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We are in the process of updating and extending the OPAL equation-of-state (EOS) and opacity data to include low-mass stars. The EOS part of that effort now is complete, and the results are described herein. The new data cover main-sequence stars having mass � 0.1 M� . As a result of the more extreme matter conditions encountered with low-mass stars, we have added new physics. The electrons are now treated as relativistic, and we have improved our treatment of molecules. We also consider the implications of the new results for helioseismology.

Density effects on two important processes contributing to the opacity of a weakly ionized helium gas are considered. The correction to free-free absorption by the negative helium ion is treated in the Born approximation using analytical approximations for the electron-atom interaction. The correction to Rayleigh scattering uses well-known formulae obtained from density fluctuation theory. In both processes, the main density effect appears through the static structure factor, which accounts for spatial correlations between the helium atoms. These correlations significantly reduce the cross sections at the high densities encountered in cool, He white dwarf atmospheres.

Stellar evolutionary tracks have been computed for 17 [Fe/H] values from -2.31 to -0.30 assuming, in each case, [?/Fe] = 0.0, 0.3, and 0.6. The helium abundance was assumed to vary from Y = 0.2352 at [Fe/H] = -2.31 to Y = 0.2550 at [Fe/H] = -0.30 and held constant for the different choices of [?/Fe] at a fixed iron content. Masses in the range 0.5 ? ? ? 1.0, in 0.1 ? steps, were generally considered, though sequences for higher mass values were computed, as necessary, to ensure that isochrones as young as 8 Gyr could be generated for each grid. All of the stellar models are based on an equation of state that treats nonideal effects, the latest nuclear reaction and neutrino cooling rates, and opacities that were computed specifically for the adopted chemical mixtures. The tracks were extended to the tip of the giant branch or to an age of 30 Gyr, whichever came first, and zero-age horizontal-branch (ZAHB) loci were constructed using the helium core masses and chemical profiles from appropriate red giant precursors. Selected models have been compared with those computed by A. V. Sweigart, for the same masses and chemical compositions, to demonstrate that the results obtained from two entirely independent stellar evolution codes agree well with one another when very similar input physics is assumed. In the case of extremely metal-deficient stars, an enhancement in the abundance of the ?-elements causes a single, fairly significant bump in the opacity at a temperature just above 106 K, which is caused by absorption processes involving the K shell of oxygen. This peak becomes steadily more pronounced as the overall metallicity increases and a second bump, arising from the L edges of Ne, Mg, and Si, eventually appears near log T = 5.6. As far as the tracks and isochrones are concerned, we find that, as already reported by others, it is possible to mimic the computations for [?/Fe] > 0 remarkably well by those for scaled-solar mixes simply by requiring the total mass-fraction abundance of the heavy elements, Z, to be the same. However, this result holds only for metallicities significantly less than solar. Above [Fe/H] -0.8, tracks and isochrones for enhanced ?-element mixtures begin to have systematically hotter/bluer turnoffs and red giant branches than those for scaled-solar mixtures of the heavy elements. Also addressed is the extent to which our models satisfy the constraints posed by the local subdwarfs, the distances of which are based on Hipparcos parallax measurements. Our analysis suggests that the predicted metallicity dependence of the location of the lower main sequence on the C-M diagram is in good agreement with the observed dependence. In fact, we do not find any compelling evidence from the local Population II calibrators that the colors of our models require significant adjustments. In further support of our calculations, we find that, both in zero point and slope, the computed giant branches on the (Mbol, log Teff)-plane agree well with those inferred for globular clusters from observations in the infrared. Moreover, our ZAHB models have luminosities that are just outside the 1 ? error bars of the mean MV's inferred for RR Lyrae stars from Baade-Wesselink, statistical parallax, and trigonometric parallax studies. Lower helium contents or higher ?-element abundances or an increase in the conductive opacities are among the possible ways of reducing the differences that remain. To facilitate comparisons with observations, the tracks/ZAHBs are provided with predicted BV(RI)C photometry.

