-temperature opacity is also relevant. Presently, the low-temperature opacity has a somewhat higher uncertainty than the one of the interior, and this difference may influence more on high order p-modes, which spend most of their life traveling through the low-temperature opacity region. In this work we test the sensitivity of solar structure and frequencies with some up-to-date, well accepted low-temperature opacities. Title: Microphysics: Equation of State Authors: Däppen, W. Bibcode: 1998sce..conf...49D Altcode: No abstract at ADS Title: Application of the Filter Diagonal Spectral Estimator in Helioseismology Authors: Jones, Andrew R.; Belkic, Dzevad; Däppen, Werner; Lin, Chia-Hsien; Taylor, Howard Bibcode: 1998ESASP.418..249J Altcode: 1998soho....6..249J Filter Diagonalization (FD) is a non-Fourier spectral estimator that has several possible applications in helioseismology. We show an example of the analysis of synthetic data to demonstrate the enhancement gained with the FD technique over a conventional Fourier Transform (FT). We also show how FD can be used to reduce spectral noise. A preliminary application of FD to helioseismic (LOI) data is presented, and the possible application of FD to ring analysis is explored. Title: Helioseismic Probing of Fine Effects in the Equation of State Authors: Däppen, Werner Bibcode: 1998ESASP.418..445D Altcode: 1998soho....6..445D Although the gas in the solar interior is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismic measurements puts strong constraints on the nonideal part of the equation of state. The helioseismic verification of major nonideal effects in the equation of state of solar matter has become well established. The dominant contribution is the Coulomb pressure, conventionally described in the Debye-Huckel approximation. However, the increased precision of the helioseismic diagnosis has brought significant observational progress beyond the Debye-Huckel approximation. Recent studies have addressed specific nonideal effects beyond the Debye-Huckel term. A first case is the consequence of shifts in bound-state energies and of the position of the continuum for thermodynamic quantities. A second case is the subtle effect of excited states in bound systems, in particular hydrogen (Nayfonov & Däppen 1998). The effect has become apparent in recent helioseismic inversions (Basu, Däppen, & Nayfonov 1998). Title: Structure and Rotation of the Solar Interior: Initial Results from the MDI Medium-L Program Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.; Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.; de Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.; Scott, K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard, J.; Dappen, W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.; Thompson, M. J.; Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.; Title, A. M.; Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson, C. J.; Zayer, I.; Milford, P. N. Bibcode: 1997SoPh..170...43K Altcode: The medium-l program of the Michelson Doppler Imager instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to ∽ 300. The data for the program are partly processed on board because only about 3% of MDI observations can be transmitted continuously to the ground. The on-board data processing, the main component of which is Gaussian-weighted binning, has been optimized to reduce the negative influence of spatial aliasing of the high-degree oscillation modes. The data processing is completed in a data analysis pipeline at the SOI Stanford Support Center to determine the mean multiplet frequencies and splitting coefficients. The initial results show that the noise in the medium-l oscillation power spectrum is substantially lower than in ground-based measurements. This enables us to detect lower amplitude modes and, thus, to extend the range of measured mode frequencies. This is important for inferring the Sun's internal structure and rotation. The MDI observations also reveal the asymmetry of oscillation spectral lines. The line asymmetries agree with the theory of mode excitation by acoustic sources localized in the upper convective boundary layer. The sound-speed profile inferred from the mean frequencies gives evidence for a sharp variation at the edge of the energy-generating core. The results also confirm the previous finding by the GONG (Gough et al., 1996) that, in a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. Inverting the multiplet frequency splittings from MDI, we detect significant rotational shear in this thin layer. This layer is likely to be the place where the solar dynamo operates. In order to understand how the Sun works, it is extremely important to observe the evolution of this transition layer throughout the 11-year activity cycle. Title: Internal structure and rotation of the Sun: First results from MDI data Authors: Kosovichev, A. G.; Schou, J.; Scherrer, P. H.; Bogart, R. S.; Bush, R. I.; Hoeksema, J. T.; Aloise, J.; Bacon, L.; Burnette, A.; De Forest, C.; Giles, P. M.; Leibrand, K.; Nigam, R.; Rubin, M.; Scott, K.; Williams, S. D.; Basu, Sarbani; Christensen-Dalsgaard, J.; Däppen, W.; Rhodes, E. J., Jr.; Duvall, T. L., Jr.; Howe, R.; Thompson, M. J.; Gough, D. O.; Sekii, T.; Toomre, J.; Tarbell, T. D.; Title, A. M.; Mathur, D.; Morrison, M.; Saba, J. L. R.; Wolfson, C. J.; Zayer, I.; Milford, P. N. Bibcode: 1997IAUS..181..203K Altcode: No abstract at ADS Title: Helioseismic diagnosis of the equation of state Authors: Däppen, Werner Bibcode: 1996BASI...24..151D Altcode: No abstract at ADS Title: The Current State of Solar Modeling Authors: Christensen-Dalsgaard, J.; Dappen, W.; Ajukov, S. V.; Anderson, E. R.; Antia, H. M.; Basu, S.; Baturin, V. A.; Berthomieu, G.; Chaboyer, B.; Chitre, S. M.; Cox, A. N.; Demarque, P.; Donatowicz, J.; Dziembowski, W. A.; Gabriel, M.; Gough, D. O.; Guenther, D. B.; Guzik, J. A.; Harvey, J. W.; Hill, F.; Houdek, G.; Iglesias, C. A.; Kosovichev, A. G.; Leibacher, J. W.; Morel, P.; Proffitt, C. R.; Provost, J.; Reiter, J.; Rhodes, E. J., Jr.; Rogers, F. J.; Roxburgh, I. W.; Thompson, M. J.; Ulrich, R. K. Bibcode: 1996Sci...272.1286C Altcode: Data from the Global Oscillation Network Group (GONG) project and other helioseismic experiments provide a test for models of stellar interiors and for the thermodynamic and radiative properties, on which the models depend, of matter under the extreme conditions found in the sun. Current models are in agreement with the