Equation of state of sticky-hard-sphere fluids in the chemical-potential route

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($\mu$ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the $\mu$ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the $\mu$ route yields a general better description than the virial, energy, compressibility, and zero-separation routes.Comment: 13 pages, 7 figures; v2: Results from the zero-separation route have been adde

Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres

Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms $\hat{c}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of $\hat{c}_{ij}(k)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.Comment: 6 page

Chemical-potential route for multicomponent fluids

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are derived from the Percus-Yevick theory and the associated equation of state is obtained. This Percus-Yevick chemical-route equation of state is shown to be more accurate than the virial equation of state. An interpolation between the chemical-potential and compressibility routes exhibits a better performance than the well-known Boubl\'ik-Mansoori-Carnahan-Starling-Leland equation of state.Comment: 9 pages, 1 figure; v2: minor change

Hydrogen model atmospheres for white dwarf stars

We present a detailed calculation of model atmospheres for DA white dwarfs. Our atmosphere code solves the atmosphere structure in local thermodynamic equilibrium with a standard partial linearization technique, which takes into account the energy transfer by radiation and convection. This code incorporates recent improved and extended data base of collision induced absorption by molecular hydrogen. We analyse the thermodynamic structure and emergent flux of atmospheres in a range 2500 < Teff < 60000$ K and 6.5 < log g < 9.0. Bolometric correction and colour indices are provided for a subsample of the model grid. Comparison of the colours is made with published observational material and results of other recent model calculations. Motivated by the increasing interest on helium core white dwarfs, we analyse the photometric characteristics of these stars during their cooling, using evolutionary models recently available. Effective temperatures, surface gravities, masses and ages have been determined for some helium core white dwarf candidates, and their possible binary nature is briefly discussed.Comment: 12 pages, 13 figures. Accepted for publication in MNRA

Equation of state for five-dimensional hyperspheres from the chemical-potential route

We use the Percus-Yevick approach in the chemical-potential route to evaluate the equation of state of hard hyperspheres in five dimensions. The evaluation requires the derivation of an analytical expression for the contact value of the pair distribution function between particles of the bulk fluid and a solute particle with arbitrary size. The equation of state is compared with those obtained from the conventional virial and compressibility thermodynamic routes and the associated virial coefficients are computed. The pressure calculated from all routes is exact up to third density order, but it deviates with respect to simulation data as density increases, the compressibility and the chemical-potential routes exhibiting smaller deviations than the virial route. Accurate linear interpolations between the compressibility route and either the chemical-potential route or the virial one are constructed.Comment: 9 pages, 6 figures; v2: Change in one referenc

Evolution and colours of helium-core white dwarf stars: the case of low metallicity progenitors

The present work is designed to explore the evolution of helium-core white dwarf (HeWD) stars for the case of metallicities much lower than the solar one (Z=0.001 and Z=0.0002). Evolution is followed in a self-consistent way with the predictions of detalied and new non-grey atmospheres, time-dependent element diffusion and the history of the white dwarf progenitor. Reliable initial models for low mass HeWDs are obtained by applying mass loss rates to a 1msun stellar model. The loss of angular momentum caused by gravitational wave emission and magnetic stellar wind braking are considered. Model atmospheres, based on a detailed treatment of the microphysics entering the WD atmosphere enable us to provide accurate colours and magnitudes at both early and advanced evolutionary stages. We find that most of our evolutionary sequences experience several episodes of hydrogen thermonuclear flashes. In particular, the lower the metallicity, the larger the minimum stellar mass for the occurrence fo flashes induced by CNO cycle reactions. The existence of a mass-threshold for the occurrence of diffusion-induced CNO flashes leadss to a marked dichotomy in the age of our models. Another finding of this study is that our HeWD models experience unstable hydrogen burning via PP nuclear reactions at late cooling stages as a result of hydrogen chemically diffusing inwards. Such PP flashes take place in models with very low metal content. We also find that models experiencing CNO flashes exhibit a pronouncede turn-off in most of their colours at M_V=16 approximately. Finally, colour-magnitude diagrams for our models are presented and compared with recent observational data of HeWD candidates in the globular clusters NGC 6397 and 47 Tucanae.Comment: 14 pages, 10 figures. Accepted for publication in MNRA

Outer boundary conditions for evolving cool white dwarfs

White dwarf evolution is essentially a gravothermal cooling process, which,for cool white dwarfs, sensitively depends on the treatment of the outer boundary conditions. We provide detailed outer boundary conditions appropriate for computing the evolution of cool white dwarfs employing detailed non-gray model atmospheres for pure H composition. We also explore the impact on the white dwarf cooling times of different assumptions for energy transfer in the atmosphere of cool white dwarfs. Detailed non-gray model atmospheres are computed taken into account non-ideal effects in the gas equation of state and chemical equilibrium, collision-induced absorption from molecules, and the Lyman alpha quasi-molecular opacity. Our results show that the use of detailed outer boundary conditions becomes relevant for effective temperatures lower than 5800 and 6100K for sequences with 0.60 and 0.90 M_sun, respectively. Detailed model atmospheres predict ages that are up to approx 10% shorter at log L/L_sun=-4 when compared with the ages derived using Eddington-like approximations at tau_Ross=2/3. We also analyze the effects of various assumptions and physical processes of relevance in the calculation of outer boundary conditions. In particular, we find that the Ly_alpha red wing absorption does not affect substantially the evolution of white dwarfs. White dwarf cooling timescales are sensitive to the surface boundary conditions for T_eff < 6000K. Interestingly enough, non-gray effects have little consequences on these cooling times at observable luminosities. In fact, collision-induced absorption processes, which significantly affect the spectra and colors of old white dwarfs with hydrogen-rich atmospheres, have not noticeable effects in their cooling rates, except throughout the Rosseland mean opacity.Comment: 6 pages, 9 figures, to be published in Astronomy and Astrophysic