The solar evolution has been calculated including all the effects of the diffusion of helium and heavy elements. Monochromatic opacities are used to calculate radiative accelerations and Rosseland opacities at each evolution time step, taking into account the local abundance changes of all important (21) chemical elements. The OPAL monochromatic data are used for the opacities and the radiative accelerations. The Opacity Project data are needed to calculate how chemical species and electrons share the momentum absorbed from the radiation flux. A detailed evaluation of the impact of atomic diffusion on solar models is presented. On some elements thermal diffusion adds approximately 50% to the gravitational settling velocity. While gravitational settling had been included in previous solar models, this is the first time that the impact of radiative accelerations is considered. Radiative accelerations can be up to 40% of gravity below the solar convection zone and thus affect chemical element diffusion significantly, contrary to current belief. Up to the solar age, the abundances of most metals change by 7.5% if complete ionization is assumed, but by 8.5%-10% if detailed ionization of each species is taken into account. If radiative accelerations are included, intermediate values are obtained. Diffusion leads to a change of up to 8% in the Rosseland opacities, compared to those of the original mixture. Most of this effect can be taken into account by using tables with several values of Z. If one isolates the effects of radiative accelerations, the abundance changes they cause alter the Rosseland opacity by up to 0.5%; the density is affected by up to 0.2%; the sound speed is affected by at most 0.06%. The inclusion of radiative accelerations leads to a reduction of 3% of neutrino fluxes measured with 37Cl detectors and 1% measured with 71Ga detectors. The partial transformation of C and O into N by nuclear reactions in the core causes a ~1% change in the opacities that cannot be modeled by a change in Z alone. The evolution is allowed to proceed to 1010 yr in order to determine the impact at the end of the main-sequence life of solar-type stars. It is found that immediately below the convection zone, the radiative acceleration on some iron peak elements is within a few percent of gravity. The abundance anomalies reach 18% for He in the convection zone but are kept within 12% and 15% for most because of grad. They would have reached 18% in the absence of grad.

Monochromatic opacities from the OPAL database have been used to calculate radiative accelerations for the 21 included chemical species. The 104 frequencies used are sufficient to calculate the radiative accelerations of many elements for T > 105 K, using frequency sampling. This temperature limit is higher for less abundant elements. As the abundances of Fe, He, or O are varied, the radiative acceleration of other elements changes, since abundant elements modify the frequency dependence of the radiative flux and the Rosseland opacity. Accurate radiative accelerations for a given element can only be obtained by allowing the abundances of the species that contribute most to the Rosseland opacity to vary during the evolution and recalculating the radiative accelerations and the Rosseland opacity during the evolution. There are physical phenomena that cannot be included in the calculations if one uses only the OPAL data. For instance, one should correct for the momentum given to the electron in a photoionization. Such effects are evaluated using atomic data from Opacity Project, and correction factors are given.

We present new calculations that strongly reinforce the idea—originally proposed by Charpinet et al.—that pulsation modes are driven through an opacity bump due to a local enhancement of the iron abundance in the envelopes of sdB stars. Our improved models incorporate nonuniform iron abundance distributions obtained through the condition of diffusive equilibrium between gravitational settling and radiative levitation. They also include special Rosseland opacity tables that take into account the large variations of the iron abundance about the cosmic value that are predicted by equilibrium radiative levitation theory. For representative models with M = 0.48 M☉ and log g = 5.8, we find strong instabilities for low-order radial and nonradial (p and f) pulsation modes in the range 36,500 K Teff 29,000 K. The four pulsating sdB stars currently known all have effective temperatures in that range. In addition, one of our models with Teff = 34,000 K has a band of unstable modes with periods in the range 116-195 s, in excellent agreement with those of the known pulsators. We therefore claim that our proposed iron bump mechanism provides a natural explanation for the instabilities found in the newly discovered class of pulsating sdB stars.

The reexamination of astrophysical opacities has eliminated gross discrepancies between a variety of observations and theoretical calculations; thus allowing for more detailed tests of stellar models. A number of such studies indicate that model results are sensitive to modest changes in the opacity. Consequently, it is desirable to update available opacity databases with recent improvements in physics, refinements of element abundance, and other such factors affecting the results. Updated OPAL Rosseland mean opacities are presented. The new results have incorporated improvements in the physics and numerical procedures as well as corrections. The main opacity changes are increases of as much as 20{percent} for Population I stars due to the explicit inclusion of 19 metals (compared to 12 metals in the earlier calculations) with the other modifications introducing opacity changes smaller than 10{percent}. In addition, the temperature and density range covered by the updated opacity tables has been extended. As before, the tables allow accurate interpolation in density and temperature as well as hydrogen, helium, carbon, oxygen, and metal mass fractions. Although a specific metal composition is emphasized, opacity tables for different metal distributions can be made readily available. The updated opacities are compared to other work. {copyright} {ital 1996 Themore » American Astronomical Society.}« less

