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.

Abstract

Model sequences computed with the recently-published OPAL radiative opacities, Itoh et al. conductive opacities, and Itoh et al. neutrino rates are presented. Cooling times for DA model sequences are found to be independent of metallicity for Z ≤ 0.001.

Introduction

In the past decade, many improvements in the constitutive physics relevant to white dwarf evolutionary models have been published. These include improved radiative opacities (Rogers & Iglesias 1992; Iglesias & Rogers 1993), conductive opacities for pure (Itoh et al. 1993 and references therein) and mixed (Itoh & Kohyama 1993) compositions, and updated neutrino rates (Itoh et al. 1992 and references therein). We have incorporated these results into our white dwarf evolution code (=WDEC; see Lamb & Van Horn 1975, and Wood 1990), and present here selected C-core DA model sequences computed with the updated code. Stellar masses for the sequences are 0.4, 0.6, and 0.8 M⊙ and surface layer masses are log q(H) = −6 and log q(He) = −4. To determine the effect of metallicity on the evolutionary timescale, we computed parallel sequences with Z = 0.000 and 0.001.

Opacities

The radiative opacities used in WDEC in the past (Cox & Stewart 1970) had an unrealistically-high metallicity of Z = 0.001 (Zobs ≲ 10−5) The new OPAL opacities span a wide range of metallicities and compositions, and therefore allow the inclusion of more plausible composition profiles in the models. The OPAL opacities only extend to a minimum temperature of 6000 K, however, so for DA models WDEC references the pure-H opacities of Lenzuni et al. (1991) below this point.

Abstract

In the limit of short wavelengths, it has been shown that superfluidity significantly affects wave propagation in neutron stars. Here we abandon the short-wavelength restriction and extend these calculations to global oscillation modes. In the present analysis, the solid crust of the neutron star is divided into an outer crust and an inner crust, and a superfluid of neutrons coexists with the solid lattice in the inner crust. We have computed several low-order global spheroidal modes for l = 2 both with and without superfluidity. We find that superfluidity in the inner crust affects the frequency spectra of acoustic (p-) modes, shear (s-) modes, and interfacial (i-) modes, although the surface gravity (g-) modes are not affected at all.

Introduction

Most previous calculations of the non-radial oscillations of neutron stars have completely neglected the effects of superfluidity (cf McDermott, Van Horn, and Hansen 1988 and references therein). Epstein (1988) has previously considered superfluid effects, but only in the short-wavelength limit, where the length scales for variations in equilibrium quantities are all assumed to be much longer than the typical wavelength of an oscillation. In general, global oscillations may be either spheroidal or toroidal in character. Van Horn and Epsetein (1990) extended Epstein's short-wavelength results to include the global toroidal oscillation modes of neutron stars. More recently, Mendell (1991) and his colleagues have also considered the effects of superfluidity, but they employed simple models for neutron stars, and their analysis did not reflect the variety of oscillation modes of realistic, neutron stars.

Abstract

This paper reviews a new astrophysical subject: seismology of the giant planets. Seismology is dedicated to the sounding of the interior structure of any object; on the other hand, the interiors of the Jovian planets need to be constrained, in order to improve our knowledge of their structure and of their evolution, as well as the thermodynamical laws involved at high pressures and low temperatures. The relationship between Jovian seismology and, first, Jovian internal structure, and second, high pressure physics, is examined, in order to determine the task of “dioseismology” in the next years. We present then the seismological theoretical approaches developped since the pionnering work of Vorontsov et al. (1976), who calculated the frequencies of the Jovian eigenmodes. We report the first observational attempts for the detection of the oscillations of Jupiter. We discuss the observational results and examine what can be done in the future.

La sismologie des planètes géantes apparaît comme un centre d'intérêt astrophysique d'avenir. Elle doit permettre en effet – et il s'agit en fait du seul outil dont l'on dispose – de sonder les intérieurs de ces planètes, actuellement mal connus, mais dont la détermination représente un intérêt majeur. Cet article récapitule aussi bien les diverses approches théoriques développées depuis l'article précurseur de Vorontsov et al. (1976) que les diverses expériences menées pour détecter les oscillations de la planète Jupiter. L'accent est mis sur les liens reliant l'étude sismologique des planètes géantes avec d'une part leur structure interne, d'autre part la physique hyperbare gérant les équations d'état utilisées pour décrire le comportement de l'enveloppe fluide.