helioseismic inferences, which suggests, for example, that the disagreement between the predicted and observed fluxes of neutrinos from the sun is not caused by errors in the models. However, the GONG data reveal subtle errors in the models, such as an excess in sound speed just beneath the convection zone. These discrepancies indicate effects that have so far not been correctly accounted for; for example, it is plausible that the sound-speed differences reflect weak mixing in stellar interiors, of potential importance to the overall evolution of stars and ultimately to estimates of the age of the galaxy based on stellar evolution calculations. Title: Testing Solar Models with the GONG Data Authors: Christensen-Dalsgaard, J.; Dappen, W.; Demarque, P.; GONG Models Team Bibcode: 1996AAS...188.5302C Altcode: 1996BAAS...28..903C The wealth of very precise data from the GONG network and other helioseismic experiments provide a unique opportunity for testing the modeling of stellar interiors. Stellar modeling forms the basis for much of astrophysics. Furthermore, the application and calibration of solar models to the helioseismic data provides a test of the physics on which the models depend; thus we can investigate the thermodynamic and radiative properties of matter under the extreme conditions found in the Sun. Current models are in remarkable agreement with the helioseismic inferences within the errors in the input data; this suggests, for example, that the disagreement between the predicted and observed fluxes of neutrinos from the Sun is unlikely to be caused by errors in the standard solar model. However, careful analysis of the GONG data reveals subtle discrepancies that we attribute to uncertainties in some of the model input physics and the neglect of other subtle physical processes. The role of mixing inside the Sun, due for example to rotationally induced instabilities during its past evolution, the precise form of the hydrogen depletion profile near the center, the efficiency of helium and heavier element diffusion below the convection zone, and the structure of the highly superadiabatic layer just below the photosphere, are among the significant details in solar models, which the high-quality GONG data will greatly help to resolve. Comparisons between theoretical predictions of solar p-mode frequencies, previous p-mode observations and the first GONG data are used to illustrate these points. Title: VIRGO: Experiment for Helioseismology and Solar Irradiance Monitoring Authors: Fröhlich, Claus; Romero, José; Roth, Hansjörg; Wehrli, Christoph; Andersen, Bo N.; Appourchaux, Thierry; Domingo, Vicente; Telljohann, Udo; Berthomieu, Gabrielle; Delache, Philippe; Provost, Janine; Toutain, Thierry; Crommelynck, Dominique A.; Chevalier, André; Fichot, Alain; Däppen, Werner; Gough, Douglas; Hoeksema, Todd; Jiménez, Antonio; Gómez, Maria F.; Herreros, José M.; Cortés, Teodoro Roca; Jones, Andrew R.; Pap, Judit M.; Willson, Richard C. Bibcode: 1995SoPh..162..101F Altcode: The scientific objective of the VIRGO experiment (Variability of solar IRradiance and Gravity Oscillations) is to determine the characteristics of pressure and internal gravity oscillations by observing irradiance and radiance variations, to measure the solar total and spectral irradiance and to quantify their variability over periods of days to the duration of the mission. With these data helioseismological methods can be used to probe the solar interior. Certain characteristics of convection and its interaction with magnetic fields, related to, for example, activity, will be studied from the results of the irradiance monitoring and from the comparison of amplitudes and phases of the oscillations as manifest in brightness from VIRGO, in velocity from GOLF, and in both velocity and continuum intensity from SOI/MDI. The VIRGO experiment contains two different active-cavity radiometers for monitoring the solar `constant', two three-channel sunphotometers (SPM) for the measurement of the spectral irradiance at 402, 500 and 862 nm, and a low-resolution imager (LOI) with 12 pixels, for the measurement of the radiance distribution over the solar disk at 500 um. In this paper the scientific objectives of VIRGO are presented, the instruments and the data acquisition and control system are described in detail, and their measured performance is given. Title: Rigorous Constraints on the Ionization of Elements in the Solar Center Authors: Perez, A.; Däppen, W. Bibcode: 1995ESASP.376b..15P Altcode: 1995help.confP..15P; 1995soho....2...15P Results from a rigorous quantum-statistical formalism for Coulomb systems are used to study the transition to full ionization of astrophysically relevant elements. The authors find that, although the formalism is in principle a low-density development, the relevant parameters are such that it can be applied to the physical conditions of the solar center. However, the conditions of the solar center do not admit an isolated-atom picture. Special care has therefore to be taken to define what is a bound state. Title: Some Aspects of Model Entropy Calculations for Stellar Plasmas Authors: Däppen, W.; Nayfonov, A. Bibcode: 1995ESASP.376b..19D Altcode: 1995help.confP..19D; 1995soho....2...19D The helioseismic determination of specific entropy inside the Sun could provide an interesting constraint on solar models. Unlike with more intuitive thermodynamic quantities, a greater effort has to be made to define entropy. In models of plasmas, the arbitrary additive constant of entropy can be normalized by applying the third law of thermodynamics. This presents difficulties, however, because although quantum statistical models of Coulomb systems might satisfy the third law, their concrete (approximate) realizations of these models, such as those used in stellar calculations, might not. The authors examine a popular representative stellar equation of state in view of their suitability for entropy calculations. Title: GONG '94: Helio- and Astero-Seismology from the Earth and Space Authors: Ulrich, R. K.; Rhodes, E. J., Jr.; Dappen, W. Bibcode: 1995ASPC...76.....U Altcode: 1995gong.conf.....U; 1995QB539.O83G67... No abstract at ADS Title: Solar Models and Oscillation Theory Authors: Däppen, W. Bibcode: 1995ESASP.376a..19D Altcode: 1995heli.conf...19D; 1995soho....1...19D The most important techniques used to analyze helioseismic data are reviewed. Emphasis is on the spherically symmetric aspects of solar