OPAL opacities have recently helped to resolve a number of long-standing discrepancies between theory and observation. This success has made it important to provide the associated equation-of-state (EOS) data. The OPAL EOS is based on an activity expansion of the grand canonical partition function of the plasma in terms of its fundamental constituents (electrons and nuclei). The formation of composite particles and many-body effects on the internal bound states occur naturally in this approach. Hence, pressure ionization is a consequence of the theory. In contrast, commonly used approaches, all of which are based on minimization of free energy, are forced to assert the effect of the plasma on composite particles and must rely on an ad hoc treatment of pressure ionization. Another advantage of the OPAL approach is that it provides a systematic expansion in the Coulomb coupling parameter that includes subtle quantum effects generally not considered in other EOS calculations. Tables have been generated that provide pressure, internal energy, entropy, and a variety of derivative quantities. These tables cover a fairly broad range of conditions and compositions applicable to general stellar-evolution calculations for stars more massive than {approximately}0.8 {ital M}{sub {circle_dot}}. An interpolation code is provided along with themore » tables to facilitate their use. {copyright} {ital 1996 The American Astronomical Society.}« less

Recent OPAL calculations have obtained significant differences in the Rosseland mean opacities compared with earlier Los Alamos work. These new opacities have had a favorable impact on several astrophysical problems, but the efforts have concentrated on hydrogen main-sequence stars or stellar envelopes. The present calculations consider carbon- and oxygen-rich mixtures. It is shown that for such mixtures the Coulomb corrections beyond the weak-coupling approximation are not negligible in the ionization-balance calculations when Rosseland mean opacities are computed. As for hydrogen-rich compositions, the hydrogen-depleted mixtures can show factors of 2-3 enhancements in the opacity compared with the Los Alamos results at temperatures of a few hundred thousand degrees

We have undertaken a long-term effort to provide improved Rosseland mean opacity tables. Our earlier work has shown that detailed atomic physics data is crucial to the accurate calculation of opacities. In particular, we showed that the inclusion of LS coupling in the configuration term structure can increase the opacity by factors of 3-4 over the Los Alamos results. Recently, we showed that the additional lines and the shifting of oscillator strength introduced by intermediate coupling can further increase the opacity by as much as 50%. In the present paper we present a method to expand our existing tables to include arbitrary values of hydrogen mass fraction

Recently published opacity tables for astrophysical mixtures using the OPAL code showed significant differences when compared to the commonly used Los Alamos results. An important finding of the OPAL calculations was a large opacity enhancement (approximately factors of 3) in the few hundred-thousand degree temperature range. This new opacity bump is a consequence of improvements in the atomic data generation

It is proposed that the sudden appearance of a tremendous number of same-shell transition iron lines, as the temperature rises above 100,000 K, gives a high sensitivity of the opacity to temperature at the very low densities found in OB giants. This produces kappa effect pulsations. The reason not all B stars pulsate could be that a slight primordial deficit in the iron abundance in the surface layer reduces the opacity and its sensitivity to temperature and reduces the kappa effect driving. A slight amount of iron concentration by radiative levitation could cause a star to pulsate even if it did not originally have enough primordial iron to cause this mechanism to operate. Then any slow slight mixing caused by the unstable shearing nonradial pulsations could restabilize the pulsations as actually observed in Alpha Vir and Beta CMa. Rapid levitation and mixing for the very luminous B stars with their very low density envelopes could even explain luminous blue variables that pulsate only a few cycles before they stabilize again. Large amplitude pulsations like those seen in BW Vul would indicate a somewhat large primordial iron abundance compared to all other B stars. Multimode behavior is theoretically expected for thismore » pulsation mechanism, and for some B stars only a few nonradial modes (possibly selected by rotation) may survive to observable amplitudes. 39 refs.« less

An attractive explanation of discrepancies between observations and theories of Cepheid variables has been the hypothesis of enhanced opacities. New opacity tables for Population I and Population II stars computed using the OPAL code are presented.

Opacities for the solar radiative interior are computed and compared to previous calculations. A significant enhancement of the Rosseland mean opacity near the bottom of the convection zone is reported when compared to the Los Alamos Astrophysical Opacity Library. The discrepancy is attributed mainly to the equation of state. Absorption processes are investigated and their uncertainties estimated. The new results using the OPAL opacity code are given in tabular form for the Ross-Aller, Aller, Grevesse and Anders-Grevesse solar mixtures.

Les opacites moyennes de Rosseland d'un modele de Cepheides classiques sont determinees avec le melange King IVa (Cox A. N. et Tabor T. E., 1976, Astrophys. J. Suppl., 19) et comparees aux resultats de Andreasen G. K. (1988, Astron. Astrophys., 201).

Resultats d'un nouveau code d'opacite montrant que l'opacite moyenne de Rosseland pour des metaux (nombre atomique>2) est plus grande que l'opacite standard pour des densites et temperatures importantes dans les modeles de Cepheides