The following is an edited excerpt of the DVD recording of Session C's Round Table Discussion. Due to the tight publication schedule, participants have not been given much time to review its contents in detail. There may be unclear and inaccurate spots, but it should give an illustrative description of the dynamics of the interesting discussions.

Differential rotation, similar to that seen on our gas giants, is manifested at the surface of three-dimensional (3D) computer simulations of thermal convection in density-stratified rotating planets without solid cores. Below the surface, the flow forms short axially-aligned vortices, generated by fluid expanding as it rises and contracting as it sinks. The convergence of the nonlinear Reynolds stresses resulting from the vorticity generated by fluid flowing through the density stratification maintains the surface banded zonal flow without the classical vortex stretching of Taylor columns. These preliminary simulations demonstrate that large non-convecting cores are not required to obtain multiple zonal jets at the surface, and show greater convective heat flux towards the poles relative to that seen at the equator. This result could help explain the nearly uniform with latitude thermal emission observed at the surface of Jupiter.

Brown dwarf atmospheres are largely convective. These convective gas flows collide and feed back a whole spectrum of turbulent fluctuations into the atmospheric fluid field. Resulting non-static density and temperature fields influence the local chemistry concerning gas phase and dust formation. Numerical simulations are used to show the large and inhomogeneous changes of the gas phase chemistry in a turbulent dust forming cloud region of a brown dwarf atmosphere. The relaxation time scale of the gas phase composition towards steady state is considerably longer than for the dust component.

Convection is the main energy transport mechanism in brown dwarf atmospheres. The overshoot of ascending bubbles affects the upper and cooler region where dust formation can occur. In order to understand the observed presence of dust, the formation of grains and their gravitational settling must be balanced by up-mixing of condensible elements via convective overshoot. Otherwise, brown dwarf atmospheres would be completely dust-free (Woitke & Helling 2004).

We present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

We summarize the results of stellar evolution theory obtained over the past three decades and highlight the points of disagreement with the present-day observational information. Arguments are given to favour stellar models in which the classical treatment of convection and mixing is abandoned and more complex schemes are adopted.

Careful choice of of method, problem, and zoning has allowed us to do three-dimensional (3D) simulations of thermally relaxed, nearly adiabatic convection (with nuclear burning). The simulations are run long enough so that a robust statistical state is found. We find that 2D simulations are biased relative to 3D simulations: 2D shows larger velocities and less mixing than their 3D counterparts. Detailed theoretical analysis of these numerical experiments allows us to begin to build a simple theoretical model of turbulent convection in stars, which may be used in 1D calculations of stellar evolution. Implications for stellar evolution, will be discussed. Oxygen shell burning simulations in 3D, and multishell burning of C, Ne, O, and Si in 2D will be presented, as will aspherical distortion in supernovae progenitors (Meakin and Arnett, 2006a). Contact will be made with convective driving of waves, convective zone growth by entrainment, the velocity scale and the geometric parameters in mixing length theory, and the solar Ne abundance problem. Explicit comparisons of compressible and anelastic methods at modest Mach numbers (M ≈ 0.01 to 0.1), as well as solutions of the nonradial wave equations, are presented here. Additional detail is presented in the poster by Meakin.

The modeling of the Asymptotic Giant Branch phase is made highly uncertain by some still unsolved issues related to the input macro-physics used to calculate the stellar evolution, namely mass loss, nuclear cross sections, overshooting and convective modeling. We show that in the massive intermediate mass models, which achieve at the bottom of their convective envelope temperatures sufficiently high to favour an advanced nucleosynthesis, the treatment of convection plays a major role in determining the physical and chemical evolution of the stellar models during this evolutionary phase.