structure. This is the framework of "conventional" stellar evolution models and their oscillations. The importance of understanding stellar physics to the prediction of helioseismic data is stressed. By doing this the author shows that progress can be made on the inverse path: constraining stellar physics by helioseismology, in other words, using the Sun as a laboratory. Examples of physics issues addressed by helioseismology are, in the spirit of the simplified spherical models, opacity, equation of state, nuclear reaction rates, and neutrino physics. Title: Nonideal Effects in the Solar Equation of State Authors: Baturin, V. A.; Däppen, W.; Wang, X.; Yang, F. Bibcode: 1995LIACo..32...33B Altcode: 1995sews.book...33B No abstract at ADS Title: HELIO- AND ASTEROSEISMOLOGY: Introduction Authors: Däppen, W. Bibcode: 1995HiA....10..319D Altcode: No abstract at ADS Title: Applications of Massively-Parallel Computing in Solar Modeling Authors: Reiter, J.; Rhodes, E. J., Jr.; Dappen, W.; Korzennik, S. G. Bibcode: 1995ASPC...76..140R Altcode: 1995gong.conf..140R No abstract at ADS Title: Asteroseismologie: muziek van de sterren. Authors: Dappen, W. Bibcode: 1994Zenit..21..346D Altcode: 1994Zenit...21.346D No abstract at ADS Title: Towards a helioseismic calibration of the equation of state in the solar convective envelope Authors: Vorontsov, S. V.; Baturin, V. A.; Dappen, W.; Gough, D. O. Bibcode: 1994esa..conf..545V Altcode: 1994IAUCo.147..545V No abstract at ADS Title: Helioseismology: the Sun as a strongly-constrained, weakly-coupled plasma Authors: Dappen, W. Bibcode: 1994esa..conf..368D Altcode: 1994IAUCo.147..368D No abstract at ADS Title: The solar interior Authors: Turck-Chièze, S.; Däppen, W.; Fossat, E.; Provost, J.; Schatzman, E.; Vignaud, D. Bibcode: 1993PhR...230...57T Altcode: This report confronts the different aspects of the solar interior from the experimental and theoretical points of view, discussing photospheric abundances, neutrinos and acoustic mode measurements. The theoretical approach mainly concerns the classical framework of stellar evolution, nevertheless, particle interpretation of the data and astrophysical solutions invoked in the last 10 years are coherently examined. Title: On the Influence of Treatment of Heavy Elements in the Equation of State on the Resulting Values of the Adiabatic Exponent Authors: Däppen, W.; Gough, D. O.; Kosovichev, A. G.; Rhodes, E. J., Jr. Bibcode: 1993ASPC...40..304D Altcode: 1993ist..proc..304D No abstract at ADS Title: Theory of Delta-Scuti Stars Authors: Dappen, W. Bibcode: 1993ASPC...42..317D Altcode: 1993gong.conf..317D No abstract at ADS Title: The equation of state. Authors: Daeppen, Werner Bibcode: 1993ASPC...40..208D Altcode: 1993ist..proc..208D; 1993IAUCo.137..208D There are two basic approaches to the equation of state for stellar envelopes and interiors. The traditional method chooses the so-called "chemical picture", in which the notion of atoms is maintained despite the plasma environment. A mixture of atoms, molecules, ions, electrons and nuclei is considered, and the occurring ionization and dissociation reactions (thus the name chemical picture) are treated according to the entropy-maximum (or free-energy-minimum) principle. The alternative method is based on the so-called "physical picture", where only fundamental particles (electrons, nuclei) explicitly enter. Through the means of activity expansions, the problems of plasma physics and statistical mechanics are treated simultaneously and on the same footing. For helio- and asteroseismology, an accurate and precise equation of state is essential. Progress towards a better equation of state can be made in several ways: purely theoretical efforts, checks with experiments, including astrophysical data, and comparisons between different theoretical formalisms. Comparisons are useful to assess the domain of temperature and density where the theoretical complications matter, and to determine the diagnostic potential of astrophysical observables for equation of state issues. Title: Plans for MT.WILSON - Crimean Observatory High-Degree Helioseismology Network Authors: Rhodes, E. J., Jr.; Cacciani, A.; Dappen, W.; Didkovsky, L. V.; Hill, F.; Korzennik, S. G.; Kosovichev, A. G.; Kotov, V. A.; Scherrer, P. H. Bibcode: 1993ASPC...42..477R Altcode: 1993gong.conf..477R No abstract at ADS Title: Sources of uncertainty in direct seismological measurements of the solar helium abundance Authors: Kosovichev, A. G.; Christensen-Dalsgaard, J.; Daeppen, W.; Dziembowski, W. A.; Gough, D. O.; Thompson, M. J. Bibcode: 1992MNRAS.259..536K Altcode: The methods by which Dappen et al. (1988, 1990, 1991) and Dziembowski et al. (1990, 1991, 1992) recently obtained discrepant estimates of the helium abundance in the solar convection zone are compared. The aim of the investigation reported in this paper is to identify the main source of the discrepancy. Using as proxy data eigenfrequencies of a set of modes of a theoretical solar model, computed with the same physics as were the frequencies of a reference model with which these data are compared, the two methods yield similar results. Thus we ascertain that the principal source of the discrepancy is not in the inversions themselves, which yield essentially a measure of the variation of the adiabatic exponent gamma of the material in the He II ionization zone. Instead it is in the approximations adopted in the treatment of heavy elements in the equation of state used to relate the variation of gamma to chemical composition. We obtain acceptably consistent results when inverting solar data by two methods using the same equation of state. We attempt to identify the likely residual sources of uncertainty. Title: The Equation of State for Stellar Envelopes: Comparison of Theoretical Results Authors: Dappen, W. Bibcode: 1992RMxAA..23..141D Altcode: A previous comparison of thermodynamical quantities, computed in the chemical and physical pictures, revealed a remarkable agreement in the H and He ionization zones of the Sun, despite the radically different treatment of bound states in the two formalisms. This agreement was due to an unexpectedly dominating (classical) Coulomb pressure term. New comparisons, for higher temperatures and densities, and for a representative solar mixture (H, He and 0), have demonstrated substantial differences in the 0-ionization fractions. Also, the thermodynamic quantities reflect these differences to a degree that