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.

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.

In this review, we consider a quantum Coulomb fluid made of charged point particles (typically electrons and nuclei). We describe various formalisms which start from the first principles of statistical mechanics. These methods allow systematic calculations of the equilibrium quantities in some particular limits. The effective-potential method is evocated first, as well as its application to the derivation of low-density expansions. We also sketch the basic outlines of the standard many-body perturbation theory. This approach is well suited for calculating expansions at high density (for Fermions) or at high temperature. Eventually, we present the Feynman-Kac path integral representation which leads to the introduction of an auxiliary classical system made of extended objects, i.e., filaments (also called “polymers”). The familiar Abe-Meeron diagrammatic series are then generalized in the framework of this representation. The truncations of the corresponding virial-like expansions provide equations of state which are asymptotically exact in the low-density limit at fixed temperature. The usefulness of such equations for describing the inner regions of the sun is briefly illustrated.

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.

The rate of nuclear reactions depends on the influence of the surrounding particles that compose the plasma. At high densities the situation is far from being satisfactory and the influence of electron polarization has not been completely elucidated. In particular, it is shown that the possibility of an accretion induced collapse of a carbon-oxygen white dwarf instead of a supernova explosion completely depends on the screening factors and pycnonuclear rates that are adopted. Similarly, the possibility of detecting isolated neutron stars that accrete matter from the interstellar medium depends on the adopted pycnonuclear rates. Low rates allow the formation of a metastable layer that can release energy explosively and produce aγ-ray burst. Nevertheless, current rates seem to prevent such a situation.

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.

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 Log L/L⊙ ≤ −3, we can build little more than test models

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.

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 carbonoxygen cores), the outcome fits quite well the observed properties of Type Ia 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.

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.

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.

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 derealization 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.

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 gem−3. The transition occurs between a weakly ionized phase and a partially ionized (~ 50%) phase.

The numerous complexities underlying large tables of thermodynamic quantities act as a deterrent to a careful evaluation of their reliability. As a consequence, equations of state are often used as black boxes. To clarify this situation, some of the more critical issues of equation of state physics are discussed from the point of view of the user. They are illustrated by a comparison of four equations of state for hydrogen. The flaws and disagreements thus brought into light are explained and evaluated with simple physical arguments.

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 °K) for miscibility of He in ionized H at 10 Mb.

We present the results of numerical experiments aimed at demonstrating how the g-mode period spectra of pulsating DA white dwarfs depend on the various components of the input physics. We take advantage of recent developments on many fronts of physics (equation of state, opacity, convection) to compare the theoretical pulsation periods of models with different pieces of the constitutive physics, but with otherwise fixed values of their stellar parameters. This exercise is necessary to assess the reliability of the pulsation analyses of white dwarfs which have started to come out.

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 the solar structure, and on the properties of the plasma in the Sun. Except in the very outer layers, the stratification of the convection zone is almost adiabatic. There, the sound-speed profile is governed principally by the specific entropy, the (homogenous) chemical composition and the equation of state. It is therefore essentially independent of the uncertainties in the radiative opacities. The sensitivity of the observed frequencies is such that it enables to distinguish rather subtle features of the equation of state. An example is the signature of the heavy elements in the equation of state. This opens the possibility to use the Sun as a laboratory for thermodynamic properties.