It follows from the local mixing length theory that the convection in the atmospheres of yellow and red giants and super-giants become supersonic. In this work we studied the physical reality of such phenomenon and its possible consequences on the structure and evolution of stars involving such situations. The main conclusion is that the supersonic nature of convection as predicted by the local mixing length theory has been overestimated. If supersonic convection is not an artifact in all situations, it is the case at least for all yellow giants and super-giants. We believe that such an artifact is due to the imperfect of the mixing length theory. Owing to the fact that convective energy transport in the atmospheres of yellow giants and super-giants is quite negligible, these artifacts have very limited consequences on the structure and evolution of these stars. However, it is not the case for red giants and super-giants whose properties can be seriously affected by this overestimation. Our investigation shows that the theoretical red phases of stars under consideration are somewhat too blue as predicted with the usual mixing length theory. To this aim, full hydrodynamic simulation is needed in order to clear the doubts on the existence of supersonic convection in these red objects.

A remarkable and intriguing fact is that few DB white dwarfs, i.e., objects with a helium-rich atmosphere, are found in the effective temperature range between 45000-30000 K, and this exclusion zone is known as the DB gap. Since the temperatures of the blue and the red edges of the DB gap coincide with the effective temperatures where HeII/III and HeI/II convection zones show up respectively, convective mixing is suspected to be the cause of the appearance of DBs outside the DB gap. Chemical separation due to gravitational settling in the convectively stable atmosphere is then suspected to be the cause of the presence of the DB gap. The white dwarfs which turn back to DBs after the DB gap phase are expected to have a semiconvective layer, which is superadiabatic but convectively stable, when they are located near the red edge of the DB gap. Such white dwarfs are expected to be pulsationally unstable. Discovery of pulsation in them will open up a new class of pulsating white dwarfs to asteroseismic study.

We show that in a sample of Extremely Metal-Poor (EMP) giants (<[Fe/H]>=−3.1) all the stars with a luminosity higher than logL/L⊙ ≈ 2.6 present the characteristics of a mixing of the surface with the H-burning layer: low abundance of carbon and high abundance of nitrogen. In these “mixed stars” the lithium abundance and the ratio 12C/13C are very low. Some of these stars are also Na or/and Al rich.

Low-mass stars, ∼ 1–2 solar masses, near the Main Sequence are efficient at producing 3He, which they mix into the convective envelope on the giant branch and distribute into the Galaxy by way of envelope loss. This process is so efficient that it is difficult to reconcile the observed cosmic abundance of 3He with the predictions of Big Bang nucleosynthesis. In this paper we find, by modeling a red giant with a fully three-dimensional hydrodynamic code and a full nucleosynthetic network, that mixing arises in the supposedly stable and radiative zone between the hydrogen-burning shell and the base of the convective envelope. This mixing is due to Rayleigh-Taylor instability within a zone just above the hydrogen-burning shell. In this zone the burning of the 3He left behind by the retreating convective envelope is predominantly by the reaction 3He + 3He → 4He + 1H + 1H, a reaction which, untypically for stellar nuclear reactions, lowers the mean molecular weight, leading to a local minimum. This local minimum leads to Rayleigh-Taylor instability, and turbulent motion is generated which will continue ultimately up into the normal convective envelope. Consequently material from the envelope is dragged down sufficiently close to the burning shell that the He in it is progressively destroyed. Thus we are able to remove the threat that He production in low-mass stars poses to the Big Bang nucleosynthesis of 3He.

Some slow mixing mechanism has long been suspected, that connects the convective envelope of a red giant to the burning shell. It appears to be necessary to account for progressive changes in the C/C and N/C ratios on the First Giant Branch. We suggest that these phenomena are also due to the Rayleigh-Taylor-unstable character of the He-burning region.

Summary of the round table discussion following Session IV on “Stellar evolution, nucleosynthesis, and convective mixing”.

We simulate the reactive-hydrodynamic flow for a variety of convective shell burning epochs in supernova progenitor models. The neutrino-cooled stages of carbon, neon, oxygen, and silicon burning are simulated in two and three dimensions. Even in the absence of rotation significant symmetry breaking occurs (10% in rms variation in thermodynamic variables such as temperature and density). These distortions are caused by turbulent convection interacting with stably stratified boundaries. Strong interactions of multiple active shells is seen; it is mediated by waves generated by convection. Some implications for supernova progenitors are presented.