is within reach of helioseismology. Key words: EQUATION OF STATE - STARS: INTERIOR Title: Solar oscillations and the equation of state Authors: Christensen-Dalsgaard, Jorgen; Daeppen, Werner Bibcode: 1992A&ARv...4..267C Altcode: 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. Title: Observations of the phase differences between irradiances and velocity for low-degree solar acoustic modes Authors: Schrijver, C. J.; Dappen, W.; Jimenez, A. Bibcode: 1991A&A...251..655S Altcode: Irradiance measurements from the IPHIR instrument flown on the Phobos 2 mission to Mars are used to derive phase differences and gains between broadband relative irradiance signals and full-disk velocity variations for l = 0, 1, and 2 mode with order ranging from 12 to 32. These data are compared with contemporaneous measurements of photospheric velocities obtained during four intervals within the 155 d observation period of Phobos 2. It is found that the phase difference between irradiance at 500 nm and velocity is roughly constant with an average value of -119 +/- 3 deg from 2.5 mHz up to about 4.3 mHz with a slight increase suggested by data up to 4.6 mHz. The phase differences between the green and red channels do not differ significantly from zero below 2.8 mHz, while a small difference of about 13 +/- 5 deg exists at higher frequencies, with the red signal ahead of the green. This jump appears to coincide with a jump in the separation between the l = 0 and l = 2 eigenfrequencies. Title: A calibration of solar envelope models using the frequencies of intermediate-degree solar acoustic oscillations Authors: Pamiatnykh, A. A.; Vorontsov, S. V.; Dappen, W. Bibcode: 1991A&A...248..263P Altcode: The frequency dependence of the phase shift, which arises from the reflection of internal acoustic waves (p-modes) at the outer solar layers, can be determined from the accurately measured frequencies of intermediate-degree p-modes. This dependence is sensitive to the complicated structure of the outer solar layers, down to the depth of the second ionization zone of helium. It can be used to calibrate solar envelope models. The results of the direct tests of a variety of solar envelope models using the phase shift inferred from the solar oscillation frequencies are reported. Title: A theorical interpretation of the Delta Scuti-like pulsation of the star 63 Herculis. Authors: Mangeney, A.; Daeppen, W.; Praderie, F.; Belmonte, J. A. Bibcode: 1991A&A...244..351M Altcode: Theoretical pulsation frequencies derived from a typical model computation are used to identify the periods during which the Delta Scuti star 63 Herculis oscillates. The frequencies are computed in the adiabatic and linear approximations and consideration is given to p and g modes. The possibility of rotational splitting is considered. Title: Probing the solar interior Authors: Dappen, W. Bibcode: 1991AdSpR..11d...5D Altcode: 1991AdSpR..11....5D Solar oscillation frequencies have become an important tool to obtain detailed information about the solar interior. The physical nature of the oscillations is well understood: the modes observed so far are standing acoustic waves (or p modes). Thus identified, they allow an immediate diagnosis of the physical conditions in the solar interior, through the relation of the oscillation frequencies with the local sound speed. Besides giving an introduction to current techniques, I describe the observational situation. The connection between solar oscillations and the equation of state is discussed in some detail. A separate section contains a short general review of recent progress. Title: Summary of the Institute of Theoretical Physics (ITP) program on helioseismology (Santa Barbara, January-June 1990) Authors: Däppen, Werner; Rhodes, Ed Bibcode: 1991AdSpR..11d..15D Altcode: 1991AdSpR..11...15D The authors presented their view as participants of the ITP programme on helioseismology, which was coordinated by D.O. Gough and J. Toomre (Santa Barbara, Jan 1990 - June 1990). Detailed proceedings can be found in ``Challenges to theories of the structure of moderate-mass stars'' (eds. D.O. Gough and J. Toomre, Springer, Heidelberg, 1991). Title: A New Inversion for the Hydrostatic Stratification of the Sun Authors: Däppen, W.; Gough, D. O.; Kosovichev, A. G.; Thompson, M. J. Bibcode: 1991LNP...388..111D Altcode: 1991ctsm.conf..111D Inversions for the spherically symmetric component of the hydrostatic stratification of the Sun are presented. These employ the Backus-Gilbert optimally localized averaging procedure applied to oscillation multiplet frequencies in the range 1.5 - 3 mHz of modes with 4 l 140 determined by Libbrecht et al. (1990) from observations carried out in 1986. We also obtain an estimate of the helium abundance in the solar convective envelope. Title: Equation of state and opacity. Authors: Daeppen, Werner; Keady, John; Rogers, Forrest Bibcode: 1991sia..book..112D Altcode: The three most important physical ingredients of stellar models are the nuclear-energy generation rates, the equation of state and the opacity. The authors begin this chapter with a discussion of the equation of state, not only because the equation of state plays an important role in stellar structure, but also because it is by itself a fundamental part of any opacity calculation. Furthermore, the computation of the equation of state is the simpler problem. There are two reasons for this. First, already at lower densities, where atoms exist (i.e. where many-body effects can be neglected), it suffices for the equation of state to know the energy levels of atoms (and their occupation). Second, at higher densities, where many-body effects become important (and where one cannot speak of atoms), there are at least roads to a correct treatment of the equation of state (the authors will show some of them in this chapter). Extending these techniques to opacity calculations faces the difficulty that again more detailed information about the quantum-mechanical many-body states is required. Title: The Equation of State of the Solar Interior - a Comparison of Results from Two Competing Formalisms Authors: Daeppen, Werner; Lebreton, Yveline; Rogers, Forrest Bibcode: 1990SoPh..128...35D Altcode: 1990IAUCo.121P..35D A recently developed treatment of partition functions in the equation of state (Mihalas, Hummer, Däppen, MH&D) has led to a substantial improvement in the agreement between observed and theoretically predicted solar p-mode