Georges Michaud

The Evolution of AmFm Stars, Abundance Anomalies, and Turbulent Transport

Stellar evolution models of stars of 1.45-3.0 M☉ have been calculated, including the atomic diffusion of metals and radiative accelerations for all species in the OPAL opacities. As the abundances change, the opacities and radiative accelerations are continuously recalculated during evolution. These models develop iron-peak convection zones centered at a temperature of approximately 200,000 K. If one then assumes that there is sufficient overshoot to homogenize the surface regions between the hydrogen, helium, and iron-peak convection zones, it is shown here that the surface abundance variations that are produced, without any arbitrary parameter, closely resemble the abundance anomalies of AmFm stars, except that they are larger by a factor of about 3. Detailed evolutionary model calculations have been carried out, varying the turbulence in the outer stellar regions in order to improve the agreement with the observed anomalies in AmFm stars. The outer mass mixed by turbulence has been varied, as well as the density dependence of the turbulent diffusion coefficient. It is shown that the anomalies depend on only one parameter characterizing turbulence, namely, the depth of the zone mixed by turbulence. The calculated surface abundances are compared to observations of a number of recently observed AmFm stars. For Sirius A, 16 abundances (including four upper limits) are available for comparison. Of these, 12 are well reproduced by the model, while three are not so well reproduced, and one is a very uncertain observation. In cluster AmFm stars, the age and initial abundances are known. There is then less arbitrariness in the calculations, but fewer chemical species have been observed than in Sirius. The available observations (Hyades, Pleiades, and Praesepe stars are compared) agree reasonably well with the calculated models for the five stars that are compared. The zone mixed by turbulence is deeper than the iron convection zone, reducing the abundance anomalies to values that are too small for iron-peak convection zones to develop in many of the models. The origin of the mixing process then remains uncertain. There is considerable scatter in the observations between different observers, so it is premature to conclude that hydrodynamical processes other than turbulence are needed to explain the observations. We do not rule out the possibility that this might be the case, but the observations do not appear to us to be good enough to establish it.

Implications of WMAP observations on Li abundance and stellar evolution models

The Wilkinson Microwave Anisotropy Probe (WMAP) determination of the baryon-to-photon ratio implies, through big bang nucleosynthesis, a cosmological Li abundance larger, by a factor of 2-3, than the Li abundance plateau observed in the oldest Population II stars. It is, however, inescapable that there be a reduction by a factor of at least 1.6-2.0 of the surface Li abundance during the evolution of Population II field stars with [Fe/H] ≤ -1.5. That the observed Li should be lower than cosmologically produced Li is expected from stellar evolution models. Since at turnoff most of the Li abundance reduction is caused by gravitational settling, the presence of 6Li in some turnoff stars is also understood. Given that the WMAP implications for Li cosmological abundance and the Li Spite plateau can be naturally explained by gravitational settling in the presence of weak turbulence, there appears little need for exotic physics as suggested by some authors. Instead, there is a need for a better understanding of turbulent transport in the radiative zones of stars. This requires simulations from first principles. Rather strict upper limits to turbulent transport are determined for the Sun and Population II stars.

Consistent Solar Evolution Model Including Diffusion and Radiative Acceleration Effects

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.

Models of Metal-poor Stars with Gravitational Settling and Radiative Accelerations. I. Evolution and Abundance Anomalies

Evolutionary models have been calculated for Population II stars of 0.5-1.0 M? from the pre-main sequence to the lower part of the giant branch. Rosseland opacities and radiative accelerations were calculated taking into account the concentration variations of 28 chemical species, including all species contributing to Rosseland opacities in the OPAL tables. The effects of radiative accelerations, thermal diffusion, and gravitational settling are included. While models were calculated for both Z = 0.00017 and 0.0017, we concentrate on models with Z = 0.00017 in this paper. These are the first Population II models calculated taking radiative acceleration into account. It is shown that, at least in a 0.8 M? star, it is a better approximation not to let Fe diffuse than to calculate its gravitational settling without including the effects of grad(Fe). In the absence of any turbulence outside of convection zones, the effects of atomic diffusion are large mainly for stars more massive than 0.7 M?. Overabundances are expected in some stars with Teff ? 6000 K. Most chemical species heavier than CNO are affected. At 12 Gyr, overabundance factors may reach 10 in some cases (e.g., for Al or Ni), while others are limited to 3 (e.g., for Fe). The calculated surface abundances are compared to recent observations of abundances in globular clusters as well as to observations of Li in halo stars. It is shown that, as in the case of Population I stars, additional turbulence appears to be present. Series of models with different assumptions about the strength of turbulence were then calculated. One series minimizes the spread on the Li plateau, while another was chosen with turbulence similar to that present in AmFm stars of Population I. Even when turbulence is adjusted to minimize the reduction of Li abundance, there remains a reduction by a factor of at least 1.6 from the original Li abundance. Independent of the degree of turbulence in the outer regions, gravitational settling of He in the central region reduces the lifetime of Population II stars by 4%-7% depending on the criterion used. The effect on the age of the oldest clusters is discussed in a forthcoming paper (Paper II). Just as in Population I stars where only a fraction of stars, such as AmFm stars, have abundance anomalies, one should look for the possibility of abundance anomalies of metals in some Population II turnoff stars but not necessarily in all. Expected abundance anomalies are calculated for 28 species and compared to observations of M92 as well as to Li observations in halo field stars.