The carbon isotopic ratio, 12C/13C, is a tracer of the mixing events during the evolution along the giant branch, due to the conversion of 12C into 13C (and 14N) via the CN cycle. A decrease of this ratio from 90, the solar value, to 20–25, is expected due to the first dredge-up. However, ratios down to 3–4, the CN cycle equilibrium value, have been observed in giants of the field, of globular and of open clusters. Observations seem to indicate a non-standard mixing in the RGB, probably beginning in the luminosity bump, when the outward moving hydrogen burning shell crosses the molecular weight barrier left by the convective layer in its maximum extent. We are currently analyzing a sample of 24 giants in 8 open clusters for which we determined 12C/13C from high resolution, high signal to noise spectra using spectrum synthesis. In this work we discuss the general characteristics of our results in comparison to previous analyses of giants in open clusters available in the literature.

A large population of helium-core-burning clump stars of the Galactic field, revealed by the Hipparcos orbiting observatory, is an excellent target for the analysis of mixing processes in evolved low-mass metal-abundant stars. In this contribution we overview first result of 12C, 13C, N and O abundance determinations in our extensive project which we started with the aim at deriving the fundamental parameters and abundances of more than 20 chemical elements in a large sample of Galactic clump stars.

CNO and Li abundances and 12C/13C isotopic ratios have been derived for two metal-poor Ba giants, HD 104340 and HD 206983, and two CH subgiants, HD 50264 and HD 87080. High resolution spectra obtained with the 1.52 m telescope and the FEROS echelle spectrograph at ESO, La Silla, Chile, were used in this study. CNO and Li abundances so as 12C/13C isotopic ratios were determined by applying the synthetic spectrum method to the lines of C2, CH, CN, [O I’ and Li I. Our analysis showed that the giant stars studied here have quite different natures: HD 206983 is a metal-poor barium star while HD 104340, although showing enhancement of s-process elements, should not be considered as a classical barium star: its barium syndrome can be explained by internal nucleosynthesis. The low metallicity giant HD 104340 can experience deeper convective mixing and, consequently, a larger dredge-up of CNO-cycle products compared to normal red giants. Light element abundance pattern of HD 104340 resembles anomalies resulting from the appearance on the stellar surface of material enriched in triple-α and CNO cycling.

16O/17O and 12C/13C ratios in 23 M giants are determined from high resolution IR spectra. The results are confronted with the current models on the convective mixing.

The observational data of the Orion Nebula Cluster (ONC) is reanalyzed by means of new sets of pre-main sequence (PMS) evolutionary tracks including rotation, non-gray boundary conditions (BC's) and either low (LCE) or high convection efficiency (HCE), aiming better understanding of the appropriate physical constraints for the rotational evolution of the stars within the ONC. The role played by convection is a key aspect of our analysis, since there are conflicting results from theory and observations. We derived stellar masses and ages for the ONC by using both LCE and HCE and considered was the role of non-gray atmospheres. Our results show that the resulting mass distribution for the bulk of the ONC population is in the range 0.2-0.4M⊙ for our non-gray models, and in the range 0.1-0.3M⊙ for gray models. In agreement with previous works, we found that a large percentage (∼70%) of low-mass stars (M≤Mtr, where Mtr is a transition mass) in the ONC appears to be fast rotators (P<4days). Mtr depends on the model choosen, being Mtr=0.5 for LCE, Mtr=0.35 for HCE and, as found in previous works, Mtr=0.25 for gray models. Finally, our analysis indicates that a second parameter is needed for a proper description of convection in the PMS phase.

The non-local, time-dependent convection theory of Kuhfuß (1986) in both its one- and three-equation form has been implemented in the Garching stellar evolution code. We present details of the implementation and the difficulties encountered. Specific test cases have been calculated, among them a 5 M⊙ star and the Sun. These cases point out deficits of the theory. In particular, the assumption of an isotropic velocity field leads to too extensive overshooting and has to be modified at convective boundaries. Some encouraging aspects are indicated as well.