Abstract

The equation of state (EOS) of astrophysical plasmas is, for a wide range of stars, nearly ideal; with only small non-ideal Coulomb corrections. Calculating the EOS of an ionizing plasma from a ground state ion, ideal gas model is easy, whereas, fundamental methods to include the small Coulomb corrections are difficult. Attempts to include excited bound states are also complicated by plasma screening and microfield phenomena that weaken and broaden these states. Nevertheless, the high quality of current observational data, particularly seismic, dictates that the best possible models should be used. The present article discusses these issues and describes how they are resolved by fundamental many-body quantum statistical methods. Particular emphasis is placed on the activity expansion method that is the basis of the OPAL opacity code. Some comparisons with standard methods are given.

Abstract

L'equation d'etat des plasmas astrophysiques est, pour un large domaine d'etoiles, pratiquement ideale; avec de petites corrections coulombiennes. Calculer l'equation d'etat d'un plasma ionise a partir d'un modele de gaz ideal d'ions dans leur etat fondamental est facile, alors que les methodes fondamentales pour inclure les petites corrections coulombiennes sont difficiles. Des tentatives pour inclure des etats lies excites sont aussi rendues difficiles par les effets d'ecran et le phenomene de microchamp qui affaiblissent et elargissent ces etats. Neanmoins, la haute qualite des observations actuelles, en particulier en sismologie, impose l'utilisation des tous meilleurs modeles.

Abstract

We discuss problems related to the electronic and ionic structure of fluid Hydrogen, for equation of state calculations in the domain where a “plasma phase transition” (PPT) may occur. It is argued that the ionization of an electron bound to a particular nucleus proceeds through a progressive delocalization involving “hopping” electron states (i.e. cluster states). A description of the plasma containing pseudoatoms, pseudomolecules and free electrons is proposed. The PPT, if it exists, might be a mobility edge transition across a percolation threshold. It is shown how the effect of electron density, field-particle distributions and temperature on the binding energy of these pseudoatoms and pseudomolecules, can be included. Finally the abundances of these objects is determined by a minimization which allows the self-consistent optimization of ionic as well as electronic parameters contributing to the total free energy.

On discute les problèmes associés à la structure electronique et ionique de l'Hydrogène en phase fluide, en vue de calculs d'équation d'état dans le domaine d'une éventuelle transition de phase vers l'état de plasma (TPP). L'argument essentiel est que l'ionization d'un électron lié attaché à un atome se produit par une délocalisation progressive mettant en jeu des “états de grappe” (cluster states). La TPP pourrait être une transition de la mobilité se produisant au seuil de percolation. On propose une description du plasma où “pseudoatomes”, “pseudomolécules” et électrons libres coexistent.

Abstract

The cyclotron and the one-photon annihilation emissions are investigated for a strongly magnetized thermal electron-positron plasmas. The annihilation spectral component is significant when the particle number density N exceeds some critical value, Ncr(T, B). For T ∼ 108 – 109 K and B ∼ 1012 – 1013 G, this condition can be fulfilled at N < 1022 cm−3, which is realistic for neutron star magnetospheres.

Introduction

The e−e+-plasma in strong magnetic fields of neutron stars can be thought to be responsible for X-ray and γ-ray radiation of radio pulsars and γ-ray bursters. In the emitting regions of these objects, the cyclotron emission and one-photon pair annihilation can be important. Separately, they have been investigated by many authors (see, e.g., Bezchastnov and Pavlov 1991, Harding 1986, 1991, and the references therein). However the comparison of these mechanisms has not been performed even for the simplest case of thermal plasmas. We consider the total emission spectra and find the domain of temperatures T and magnetic fields B where the annihilation component is significant for realistic particle number densities N < 1022 cm−3.

Spectra of radiation

Quantum cyclotron emission and one-photon pair annihilation are characterized by the emissivities (summed over polarizations) jc and ja, respectively.

Abstract

In the past decade, measurements of the properties of H2 and He systems at very high pressures have made great progress, now reaching density at the limit of the plasma phase transition of hydrogen. The potentialities and limits of static and dynamic methods will be reviewed. Then, a survey of the major experimental results is presented. It is the intention of this article to show how these measurements can bring information to model low-mass astrophysical objects. Three levels of usefulness are distinguished on selected examples: data for codes of planetary interiors, constraints for theoretical descriptions of dense matter, observations of unsuspected properties at very high density.