Diffusion in main-sequence stars: Radiation forces, time scales, anomalies

The abundance anomalies generated by diffusion in the envelope of main-sequence stars are studied. It is shown that in low-mass stars (Mapproximately-less-than1.2M/sub sun/) diffusion leads to underabundances while in more massive stars (Mapproximately-greater-than1.3M/sub sun/) diffusion leads to overabundances of at least some elements. In general the overabundance and underabundance factors generated (up to 10/sup 7/) are larger than the observed anomalies in stars of the main sequence (rarely up to 10/sup 6/). It is established that diffusion can lead to the largest anomalies observed. For particular elements (Sr, Eu,...), it is shown where more accurate calculations are needed. Approximate formulae are developed for radiative accelerations. They allow the reader to carry out calculations for cases of special interest to him and also to evaluate the uncertainty of the calculations. (AIP)

Consistent Evolution of F Stars: Diffusion, Radiative Accelerations, and Abundance Anomalies

Consistent stellar evolution models of F stars (1.1-1.5 M☉) are calculated with radiative forces, opacities, and diffusion for all elements included in OPALs opacity tables. The opacities and radiative forces are continuously recomputed during evolution from OPALs monochromatic data (~1.5 Gbyte) in order to include all effects of abundance changes due to diffusion and nuclear evolution. TOPbase is also used for radiative accelerations. Iron surface overabundances occur in stars more massive than 1.3 M☉. Local overabundances of iron peak elements increase the Rosseland opacity in a region at the base of the convection zone by a factor of 3-6; this increases the mass of the convective zone by up to a factor of 5. It is important to follow Cr, Mn, and Ni independently of Fe, since they peak at different temperatures within the star. The predicted abundance anomalies are much larger than observed in most F-type stars of open clusters. This suggests that atomic diffusion is not the only process responsible for the Li gap in open clusters. The predicted iron peak element overabundances indicate trends that are compatible with those observed in Fm stars. They however tend to be larger than the observed overabundances, leaving room for some perturbing hydrodynamical process. The present models, devoid of free parameters, are a necessary step in constraining the additional hydrodynamical processes required to better reproduce observed surface abundances. Since the abundances of 28 elements are calculated, one may have 27 constraints on stellar hydrodynamics, once the relative abundances of all species have been determined observationally.

Iron Convection Zones in B, A, and F Stars

Stellar models, including all effects of atomic diffusion and radiative accelerations, are evolved from the pre-main sequence to the giant branch for stars of 1.3 to 4.0 M☉, with metallicity ranging from Z0 = 0.01 to 0.03. It is shown that radiative accelerations lead to the accumulation of iron-peak elements around 200,000 K; this increases the opacity and causes the appearance of Fe convection zones when macroscopic motions are not rapid enough to wipe out the effects of particle transport. The behavior of Fe convection zones and conditions for their appearance are studied in detail. Iron-peak convection zones appear naturally in all solar metallicity models more massive than 1.5 M☉. In the 1.5 M☉ model, it is present only for a fraction of the main-sequence lifetime, but in models without turbulence of 1.7 M☉ and more, the Fe convection zone rapidly develops after arrival on the main-sequence and remains until its end. For a metallicity of Z = 0.01, an Fe convection zone appears even in a 1.3 M☉ model. Moreover, the interaction between the diffusion velocities of different species leads to an accumulation of heavy elements around the convective core, causing semiconvection. A detached semiconvection zone develops in the 1.5 M☉ model. Finally, the surface abundances are calculated using a number of turbulence models and compared to observations of τ UMa in order to show how abundance anomalies may be used to test various turbulence models; the gravity at which abundance anomalies should be expected to disappear is determined. It is shown that in Am stars, the Ca underabundance should disappear during evolution at the same gravity as iron-peak overabundances.

Models for Solar Abundance Stars with Gravitational Settling and Radiative Accelerations: Application to M67 and NGC 188

Evolutionary models taking into account radiative accelerations, thermal diffusion, and gravitational settling for 28 elements, including all those contributing to OPAL stellar opacities, have been calculated for solar metallicity stars of 0.5-1.4 M☉. The Sun has been used to calibrate the models. Isochrones are fitted to the observed color-magnitude diagrams (CMDs) of M67 and NGC 188, and ages of 3.7 and 6.4 Gyr are respectively determined. Convective core overshooting is not required to match the turnoff morphology of either cluster, including the luminosity of the gap in M67, because central convective cores are larger when diffusive processes are treated. This is due mainly to the enhanced helium and metal abundances in the central regions of such models. The observation of solar metallicity open clusters with ages in the range of 4.8-5.7 Gyr would further test the calculations of atomic diffusion in central stellar regions: according to nondiffusive isochrones, clusters should not have gaps near their main-sequence turnoffs if they are older than ≈4.8 Gyr, whereas diffusive isochrones predict that gaps should persist up to ages of ≈5.7 Gyr. Surface abundance isochrones are also calculated. In the case of M67 and NGC 188, surface abundance variations are expected to be small. Abundance differences between stars of very similar Teff are expected close to the turnoff, especially for elements between P and Ca. Moreover, in comparison to the results obtained for giants, small generalized underabundances are expected in main-sequence stars. The Li/Be ratio is discussed briefly and compared with observations. The inclusion of a turbulent transport parameterization that reduces surface abundance variations does not significantly modify the computed isochrones.

Radiative Accelerations for Evolutionary Model Calculations

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.

Gravitational settling in solar models

Calculations of the effects of gravitational settling and atomic diffusion in solar models are presented, with the goal of constraining the actual amount of gravitational settling that has occurred in the Sun. Most of the discrepancies between the results of previous workers are explained. The observed solar Li abundance is used to contrain the amount of turbulent mixing below the solar convection zone and thereby set a lower limit to the amount of gravitational settling in the Sun.