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

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

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

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

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

The role of male caretakers and pre-school teachers for father involvement in ECEC

‘Children need men!’ This rallying cry is a common argument for father involvement in the family as well as in the context of strategies for more men in ECEC. In what way are these two issues linked? Based on international research on the issue, this paper asks what role male EC workers can have for the involvement of fathers in the work of ECEC institutions / pre-schools. A critical gender perspective is crucial for the understanding of these links. The relevance of fathers for children’s development in the early years is widely accepted nowadays. At the same time, institutional care for children remains a female-dominated field worldwide. However, in some countries, campaigns for more men in ECEC have showed some success, e.g. Norway and Germany. One of the arguments in such campaigns is that male practitioners can encourage father involvement in ECEC institutions. The connection between father involvement and men in ECEC was already present in European debates on men and childcare more than two decades ago. But what do we really know about the role of male workers for cooperation with fathers? This paper gives an international overview on studies on the issue, and connects their results to the realms of practice. Finally, arguments for a specific role for male ECEC professionals in approaching and supporting fathers are presented and critically discussed

Lyman-alpha wing absorption in cool white dwarf stars

Kowalski & Saumon (2006) identified the missing absorption mechanism in the observed spectra of cool white dwarf stars as the Ly-alpha red wing formed by the collisions between atomic and molecular hydrogen and successfully explained entire spectra of many cool DA-type white dwarfs. Owing to the important astrophysical implications of this issue, we present here an independent assessment of the process. For this purpose, we compute free-free quasi-molecular absorption in Lyman-alpha due to collisions with H and H2 within the one-perturber, quasi-static approximation. Line cross-sections are obtained using theoretical molecular potentials to describe the interaction between the radiating atom and the perturber. The variation of the electric-dipole transition moment with the interparticle distance is also considered. Six and two allowed electric dipole transitions due to H-H and H-H2 collisions, respectively, are taken into account. The new theoretical Lyman-alpha line profiles are then incorporated in our stellar atmosphere program for the computation of synthetic spectra and colours of DA-type white dwarfs. Illustrative model atmospheres and spectral energy distributions are computed, which show that Ly-alpha broadening by atoms and molecules has a significant effect on the white dwarf atmosphere models. The inclusion of this collision-induced opacity significantly reddens spectral energy distributions and affects the broadband colour indices for model atmospheres with Teff<5000 K. These results confirm those previously obtained by Kowalski & Saumon (2006). Our study points out the need for reliable evaluations of H3 potential energy surfaces covering a large region of nuclear configurations, in order to obtain a better description of H-H2 collisions and a more accurate evaluation of their influence on the spectrum of cool white dwarfs.Comment: 11 pages, 12 figures, 1 table, to be published in MNRA

The ages and colours of cool helium-core white dwarf stars

The purpose of this work is to explore the evolution of helium-core white dwarf stars in a self-consistent way with the predictions of detailed non-gray model atmospheres and element diffusion. To this end, we consider helium-core white dwarf models with stellar masses of 0.406, 0.360, 0.327, 0.292, 0.242, 0.196 and 0.169 solar masses and follow their evolution from the end of mass loss episodes during their pre-white dwarf evolution down to very low surface luminosities. We find that when the effective temperature decreases below 4000K, the emergent spectrum of these stars becomes bluer within time-scales of astrophysical interest. In particular, we analyse the evolution of our models in the colour-colour and colour-magnitude diagrams and we find that helium-core white dwarfs with masses ranging from approx. 0.18 to 0.3 solar masses can reach the turn-off in their colours and become blue again within cooling times much less than 15 Gyr and then remain brighter than M_V approx. 16.5. In view of these results, many low-mass helium white dwarfs could have had time enough to evolve to the domain of collision-induced absorption from molecular hydrogen, showing blue colours.Comment: 11 pages, 9 figures. Accepted for publication in MNRA