Abstract

De grands progrés ont été faits ces dix dernières années dans la mesure des propriétés des systèmes d'H2 et d'He sous très fortes pressions. Des densités à la limite de la transition de phase plasma de l'hydrogène peuvent maintenant être obtenues en laboratoire. Les possibilités et limites des méthodes dynamiques et statiques seront tout d'abord discutées. Ensuite, les principaux résultats expérimentaux seront présentés. Le but de cet article est de montrer comment ces études peuvent être utiles à la modélisation des intérieurs planétaires. Trois niveaux d'application seront dégagés: données pour les codes de structures internes; contraintes pour valider les descriptions théoriques; mise en évidence à très haute densité de comportements inhabituels.

Abstract

The HIPPARCOS mission will permit a decisive step forward in the comparison between observed and predicted global properties of stars, in producing distances and apparent magitudes with accuracies more than one order of magnitude higher than before. Nearby stars of intermediate and low mass will allow for statistical tests on the validity of the equation of state, like for instance the steepness of the main sequence.

La mission HIPPARCOS va permettre un pas en avant fondamental dans les tests des propriéés thermodynamiques des étoiles de masse intermédiaire en fournissant des distances et des magnitudes apparentes beaucoup plus précises que celles obtenues au sol.

Introduction.

Tests of the physical description of stellar interiors rely on a theory vs observation comparison. The stellar evolution theory predicts the variation with time of the state of the interior of a star and, also, of its fundamental, observable parameters, i.e. luminosity, surface temperature, for a given mass. The HIPPARCOS (High Precision PARallax COllecting Satellite) mission will permit a decisive step forward in this confrontation by producing distances and apparent magnitudes with accuracies more than one order of magnitude higher than before (Baglin, 1988).

For a description of the mission see for instance Perryman et al., 1992, and the ‘Hipparcos Input Catalogue’ (Turon et al., 1992).

Distances measurements.

HIPPARCOS measures parallaxes i.e. distances, and proper motions. Aproximately 120 000 stars brighter than mv ≈ 12.5 are observed; the survey is complete up to the apparent magnitude 7.5.

Abstract

The evolution of White Dwarf stars along their cooling sequences is governed not only by their thermal content, but also by the rate at which heat flows through the external, partially degenerate and non-isothermal layers. In particular, cooling is found to be largely influenced both by the optical atmosphere, and by the convective envelope. The first one, in fact, determines the internal density stratification, down to the point at which electron degeneracy takes over, while the second one affects the temperature stratification in the same layers. The reliability of the present generation of models of White Dwarf envelopes is discussed, on the grounds of the main physical inputs (thermodynamics, opacity, convection theory), for both H-rich and He-rich surface chemical compositions. The conclusion is that, below LogL/L⊙ ≤ –3, we can build little more than test models.

L'évolution des naines blanches le long de leur séquence de refroidissement est gouvernée non seulement pas leur contenu thermique, mais aussi par la vitesse à laquelle la chaleur s'échappe à travers les couches externes, non-isothermes et partiellement dégénérées. En particulier, le refroidissement est largement influencé à la fois par l'atmosphére optique et par l'enveloppe convective. La premiére détermine la stratification interne en densité jusqu'à ce que la dégénérescence électronique prenne le dessus, alors que la seconde affecte la stratification en température dans les mêmes couches.

Abstract

This paper is organized in two parts. First, phase diagrams for dense binary mixtures are computed with the density functional theory (DFT). The method of calculation is reviewed and the different approximations which are used are clearly stated. The DFT is then applied to several mixtures of astrophysical interest. A comparison is made between several existing phase diagrams and the origin of some discrepancies among them is discussed. In a second part, the consequences of these phase diagrams on the cooling of white dwarfs are presented in a pedagogical way starting from the simple Mestel theory. The importance of the partial separation of carbon and oxygen at crystallisation is emphasized and the possible effect of minor species such as 22Ne or Fe is also considered. The separation of carbon and oxygen adds 1 – 2 Gyr to age of the galactic disk estimated from the white dwarf luminosity function while the delay resulting from the presence of minor species is probably negligible when the chemical evolution of the Galaxy is properly taken into account.