oscillation frequencies. The MH&D equation of state is a realization of the free-energyminimization method, based on the so-called `chemical picture', in which ionization and dissociation reactions are assumed to be those that maximize entropy, or equivalently, minimize the free energy. An alternative equation of state has recently been developed at Livermore. It realizes a virial expansion of pressure, and is based on the `physical picture', in which explicitly only fundamental species (i.e., electrons and nuclei) appear. Results of a first comparison between thermodynamic quantities of the MH&D and Livermore equations of state are presented. For simplicity, a mixture with only hydrogen and helium (90% H and 10% He by number) is chosen. The comparison is made for a low-density and a high-density case. In the first case, the conditions are those of the hydrogen and helium ionization zones of the Sun, in the second case those of the solar centre. In both cases, the MH&D and Livermore results agree strikingly, despite the very different formalisms they are based on. Title: The Equation of State for Stellar Envelopes. IV. Thermodynamic Quantities and Selected Ionization Fractions for Six Elemental Mixes Authors: Mihalas, Dimitri; Hummer, D. G.; Mihalas, Barbara Weibel; Daeppen, Werner Bibcode: 1990ApJ...350..300M Altcode: The free-energy minimization technique in the form developed in the preceding papers in this series is employed to evaluate thermodynamic quantities and ionization fractions on a fine temperature and density grid for six astrophysical mixtures of 15 elements. The mixtures range from that appropriate to super-metal-rich stars, through solar abundance, to that for extreme Population II objects. In this paper, the results for solar abundances are summarized in a form that is illustrative and which facilitates comparison with the results from other equation of state calculations. Title: The Internal Rotation of the Sun Authors: Däppen, Werner Bibcode: 1990LNP...366...69D Altcode: 1990rmsi.conf...69D An introduction to current techniques to infer the Sun's internal rotation from observed acoustic oscillation modes is given, and some representative results are shown. Title: Stellar Seismology Authors: Däppen, Werner Bibcode: 1990ASSL..159..357D Altcode: 1990IAUCo.121..357D; 1990insu.conf..357D No abstract at ADS Title: Progress Towards a Unified Equation of State Authors: Däppen, Werner Bibcode: 1990LNP...367...33D Altcode: 1990psss.conf...33D A recent comparison of thermodynamical quantities, computed in the chemical and physical picture, has revealed a remarkable agreement in the hydrogen and helium ionization zones (on an isochore of log p = -5.5, with p in g cm-3). This agreement is due to an unexpectedly dominating (classical) Coulomb pressure term. The analogous comparison at a somewhat higher density (log p = -3.5) shows still striking similarities, despite the different treatment of bound states in the two formalisms. The results suggest use of a relatively simple parametrized equation of state for solar purposes. Title: Effects of Magnetic Fibrils on Solar Oscillation Frequencies: Mean Field Theory Authors: Zweibel, Ellen G.; Daeppen, Werner Bibcode: 1989ApJ...343..994Z Altcode: It is quite likely that the solar interior magnetic field retains the fibril structure observed at photospheric levels down to some significant depth in the convection zone. Furthermore, previous work has shown that the effect of magnetic fibrils on p-mode oscillation frequencies is enhanced by 1/f, the reciprocal of the fibril filling factor, over the effect of an equal amount of flux in diffuse form. Previous calculations have used multiple scattering methods which effectively preclude the inclusion of stratification or consideration of realistic geometries. In this paper an alternative simpler method of treating fibrils is developed on the basis of mean-field theory originally developed by Parker (1982). Title: Modeling Epsilon Eridani and Its Oscillations Authors: Soderblom, David R.; Dappen, Werner Bibcode: 1989ApJ...342..945S Altcode: Models of the structure of the K2 V star Epsilon Eridani which are based on star luminosity, temperature, composition, age, and mixing-length parameter (alpha) are discussed. Comparisons are made with models proposed by Guenther and Demarque (1986) and Guenther (1987). Predicted oscillation frequencies are presented. Title: Structure interne: le diagnostic astérosismologique. Authors: Däppen, W. Bibcode: 1989JAF....34Q...6D Altcode: No abstract at ADS Title: Stellar structure: the asteroseismological diagnostic. Authors: Däppen, W. Bibcode: 1989musi.work...11D Altcode: No abstract at ADS Title: Rapid photometry of the δ Scuti variable 63 Her. Authors: Mangeney, A.; Chevreton, M.; Belmonte, Juan A.; Daeppen, W.; Saint-Pe, O.; Praderie, F.; Roca Cortés, Teodoro; Fuensalida, J.; Alvarez, M. Bibcode: 1988ESASP.286..551M Altcode: 1988ssls.rept..551M The δ Scuti variable 63 Her has been observed during 21 nights at two observatories (Observatorio del Teide, Tenerife Island, Spain and Observatorio Astronomico Nacional de San Pedro Martir in Baja California, Mexico). Six frequencies of pulsation have been unambiguously detected, among which the fundamental radial mode, two non radial pressure-like modes and probably three gravity like modes. Title: Solar oscillation frequencies and the equation of state Authors: Christensen-Dalsgaard, J.; Dappen, W.; Lebreton, Y. Bibcode: 1988Natur.336..634C Altcode: Observed oscillation frequencies of the Sun can be used to investigate the properties of matter under conditions that cannot be achieved on Earth. In particular the frequencies are sensitive to the equation of state. A recently developed treatment of the partition functions leads to a substantial improvement in the agreement between the observed and the computed frequencies. Title: The influence of the equation of state on the zero-age main sequence and the Sun. Authors: Lebreton, Y.; Daeppen, W. Bibcode: 1988ESASP.286..661L Altcode: 1988ssls.rept..661L In the light of the present uncertainty in the equation of state of stellar interiors, the authors have calculated stellar and solar models using three different formalisms for the equation of state. They have considered (1) a mixture of ideal gases using an artificial pressure-ionization device, (2) an equation of state where pressure ionization is achieved by the confined-atom model, and (3) an equation of