Abstract

In this paper I summarize some of the recent advances in studies of dense matter. Research on phase separation in the binary ionic mixtures (BIMs) that constitute the matter in white dwarfs has been motivated by the need to obtain accurate estimates for the ages of the faintest white dwarfs and thus of the disk of our Galaxy. Substantial age increases appear possible, but it is not yet clear whether such large increases occur in real white dwarfs. A second advance is the prediction, based on state-of-the-art physical calculations, that ionization of H at low temperatures and increasing densities may occur via a first-order “plasma phase transition” (PPT). Astrophysical consequences of this result are still being explored in an effort to test this prediction. Related to these equation-of-state calculations are calculations of the enhancement of nuclear reaction rates at high densities. New thermonuclear rates have been computed for C+C reactions in BIMs, although there is currently some controversy about results at the highest densities. New pycnonuclear reaction rates have also been calculated for BIMs, and it has been suggested that He-burning at T = 0 may occur through a first-order phase transition. Finally, calculations of the equation of state of matter in strong magnetic fields and of radiative opacities at high densities have undergone very recent and substantial improvements, which are just beginning to be utilized in astrophysical calculations.

Abstract

The EVRIS experiment is an exploratory mission devoted to stellar seismology. It will observe approximately ten bright stars, for 20 days each, during the cruise of the Russian MARS 94 mission. The photometer will be able to detect amplitudes of modes as small as a few 10−6 magnitude. Some objects of masses lower than the solar one will allow to test the thermodynamics.

EVRIS est la première expérience dévouée à la sismologie des étoiles. Elle sera lancée par la mission Russe MARS 94. Elle observera une dizaine d'objets, chacun pendant une vingtaine de jours, avec un seuil de détection de quelques 10−6 magnitude. Plusieurs étoiles de masse plus faible que celle du Soleil devraient permettre des tests significatifs de leur thermody-namique.

An exploratory instrument for asteroseismology.

Scientific objectives and strategy.

After the success of detection, measurements and interpretation of the eigemodes of the Sun, it is tempting to try to achieve similar progress on other stars and to allow for a comparative and differential study of the seismical stellar behavior.

The major difficulties when going from the Sun to stars is the lack of photons and the lack of spatial resolution. The rationale for such an aim has already been developed several times (i.e. Hudson et al. 1986, Praderie et al. 1988).

The need to go to space has also been extensively documented (see i.e. Mangeney and Praderie 1984, Hudson et al. 1986, Baglin 1990, Weiss 1992).

Abstract

We present briefly a new generation of white dwarf models incorporating the latest developments of the constitutive physics. These are static models especially designed for accurate seismological studies.

Introduction

The main goal of asteroseismology is the determination of the internal structure of a pulsating star through the analysis of its observed pulsation properties. One way to fulfill this goal is by producing a stellar model that reproduces to high accuracy the observed periods of oscillation. This is generally not possible through full evolutionary calculations as the parameters of a model must be tuned rather finely to satisfy the requirement of accuracy. However, computations of static models can be used with profit here. We have therefore developed the capacity to rapidly build complete static models of stratified H-rich (DA) or He-rich (DB) white dwarfs, especially suited for asteroseismological studies, by specifying the stellar mass, the H-layer thickness, the He-layer thickness, the convective efficiency and the effective temperature.

Method

To build our models, we integrate with the help of a Runge-Kutta technique the equations of stellar structure and stellar grey atmosphere (see, e.g., Cox & Guili 1968 and Mihalas 1978) from the high atmosphere (ρ ≲ 10−13) down to the center of the star. We iterate this procedure until we find a model with Mr = 0 at r = 0. To have a good spatial resolution both in the interior and the external regions, we use the integration variable x[≡ ln(r/P)].

Abstract

The solution of the exact integral equation for the liquid pair-structure in the asymptotic strong coupling limit for the plasma, as mapped on the Onsager charge-smearing optimization for the energy lower bound, features “Onsager atoms” and “Onsager molecules”. The universal properties of this asymptotic limit make it a natural reference starting point for an asymptotic strong coupling expansion for the fluid structure and thermodynamics, playing the role of an “ideal liquid” state. In particular, the leading strong coupling terms for the potential energy, direct correlation functions, and screening potentials for the Coulomb and Yukawa mixtures (corresponding to classical plasmas and electron screened classical plasmas), with full thermodynamic consistency, are presented. These are in complete agreement with the Alastuey-Jancovici analysis of early simulations data by Hansen in strong coupling, and with recent highly accurate simulations data of Ogata, Iyetomi, and Ichimaru. Data analysis errors lead Ogata, Iyetomi, and Ichimaru to incorrect results for the short range screening potentials in strong coupling. Their calculations for the short range screening potentials, bridge functions, and enhancement factors for nuclear reaction rates in strongly coupled plasmas, should be revised.