Cet article est organisé en deux parties. Tout d'abord, les diagrammes de phase des mélanges binaires denses sont calculés à l'aide de la théorie de la fonctionnelle de densité. La méthode de calcul est détailleé et les différentes approximations utilisées sont clairement expliquées. Le théorie est ensuite appliquée à plusieurs mélanges d'intérêt astrophysique.

Abstract

We present a free energy model for fluid hydrogen at high-density and high-temperature. This model aims at describing pressure dissociation and ionization, which occur in partially ionized plasmas encountered in the interiors of giant planets and low-mass stars. The model describes an interacting mixture of H2,H,H+ and e− in chemical equilibrium. The concentrations of H2+ and H− ions are found to be negligible for equation of state purposes. Our model relies on the so-called chemical picture approach, based on the factorization of the partition function into translational, internal and configurational degrees of freedom. The present model is found to be unstable in the pressure-ionization regime and predicts the existence of a first-order plasma phase transition (PPT) which ends up at a critical point given by Tc = 15300 K, Pc = 0.614 Mbar, and ρc = 0.35 gcm−3. The transition occurs between a weakly ionized phase and a partially ionized (∼ 50%) phase.

Nous présentons un modèle d'énergie libre pour l'hydrogène fluide à haute densité et haute température. Le but de ce modèle est de décrire la dissociation et l'ionisation en pression, telles qu'elles se produisent dans les plasmas partiellement ionisés rencontrés à l'intérieur des planètes géantes et des étoiles de faible masse. Le modèle décrit un fluide en interaction composé de H2,H,H+ et e− en équilibre chimique.

Abstract

Present available interior models of giant planets assume that the internal transport of energy is entirely convective and, accordingly, rule out any possibility of radiative transport. New opacity calculations at temperatures and densities occurring within the giant planets, taking into account H2-H2 and H2-He collision-induced absorption as well as infrared and visible absorption due to hydrogen, water, methane and ammonia are presented. These opacities are not high enough to exclude the presence of a radiative zone in the molecular H2 envelope of Jupiter, Saturn and Uranus.

Abstract

Les modèles de structure interne des planètes géantes développés actuellement supposent que le transport de l'énergie s'effectue entièrement par convection, ce qui élimine toute possibilité de transport radiatif. Des nou-veaux calculs d'opacité aux températures et densités caractéristiques des planètes étudiées, tenant compte de l'absorption induite par collisions H2-H2 et H2-He ainsi que de l'absorption dans l'infrarouge et dans le visible de l'hydrogène, l'eau, le méthane et l'ammoniaque, sont présentées. Ces opacités ne sont pas suffisamment élevées pour exclure la présence d'une zone radiative dans l'enveloppe d'hydrogène moléculaire de Jupiter, Saturne et Uranus.

Introduction

Since the estimations of the conductive and radiative opacities in Jupiter by Hubbard (1968) and Stevenson (1976) all the interior models of the four giant planets have been calculated under the assumption that the energy is transferred by convection through the entire hydrogen-helium envelope. Consequently, the thermal profile is assumed to be adiabatic at all depths.

Abstract

Transport processes in dense stellar plasmas which are relevant to the interiors of white dwarfs and neutron stars are reviewed. The emphasis is placed on the accuracy of the numerical results. In this review we report on the electrical conductivity and the thermal conductivity of dense matter. The methods of the calculations are different for the liquid metal phase and the crystalline lattice phase. We will broadly review the current status of the calculations of the transport properties of dense matter, and try to give the best instructions available at the present time to the readers.

Nous présentons une revue des propoiétés de transport dans les plasmas denses stellaires caractéristiques des intérieurs de naines blanches et d'étoiles à neutrons. L'accent est mis sur la précision des résultats numériques. Nous présentons la conductivité electrique et la conductivité thermique dans la matière dense. Les méthodes de calcul sont différentes dans la phase liquide et dans la phase cristalline. Nous donnons une revue générale des calculs des propriétés de transport dans la matière dense, et nous essayons de donner les meilleures instructions quant aux données disponibles actuellement.