state containing a large number of atomic and ionic species, with detailed internal partition functions, containing weighted occupation probabilities. The authors have examined the effect of these equations of state on the position of a star in the H-R diagram: the result is either a displacement of the star on the zero-age main sequence (ZAMS) or, for masses lower than 0.7 Msun a change in the slope of the ZAMS. Furthermore they have carried out the usual calibration procedure in order to obtain the initial He abundance Y of the solar model. Title: Epsilon Eridani revisited. Authors: Daeppen, W.; Soderblom, D. Bibcode: 1988ESASP.286..653D Altcode: 1988ssls.rept..653D In the light of the unsatisfactory theoretical explanation of the observed p-mode frequency separation of ɛ Eri of 172 μHz, and of the fact that the seismological observation has not yet been confirmed, the authors have computed a new series of models. They have taken into account only the observational input available prior to the seismological determination. They have obtained predictions for the p-mode frequency separation that lie between 198 and 244 μHz. Title: High mass loss in the young Sun! Authors: Turck-Chieze, S.; Daeppen, W.; Casse, M. Bibcode: 1988ESASP.286..629T Altcode: 1988ssls.rept..629T The consequences of a possible mass loss in the early main sequence stage of solar type stars are investigated. Special attention is given to the Sun, the constraints from surface abundances and p-mode observations are taken into account. Only a total mass loss smaller than 0.2 Msun seems to be consistent with the observations. Though the ensuing modifications of the internal structure and the cosmological consequences are very small, the 3He, 7Li, 9Be surface abundances are significantly modified. Title: Further progress on the helium abundance determination. Authors: Daeppen, W.; Gough, Douglas O.; Thompson, M. J. Bibcode: 1988ESASP.286..505D Altcode: 1988ssls.rept..505D The authors report on further progress in attempting to determine the helium abundance in the solar convection zone by analysing the position and shape of the "helium hump" in a thermodynamic quantity Θ which can be inferred from the sound speed in the vicinity of the He II ionization zone. At present they are estimating the sound speed from frequencies of high-degree oscillations by a differential asymptotic technique. The helium abundance Y is then determined by fitting the hump inferred to one obtained by interpolation in a grid of theoretical model envelopes. They have tested the procedure by carrying out a double-blind experiment on artificial data, and have found that accurate knowledge of the equation of state is essential for a useful determination. The authors have also carried out the procedure on real solar data, but they judge that the frequencies are at present too poorly determined to enable us to obtain a reliable estimate of Y in the sun. Title: Current options for the equation of state of the solar interior. Authors: Daeppen, W. Bibcode: 1988ESASP.286..451D Altcode: 1988ssls.rept..451D The principal open problem of the equation of state is the number of excited states of hydrogen and helium in the zones of partial ionization. The number of excited states is affected in two ways: first by destruction of the levels due to the (neutral and charged) surrounding species, and second by statistical mechanics which governs the population of the available levels. The author discusses recent progress in this field and explains the two principal current "philosophies". One is the chemist's view, in which bound systems are interpreted as autonomous species with reactions between each other, the other is the physicist's view, in which a virial expansion of pressure is obtained starting out from fundamental species only (i.e. electrons and nuclei), and in which the so-called Planck-Larkin partition function appears. Title: Modelling the variation of solar p-mode frequencies. Authors: Daeppen, W.; Gough, Douglas O.; Turck-Chieze, S. Bibcode: 1988ESASP.286..511D Altcode: 1988ssls.rept..511D The authors present a Green's function technique to study long-term variations of the Sun (with characteristic time scales from one month to millions of years). The method is the combination of two previous analyses carried out independently by Gough and by Däppen. Their study has been motivated by the recent observational progress on solar p-mode frequency variations. Title: The Equation of State for Stellar Envelopes. III. Thermodynamic Quantities Authors: Daeppen, Werner; Mihalas, Dimitri; Hummer, D. G.; Mihalas, Barbara Weibel Bibcode: 1988ApJ...332..261D Altcode: The authors derive general formulae for the computation of the thermodynamic properties of a partially ionized (and/or dissociated) multicomponent gas in terms of second derivatives of the free energy with respect to temperature, volume, and occupation numbers. For the free energy used in previous work the authors give explicit analytical expressions for all derivatives required to construct the thermodynamic quantities. Representative results for several different thermodynamic properties of a hydrogen-helium plasma with N(He)/N(H) = 0.10 are presented as color plots. Title: The Equation of State for Stellar Envelopes. II. Algorithm and Selected Results Authors: Mihalas, Dimitri; Dappen, Werner; Hummer, D. G. Bibcode: 1988ApJ...331..815M Altcode: A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions. Title: Asteroseismology - Results and Prospects Authors: Dappen, W.; Dziembowski, W. A.; Sienkiewicz, R. Bibcode: 1988IAUS..123..233D Altcode: The main effects of stellar mass and evolution on oscillation frequencies are discussed with the help of simplified wave-propagation diagrams. Frequency separations resulting from asymptotic expressions are compared with the corresponding results from numerical computations. The seismological issues of solar-like stars and Ap stars are discussed in some detail, and a progress report on the equation of state for stellar interiors is given. The review ends with a summary of properties and important physical problems for selected classes of variable stars. Title: Modeling the Global Oscillations of Epsilon-Eridani Authors: Soderblom, D. R.; Dappen, W. Bibcode: 1988IAUS..123..281S Altcode: The authors have reviewed the observational data for ɛ Eri to derive the best estimates of luminosity, radius, temperature, composition, and age, as well as the