La solution de l'équation intégrate exacte pour la structure du liquide dans la limite asymptotique de couplage fort pour le plasma, calquée sur l'optimisation de charge d'Onsager pour la limite inférieure de l'énergie, met en évidence des “atomes d'Onsager” et des “molécules d'Onsager”.

Abstract

The importance of low temperature opacities in stellar calibrations led us to compute new sets of Rosseland mean opacities for different Z-values. For the solar metallicity, these tables have been compared to those of Alexander (1975), Cox (1983), Sharp (1991) and Kurucz (1992).

Introduction

Opacities in the atmospheric layers are generally not considered of great importance in the calculation of theoretical evolutionary tracks since the atmosphere of a star only comprises a tiny part of its mass (see however, section 1.2).

Until recently, the most commonly used “atmospheric” or “low-T” opacity tables were those of Cox & Stewart (1970), Alexander (1975) and Cox (1983) but there are rather large discrepancies between these different tables for typical T and ρ ranges encountered in stellar atmospheres of solar type stars.

Furthermore, for pop I stars, low-T opacities are calculated for very few values of the metallicity, Z, and the solar chemical composition is generally used in the calculation of tracks, whatever the actual value of Z.

Low-T opacities and stellar calibrations

Theoretical evolutionary tracks depend on mass, age, chemical composition on the zero age main sequence and convection parameter, α (ratio of mixing length to pressure scale height in the convective layers). Calibrating a star consists in computing evolutionary models that reproduce, at given age, chemical composition on ZAMS and convection parameter, the observed values of the luminosity and effective temperature of the star.

Abstract

The internal structure of a white dwarf may be changed by a strong magnetic field. A local model of the electrons is constructed within a thermal density matrix formalism, essentially a Heisenberg magnetism model. This results in a matrix Fermi function which is used to construct an isothermal model of the electron crystal. The central density of the crystal is 108kg/m3 independent of the magnetic field within the plasma and therefore lower than the relativistic density, whereas this density is constant until the Fermi momentum xf = 0.3 * me * c. Chandrasekhar masses up to 1.44 * 1.4M0 are possible for polarizations of the plasma zone lower than 0.5, if the temperature is close to the Curie point, whereas the crystal itself destabilizes the white dwarf dependent on temperature.

Introduction

From the theory of magnetic phase transitions of solid state physics (Grosse 1988) it is expected, that the structure of a single white dwarf is changed drastically by a magnetic field. The polarized electrons throughout the star may interact due to a magnetic field. The nonlinear influence of a crystallization transition and the crystal itself may change the mass and radius of a white dwarf. We construct a thermal Heisenberg model of the electrons which results in a Fermi matrix function, which predicts a plasma crystal phase transition. This Fermi function is used within the standard white dwarf theory.

Abstract

This review attempts a brief summary of the numerous and diverse searches for the so-called brown dwarfs, substellar objects having masses between giant planets and the lowest mass M dwarf stars.

Cette revue donne un bref aperçu de l'état actuel des diverses recherches de naines brunes, objects substellaires ayant des masses comprises entre les planètes géantes et les naines M de faible masse.

Introduction

Between the giant planets such as Jupiter (10−3M⊙) and stars at the bottom of the hydrogen-burning main sequence (≤0.1M⊙) – spanning more than two orders of magnitude in mass – the sequence of brown dwarfs has yet to be discovered and analyzed in detail. The previous sentence carries the positive bias of this author that – despite the current lack of a single, unambiguous example for me to discuss at this meeting – the flurry of searches now underway by a variety of techniques will identify at least some genuine brown dwarfs during the present decade. Our motivation for thinking and speaking positively is to encourage advances in the theory of both the interiors and atmospheres of such gaseous objects, in order to make possible positive identifications among the candidates found by observers. Indeed, numerous candidates exist of different kinds, some with measured masses, luminosities and temperatures which straddle the stellar mass limit (SML) near 0.08 M⊙.