Introduction

In recent years white dwarf asteroseismology opened up a new fertile land of astrophysics (Bradley & Winget 1991; Bradley, Winget, & Wood 1992). Consequently, the basic physics data which go into white dwarf models need to be sufficiently accurate that they should live up to the standard required by the asteroseismological data.

Abstract

Astrophysical objects of low mass, ranging from giant planets to extreme dwarf main-sequence stars, have a number of physical characteristics in common due to properties of their equations of state. Their luminosities are low (much less than the solar luminosity L⊙) and their evolutionary timescales are typically measured in Gyr. So far there are few observational examples of these objects, although they are undoubtedly numerous in the galaxy. The lower mass limit is set by the object's ability to retain hydrogen during accumulation (about the mass of Saturn), while the upper mass limit is set by the lifting of electron degeneracy by high internal temperature. Objects confined within this broad range, which extends up to about 0.1 M⊙, are governed by the thermodynamics of liquid metallic hydrogen. In this paper, we discuss the implications of this feature of their interior structure for their radii, interior temperatures, thermonuclear energy generation rates, and luminosities. We conclude with a brief assessment of the confrontation between observations and theory in galactic clusters and in the solar system.

L'équation d'état des corps célestes de faible masse, qui vont des planètes géantes aux étoiles naines qui sont à la limite de la séquence principle, est a l'origine d'un ensemble commun de propriétés physiques. Leur Iuminosité est de beaucoup inférieure à celle du Soleil et leur temps caractéristique d'évolution se mesure en milliards d'années.

Abstract

New technics such as asteroseismology are able to sound the deep interior of stars and to provide the data that will constrain the modelisation of the core. This information will be combined with data collected from the stellar surface which give direct access to measurements of the radiative losses, angular momentum losses and distribution of active structures. From the two sets of data, the key role of the convection zone will be clarified, as the convection zone excites the waves that propagate through the whole star and generates the magnetic field that structures the stellar surface. The PRISMA mission was developed to collect the data needed for detecting the oscillations by very accurate photometry (micromagnitude) and to derive the surface activity and rotation from accurate ultraviolet spectroscopy. A short description of the model payload is given with the observational constraints related to the needed accuracy of measurements. Following the non-selection by ESA in may 1993, some following perspectives are described.

Introduction

The sounding of the stellar interior can be traced either by neutrino detection or by reconstruction of the path of travelling waves perturbing the surface. Asteroseismology is the study of such waves detected either in brillance or in velocity fluctuation. Up-to-now the use of such fluctuations (Grec et al, 1980; Frohlich and Toutain, 1992) has been proven to be a powerful diagnostic tool to modelise the solar interior (Gough, 1985).

Abstract

The properties of plasma in neutron star crusts with strong magnetic fields B = 1010 − 1013 G are reviewed: thermodynamic properties (equation of state, entropy, specific heat), transport properties (electron thermal and electrical conductivity of degenerate electron gas, radiative thermal conductivity of very surface nondegenerate layers) and neutrino energy losses. Classical effects of electron Larmor rotation in a magnetic field are considered as well as quantum effects of the electron motion (Landau levels). The influence of the magnetic fields on density and temperature profiles in the surface layers of neutron stars and on neutron star cooling is briefly discussed.

Nous présentons la revue des proprietés du plasma dans l'écorce des étoiles neutroniques avec des champs magnétiques forts B = 1010 − 1013 G: proprietés thermodynamiques (equation d'état, entropie, chaleur specifique), proprietés de transfer (conductivité electronique thermique et electrique du gaz electronique dégénéré, conductivité radiative thermique des couches non-dégénées superficielles), et les pertes dûes à l'énergie des neutrinos. Nous examinons des effets classiques de la rotation Larmor d'un electron dans le champ magnétique, et aussi des effets quantiques (niveaux de Landau). Nous discutons en bref l'influence des champs magnétiques sur la densité et la temperáture des couches des étoiles neutroniques et sur les taux de refroidissement des étoiles neutriniques.

Introduction

Neutron stars are the densest stars known in the Universe. Their masses are M ∼ 1.4M⊙, and radii R ∼ 10 km.