Generalized Fermi-Dirac Functions and Derivatives: Properties and Evaluation

The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac functions have been found. An effective numerical method to evaluate the derivatives of the generalized Fermi-Dirac functions up to third order with respect to both degeneracy and temperature is then proposed, following Aparicio. A Fortran program based on this method, together with a sample test case, is provided. Accuracy and domain of reliability of some other, popularly used analytic approximations of the generalized Fermi-Dirac functions for extreme conditions are investigated and compared with our results.Comment: accepted for publication in Comp. Phys. Com

Dynamic screening in solar and stellar nuclear reactions

In the hot, dense plasma of solar and stellar interiors, the Coulomb interaction is screened by the surrounding plasma. Although the standard Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. In particular, Shaviv and Shaviv apply the techniques of molecular dynamics to the conditions in the solar core in order to numerically determine the dynamic screening effect. By directly calculating the motion of ions and electrons due to Coulomb interactions, they compute the effect of screening without the mean-field assumption inherent in the Salpeter approximation. Here we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of stellar nuclear reaction rates.Comment: Astrophysics and Space Science, Special Issue Solar & Stellar Modelling Corrected sign error. Now consistent with final published versio

Circumstellar Disks at White Dwarfs: Observations

The current picture painted by the observations of circumstellar dust at white dwarfs, and the consequent atmospheric pollution, is of a surviving planetary system. This chapter recounts in detail both the discovery and empirical characterization of dust disks at single white dwarfs, including all observational data available up to early 2011. Observations of the disks themselves and the accreted heavy elements within the stellar photospheres are consistent with tidally disrupted asteroid analogs. The observed chemistry supports objects that condensed within the inner regions of main-sequence stars and thus far appear similar in constitution to the terrestrial planets and their building blocks.Comment: Chapter from the book "White Dwarf Atmospheres and Circumstellar Environments", ed. D. W. Hoard (Wiley-VCH), 201

On Density and Temperature-Dependent Ground-State and Continuum Effects in the Equation of State for Stellar Interiors

The consequence of shifts in bound-state energies and the position of the continuum for thermodynamic quantities are examined. Two independent methods from different branches of physics are brought together. A simple free-energy model is used to examine the thermodynamic consequences of the results of a quantum statistical calculations of two-particle properties in a plasma using Green-function technique. A comparison with data inferred from helioseismology shows that our interdisciplinary procedure works very well for lower-level approximations, such as the static screening in the effective two-particle wave equation. However, in the case of dynamic screening in the wave equation, the resulting thermodynamic quantities are inconsistent with observations. This could be due to an inadequacy of our method to compute the thermodynamic quantities, or due to an inappropriate treatment of the ion contribution to the electronic self energy corresponding to the dielectric function used in rand..

Concluding remarks

Precision asteroseismic observations with the Kepler and CoRot satellites enable the internal structure and evolution of pulsating stars to be more exhaustively studied than has hitherto been possible. It is particularly important to study the evolutionary links between white dwarfs and subdwarf-B stars with stars considered to have been their progenitors, those on the Red Giant and Asymptotic Giant Branches. Though observations present challenges for existing stellar evolution and pulsation models, and the data (atomic, molecular and nuclear) on which they are based, excellent prospects for development are identified which will in turn facilitate studies of the Galaxy and extra-solar planets