Abstract

We consider a simple model for the evolution of a poloidal magnetic field initally trapped in a region containing normal npe matter within the outer liquid core of a neutron star. We have performed numerical computations for neutron stars with masses of 1.4, 1.6, and 1.7 M⊙ that undergo very rapid cooling due to the direct Urea process. Because the timescale for the magnetic field decay is directly proportional to T2, such a cooling history produces a rapid decline in the magnetic-field strength B, even for B as low as ∼ 1012 G. In particular, we show that an initially quasi-homogeneous magnetic field of strength B = 1012 G declines during the first ∼ 1 Myr.

Introduction

The calculations of Baym, Pethick, and Pines (1969a) have shown that the electrical conductivity of matter in the core of a neutron star is too large to permit ohmic decay of the magnetic field within the age of the Universe. Recently, Haensel, Urpin, and Yakovlev (1990; hereafter HUY) have pointed out that the magnetic-field strength |B| ∼ 1012 G typical of pulsars is sufficiently strong that the anisotropy of the transport coefficients cannot be neglected and that the “resistivity” for current flow perpendicular to B is many orders of magnitude larger than that for current flow parallel to B. Using a simple “toy” model, they found that internal fields B ≥ 1013 G can decline to ∼ 1012 G in times ∼ 107 years, but that fields ≤ 1012 G remain practically unchanged on this timescale.

Abstract

This paper summarizes recent work on the strongly coupled OCP and Binary Ionic Mixture equation of state and other thermodynamic quantities in white dwarf interior conditions for both fluid and solid phases with the assumption of a uniform background. Conditions for phase separation of different elements in fluid or solid phases is strongly dependent on deviations from the linear mixing rule which gives the equation of state as an additive function of the OCP equation of state. These deviations turn out to be small (a few parts in 105) and always positive including the case where the fraction of the higher Z component approaches 0. Also the equation of state of strongly coupled light elements (H and He particularly) obtained from simulations with a linear response description of the electrons is given for conditions appropriate to brown dwarf star interiors. Recent Livermore work on a band structure calculation of the enthalpy of H and He mixtures under jovian conditions is discussed. This work leads to a prediction of a high temperature (15000 oK) for miscibility of He in ionized H at 10 Mb.

Resume

Ce papier resume l'ouvrage recent sur le OCP à fort couplage et sur l'equation d'état et d'autres quantites thermodynamiques pour le melange binarire ionique aux conditions interieure des nains blancs. Les conditions pour seperation de phae dan les éléments divers dans l'état solide ou fluide sont très sensible aux deviations de regie lineaire qui donne l'equation d'état comme function additive sur celui du OCP.

Abstract

In this paper we review the behavior of growing stellar degenerate cores. It is shown that ONeMg white dwarfs and cold CO white dwarfs can collapse to form a neutron star. This collapse is completely silent since the total amount of radioactive elements that are expelled is very small and a burst of γ-rays is never produced. In the case of an explosion (always carbon-oxygen cores), the outcome fits quite well the observed properties of Type la supernovae. Nevertheless, the light curves and the velocities measured at maximum are very homogeneous and the diversity introduced by igniting at different densities is not enough to account for the most extreme cases observed. It is also shown that a promising way out of this problem could be the He-induced detonation of white dwarfs with different masses. Finally, we outline that the location of the border line which separetes explosion from collapse strongly depends on the input physics adopted.

Dans cet article on revise le comportement d'un noyau stellaire dégénéré qui grandit. On montre que les naines blanches d'ONeMg et celles de CO, froides et massives, peuvent s'effondrer pour former une étoile à neutrons. Cet effondrement est complètement silencieux puisque la quantité tot ale d'élements radioactifs expulsée est très petite et on ne produit pas d'eruption de rayons gamma. Dans le cas d'une explosion (toujours pour des noyaux de carbone-oxygène), le résultat des calculs reproduit assez bien les propriétés observées des supernovae de Type Ia.

Introduction

After the first success of helioseismology, it has been shown than new results could only be obtained from long set of continuous observations. Therefore different groups intented to set-up worldwide networks in order to observe the Sun 24 hours a day. This is the case of GONG and IRIS. Both are six-stations networks. Figure 1 shows the different sites of the two networks. They have one common site in Izaña.

IRIS has already 5 stations installed and running. The last site, in Australia, is under selection, and very probably will be in Culgoora, more accessible than the Western site selected by GONG team, in Learmonth. It will be set-up at the beginning of 1994. The operation, already started since 1990, will continue untill at least 2000. So far, the best piece of data obtained covers a period of three monthes, during Summer 1991, with a duty cycle of 60%, with only 3 instruments working. With 6 sites, a duty-cycle of at least 85% is expected.

The six instruments of the GONG network are constructed and under tests. The deployement is supposed to take place during the second half of 1994. The network will be fully operational in 1995. A duty-cycle higher than 90% is expected.

IRIS provides only full-disk velocity measurements, whereas GONG is designed to record images of the Sun, providing a spatial resolution. GONG will measure non-radial modes, from 1=1 to 1=200, when IRIS is only sensitive to radial and low degree non-radial modes (1=0 to 3).

Abstract

The inclusion of a detailed treatment of solidification processes in the cooling theory of carbon–oxygen white dwarfs is of crucial importance for the determination of their luminosity function. Carbon–oxygen separation at crystallization yields delays larger than 2 Gyr to cool down to luminosities corresponding to the observed cut–off. This leads to estimates of the age of the galactic disk 1.5 to 2 Gyr older than the ones obtained in previous studies (about 9 Gyr). Furthermore, the presence of minor chemical species, in particular 22Ne, alters significantly the crystallization process, and produces extra delays of 2 to 3 gigayears. However, the detailed computation of the theoretical white dwarf luminosity function, taking into account a reasonable model of galactic chemical evolution, and including the effect of these species, shows that the location of the cut–off, and then the estimated age of the disk, is not modified significantly.

Le traitement détaillé du processus de solidification revêt une importance cruciale dans l'étude du refroidissement des naines blanches carbone–oxygéne et la détermination de leur fonction de luminosité. La séparation du carbone et de l'oxygène lors de la cristallisation introduit un retard de plus de 2 109 ans pour atteindre les valeurs de la luminosité correspondant au cut–off observé. Ceci conduit à une estimation de l'âge du disque de 1.5 à 2 109 ans plus vieille que celles obtenues dans les études précédentes.

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.