Equation of state SAHA-S meets stellar evolution code CESAM2k

We present an example of an interpolation code of the SAHA-S equation of state that has been adapted for use in the stellar evolution code CESAM2k. The aim is to provide the necessary data and numerical procedures for its implementation in a stellar code. A technical problem is the discrepancy between the sets of thermodynamic quantities provided by the SAHA-S equation of state and those necessary in the CESAM2k computations. Moreover, the independent variables in a practical equation of state (like SAHA-S) are temperature and density, whereas for modelling calculations the variables temperature and pressure are preferable. Specifically for the CESAM2k code, some additional quantities and their derivatives must be provided. To provide the bridge between the equation of state and stellar modelling, we prepare auxiliary tables of the quantities that are demanded in CESAM2k. Then we use cubic spline interpolation to provide both smoothness and a good approximation of the necessary derivatives. Using the B-form of spline representation provides us with an efficient algorithm for three-dimensional interpolation. The table of B-spline coefficients provided can be directly used during stellar model calculations together with the module of cubic spline interpolation. This implementation of the SAHA-S equation of state in the CESAM2k stellar structure and evolution code has been tested on a solar model evolved to the present. A comparison with other equations of state is briefly discussed. The choice of a regular net of mesh points for specific primary quantities in the SAHA-S equation of state, together with accurate and consistently smooth tabulated values, provides an effective algorithm of interpolation in modelling calculations. The proposed module of interpolation procedures can be easily adopted in other evolution codes.Comment: 8 pages, 5 figure

Nanosystems for Health and Environment

Context. The Sun is the most studied of all stars, which serves as a reference for all other observed stars in the Universe. Furthermore, it also serves the role of a privileged laboratory of fundamental physics and can help us better understand processes occuring in conditions irreproducible on Earth. However, our understanding of our star is currently lessened by the so-called solar modelling problem, resulting from comparisons of theoretical solar models to helioseismic constraints. These discrepancies can stem from various causes, such as the radiative opacities, the equation of state as well as the mixing of the chemical elements

Ionization of heavy elements and the adiabatic exponent in the solar plasma

Context. The adiabatic exponent $\Gamma_1$ is studied as a thermodynamic quantity in the partially ionized plasma of the solar convection zone. Aims. The aim of this study is to understand the impact of heavy elements on the $\Gamma_1$ profile. We calculated $\Gamma_1$ with the SAHA-S equation of state for different chemical compositions of plasma, and we analyzed contributions of individual elements to $\Gamma_1$. Methods. We studied the decrease in $\Gamma_1$ due to the ionization of heavy elements in comparison with the value obtained for a pure hydrogen-helium plasma. These types of differences are denoted as "Z contributions", and we analyzed them for eight elements (C, N, O, Ne, Mg, S, Si, and Fe) as well as for a mixture of elements corresponding to the solar chemical composition. We compared linear combinations of individual Z contributions with the exact Z contribution. Applying a least-squares technique to the decomposition of the full Z contribution to a basis of individual-element contributions, we obtained the mass fractions of the heavy elements. Results. The Z contribution of heavy elements can be described by a linear combination of individual-element Z contributions with a high level of accuracy of 5e-6 . The inverse problem of estimating the mass fractions of heavy elements from a given $\Gamma_1$ profile was considered for the example of solar-type mixtures. In ideal numerical simulations, the mass fractions of the most abundant elements could be determined with a relative accuracy better than a few tenths of a percent. In the presence of random or systematic errors in the $\Gamma_1$ profile, abundance estimations become remarkably less accurate. If the amplitude of the errors does not exceed 1e-4, we can expect a determination of at least the oxygen abundance with a relative error of about 10%.Comment: Accepted for publication in 'Astronomy and Astrophysics

Phase transition in a strongly nonideal deuterium plasma generated by quasi-isentropical compression at megabar pressures

High-explosive driven generators of cylindrical and plane shock waves in D-2 and H-2 were used for the generation of warm and dense strongly nonideal matter with an intense interparticle interaction and Fermi statistics. Highly resolved flash x-ray diagnostics were used to measure the adiabatic plasma compressibility. The thermodynamic measurements demonstrated the 20% increase of density at megabar pressure, just in the density range, where the electrical measurements indicated a sharp - 5 orders of magnitude - increase of electrical conductivity due to pressure ionization in strongly coupled plasmas

Combining multiple structural inversions to constrain the solar modelling problem

Context. The Sun is the most studied of all stars, which serves as a reference for all other observed stars in the Universe. Furthermore, it also serves the role of a privileged laboratory of fundamental physics and can help us better understand processes occuring in conditions irreproducible on Earth. However, our understanding of our star is currently lessened by the so-called solar modelling problem, resulting from comparisons of theoretical solar models to helioseismic constraints. These discrepancies can stem from various causes, such as the radiative opacities, the equation of state as well as the mixing of the chemical elements. Aims. By analysing the potential of combining information from multiple seismic inversions, our aim is to help disentangle the origins of the solar modelling problem. Methods. We combined inversions of the adiabatic sound speed, an entropy proxy and the Ledoux discriminant with other constraints such as the position of the base of the convective zone and the photospheric helium abundance. First, we tested various combinations of standard ingredients available for solar modelling such as abundance tables, equation of state, formalism for convection and diffusion and opacity tables. Second, we studied the diagnostic potential of the inversions on models including ad hoc modifications of the opacity profile and additional mixing below the convective envelope. Results. We show that combining inversions provides stringent constraints on the required modifications to the solar ingredients, far beyond what can be achieved from sound speed inversions alone. We constrain the form and amplitude of the opacity increase required in solar models and show that a 15% increase at log T = 6.35 provides a significant improvement, but is insufficient on its own. A more global increase in the opacity, within the uncertainties of the current tables, coupled with a localized additional mixing at the bottom of the convective zone provides the best agreement for low-metallicity models. We show that high-metallicity models do not satisfy all the inversion results. We conclude that the solar modelling problem likely occurs from multiple small contributors, as other ingredients such as the equation of state or the formalism of convection can induce small but significant changes in the models and that using phase shift analyses combined with our approach is the next step for a better understanding of the inaccuracies of solar models just below the convective envelope