uncertainties associated with each of these. These quantities are then used in stellar structure models to try to reproduce the global oscillation frequencies observed by Noyes et al. The authors can reproduce the observed frequencies and splittings at least as well as the computations of Guenther and Demarque, yet for significantly different stellar parameters, most notably the age. Title: Theoretical Constraints from Asteroseismological High S/n Observations Authors: Dappen, W. Bibcode: 1988IAUS..132..211D Altcode: No abstract at ADS Title: Oscillations in Solar Models with Weakly Interacting Massive Particles Authors: Gilliland, Ronald L.; Dappen, Werner Bibcode: 1988ApJ...324.1153G Altcode: Solar models containing concentrations as low as 10-11 by number of weakly interacting massive particles (WIMPs), accreted from a galactic background population, are consistent with the observed flux of high-energy solar neutrinos. The structural changes produced in the solar core have also been shown to produce changes in the oscillation frequencies of g-modes and p-modes of low angular degree and high radial order. In this paper the authors examine the predictions for solar oscillations over a large range of possible WIMP properties. Title: Statistical Mechanics of Partially Ionized Stellar Plasmas: The Planck-Larkin Partition Function, Polarization Shifts, and Simulations of Optical Spectra Authors: Dappen, Werner; Anderson, Lawrence; Mihalas, Dimitri Bibcode: 1987ApJ...319..195D Altcode: We discuss a recent controversy about the Planck-Larkin partition function, and present optical simulations of high-quality spectra from laboratory hydrogen plasmas (Wiese, Kelleher, and Paquette) using several partition function formalisms. We point out that the controversy has arisen from a misunderstanding about the use of the Planck-Larkin partition function. A Planck-Larkin cancellation may still have its place in equations of state that are based on quantum-statistical many-body theory (i.e., the "physical picture"). However, experimental evidence shows that it is inconsistent to use the Planck-Larkin partition function as the internal partition function in simple models of reacting gases (i.e., the "chemical picture"). Moreover, the more sophisticated equations of state of the physical picture will have to be subjected to the same comparison with experimental data. We also address the question of plasma polarization shifts of bound-state energies. We discuss the static-screened Coulomb potential (SSCP) as an atomic potential: from theoretical considerations and observational constraints we conclude that it should not be used. The only useful result of the SSCP potential its prediction of the number of excited be obtained by alternative means, e.g., by an occupation probability formalism. Title: Hypercharge, Solar Structure, and Stellar Evolution Authors: Gilliland, Ronald L.; Dappen, Werner Bibcode: 1987ApJ...313..429G Altcode: The authors investigate the effect of proposed modifications to the gravitational law at short range on stellar structure and evolution. Changes to solar structure, neutrino fluxes, and oscillation frequencies are within current observational and theoretical uncertainties. Modifications to stellar lifetimes are large enough that they should be considered, if the suggested changes to gravitation prove correct. Title: Solar Oscillations and the Equation of State Authors: Däppen, W. Bibcode: 1987ASIB..154..179D Altcode: 1987scpp..conf.179D No abstract at ADS Title: Weakly interacting massive particles, solar neutrinos, and solar oscillations Authors: Dappen, W.; Gilliland, R. L.; Christensen-Dalsgaard, J. Bibcode: 1986Natur.321..229D Altcode: Weakly interacting, massive particles (WIMPs) have recently been proposed as a solution to the solar neutrino problem1-3. Whereas standard solar models consistently predict a detection rate of (high-energy) neutrinos 3 times higher than that observed in the Davis experiment4-6, the presence of hypothetical massive particles in the solar centre would resolve this discrepancy. Models which incorporate a relative number of 10-11 WIMPs with appropriate scattering cross-section would reduce the predicted neutrino detections by 37Cl to the observed value, without significant changes in the solar structure outside the central region1-3. We have subjected these models to an observational test of p-mode oscillation frequencies by computing frequency differences of low-degree, high-order oscillation frequencies. Although standard solar models also pass this test, WIMP models provide a better fit. Title: Progress report on helium abundance determination. Authors: Dappen, W.; Gough, D. O. Bibcode: 1986ASIC..169..275D Altcode: 1986ssds.proc..275D Intermediate results from a programme to determine the helium abundance of the solar convection zone are presented. The method uses the influence of helium ionization on the local sound speed, which can be gauged from inversions of solar oscillation frequencies. The resolution of the principal diagnostic function by the data justifies optimism for an abundance determination in a future step. Title: Non-linear stellar oscillations - Non-radial mode interactions Authors: Dappen, W.; Perdang, J. Bibcode: 1985A&A...151..174D Altcode: A mode-coupling formalism is developed which captures an important class of nonlinear, nonradial adiabatic stellar motions, namely genuine oscillations about a dynamically stable equilibrium state. Observational arguments suggesting nonlinear phenomena among the nonradial-oscillations and indirect theoretical arguments pointing toward hidden nonlinearities are reviewed. A scheme for mastering the general adiabatic nonradial nonlinear stellar motion problem by translating it into a Hamiltonian particle formalism is shown and then refined to ecompass only 'pure' oscillations around the radially symmetric equilibrium state, thus suppressing all stationary circulations. The formalism is used to provide constraints on 'pure' oscillations in an intrinsic fashion, without resorting to Lagrange multipliers. The final Hamiltonian equations are found to have a structure more involved than in the purely radial case. This suggests that the nonradial nonlinear oscillations may exhibit a broader spectrum of different clases of motion than the purely radial stellar oscillations. Title: Nonlinear nonradial adiabatic stellar oscillations: numerical resultsfor many-mode couplings. Authors: Däppen, W. Bibcode: 1985chas.conf..273D Altcode: The adiabatic nonlinear coupling of many linear radial modes has been extended to nonradial modes. A variational principle for fluid mechanics has been applied to obtain a Hamiltonian formalism. The numerical results presented in the paper show that the nonradial modes can cause a much more irregular motion than the radial modes. In the case of the Sun, radial and nonradial 5-minute modes are coupled, and they have been computed using a 'real' solar model. Title: Nonlinear nonradial adiabatic stellar oscillations - Numerical results for many-mode couplings Authors: Dappen, W. Bibcode: 1985ASIC..161..273D Altcode: 1985cia..conf..273D The adiabatic nonlinear coupling of many linear radial modes has been extended to nonradial modes. A variational principle for fluid mechanics has been applied to obtain a Hamiltonian formalism. The numerical results presented here show that the nonradial modes can cause a much more irregular motion than the radial modes. First, there are many near-resonant nonradial frequencies, and second, there is a nonlinear velocity-dependent term in the Hamiltonian, which has no radial analogue. In the case of the sun, the previous results included coupling only for the lowest radial modes, and the coupling coefficients were computed in a polytropic model. Here, radial and nonradial 5-minute modes are coupled, and they have been computed using a 'real' solar model. Title: The lithium abundance of Hyades main-sequence stars. Authors: Cayrel, R.; Cayrel de Strobel, G.; Campbell, B.; Dappen, W. Bibcode: 1984ApJ...283..205C Altcode: From high-quality Reticon spectra of Hyades G and K dwarfs, their lithium abundance is found to decline much more rapidly with decreasing temperature than heretofore realized. Previous observations of the 6707 Li I doublet for the cooler dwarfs have probably been contaminated by blends. However, the new lithium-temperature relation still does not agree with simple models of lithium burning in the convective zone, either with or without overshooting. Models have therefore to include other mechanisms for lithium depletion. Title: Solar oscillations - The challenge of nonlinearity Authors: Daeppen, W.; Perdang, J. Bibcode: 1984MmSAI..55..299D Altcode: Preliminary numerical and theoretical experimental results supporting the view that the observed long period of the sun may be a nonlinear phenomenon are presented. The nonlinear power spectrum of the surface displacement is noted to invariably show a peak in the 2-3 hour range. It is found that nonlinear effects set in earlier with increasing total number of interacting modes, as can be readily understood from the asymptotic behavior of eigenfunctions. A variant of Linstedt's classical perturbation method indicates that the spectral peak in the power spectrum of the surface displacement is a superposition of a large number of nonlinear contributions. Title: An Observational Test on Stellar Interior Mixing - the Lithium Depletion in Twelve Hyades Dwarfs Authors: Cayrel, R.; Cayrel, G.; Campbell, B.; Dappen, W. Bibcode: 1984IAUS..105..537C Altcode: No abstract at ADS Title: On the Determination of the Helium Abundance of the Solar Convection Zone Authors: Dappen, W.; Gough, D. O. Bibcode: 1984LIACo..25..264D Altcode: 1984tpss.conf..264D; 1984trss.conf..264D No abstract at ADS Title: Nonlinear Nonradial Adiabatic Stellar Oscillations : Numerical results for Many-mode Couplings Authors: Dappen, W. Bibcode: 1984LIACo..25..474D Altcode: 1984tpss.conf..474D; 1984trss.conf..474D No abstract at ADS Title: Hydrostatic reaction of the Sun to local disturbances. Authors: Daeppen, W. Bibcode: 1983A&A...124...11D Altcode: The reaction of the solar structure to elementary perturbations is modeled mathematically. The principal assumptions of the model of structure and equilibrium are linearization, a mixing-length formalism, and spherical symmetry. The resulting linearized boundary-value problem is solved with both analytical and numerical methods, and luminosity and radius response functions for different perturbation depths are shown. The quantity W (= delta ln R/delta ln L) is found to be quite frequency dependent, explaining the discrepancies among previous W computations. It is suggested that the model presented here can be applied to study the relationship of solar activity to luminosity, radius, the frequency of the 5-min oscillations, or other observable parameters. Title: An analytical version of the free-energy-minimization method for the equation of state of stellar plasmas Authors: Daeppen, W. Bibcode: 1980A&A....91..212D Altcode: In the free energy method statistical mechanical models are used to construct a free energy function of the plasma. The equilibrium composition for given temperature and density is found where the free energy is a minimum. Until now the free energy could not be expressed analytically, because the contributions from the partially degenerate electrons and from the inner degrees of freedom of the bound particles had to be evaluated numerically. In the present paper further simplifications are made to obtain an analytic expression for the free energy. Thus the minimum is rapidly found using a second order algorithm, whereas until now numerical first order derivatives and a steepest- descent method had to be used. Consequently time-consuming computations are avoided and the analytical version of the free energy method has successfully been incorporated into the stellar evolution programmes at Geneva Observatory. No use of thermodynamical tables is made, either. Although some accuracy is lost by the simplified analytical expression, the main advantages of the free energy method over simple ideal-gas and Sacha-equation subprogrammes (as used in the stellar programmes mentioned) are still kept. The relative errors of the simplifications made here are estimated and they are shown not to exceed 10% altogether. Densities up to those encountered in low-mass main-sequence stars can be treated within the region of validity of the method. Higher densities imply less accurate results. Nonetheless they are consistent so that they cannot disturb the numerical integration of the equilibrium equation in the stellar evolution model. The input quantities of the free energy method presented here are either temperature and density or temperature and pressure, the latter require a rapid numerical Legendre transformation which has been developed here.