Uncertainties in AGB Evolution and Nucleosynthesis

We summarise the evolution and nucleosynthesis in AGB and Super-AGB stars. We then examine the major sources of uncertainty, especially mass-loss.Comment: 8 pages, no figures. Invited review presented at The 11th Pacific Rim Conference on Stellar Astrophysics "Physics and Chemistry of the Late Stages of Stellar Evolution

Relative entropy methods for hyperbolic and diffusive limits

We review the relative entropy method in the context of hyperbolic and diffusive relaxation limits of entropy solutions for various hyperbolic models. The main example consists of the convergence from multidimensional compressible Euler equations with friction to the porous medium equation \cite{LT12}. With small modifications, the arguments used in that case can be adapted to the study of the diffusive limit from the Euler-Poisson system with friction to the Keller-Segel system \cite{LT13}. In addition, the $p$--system with friction and the system of viscoelasticity with memory are then reviewed, again in the case of diffusive limits \cite{LT12}. Finally, the method of relative entropy is described for the multidimensional stress relaxation model converging to elastodynamics \cite[Section 3.2]{LT06}, one of the first examples of application of the method to hyperbolic relaxation limits

Structure, Evolution and Nucleosynthesis of Primordial Stars

(abridge version) The evolution of population III stars (Z=0) is followed from the pre-main sequence phase up to the AGB phase for intermediate-mass stars and up to C ignition in more massive stars...We find that, thanks to the development of mixing episodes (carbon injections) at the beginning of the AGB phase, the carbon abundance of the 1, 1.5, 2, 3, 4 and 5Mo models is significantly increased in the envelope. This process then allows low- and intermediate-mass stars to achieve a ``standard'' thermally pulsing AGB phase... In the 7Mo model, the CNO envelope abundance following the second dredge-up is so large that the star does not experience the carbon injection episode and follows a more standard thermally pulsing AGB evolution. Our computations also indicate that, thanks to a small overshooting at the base of the convective envelope, the third dredge-up is already operating in stars with M >~1.5 Mo after a few pulses, and that by the end of our modeling, hot bottom burning is activated in stars more massive than ~ 2Mo. This evolutionary behavior suggests that primordial low- and intermediate stars could have been significant contributors to the production of primary 12C, 14N, and may have contributed to some extent to the production of Mg and Al and possibly s-elements (despite the lack of iron seeds) in the early universe.Comment: 26 pages, 13 figures, 6 tables, uses aastex. Accepted for publication in ApJ. Full postscript version available at http://www-astro.ulb.ac.be/~sies

Nucleosynthesis of Elements in Low to Intermediate Mass Stars through the AGB Phase

We present a review of the main phases of stellar evolution with particular emphasis on the nucleosynthesis and mixing mechanisms in low- and intermediate-mass stars. In addition to explicit studies of the effects of the first, second and third dredge-up, we also discuss cool bottom processing and hot bottom burning.Comment: 30 pages, latex, 18 figures, uses style files aipproc.cls aipproc.sty epsf.sty ; to be published in (refereed) conference proceedings "Astrophysical Implications of the Laboratory Study of Presolar Materials", ed. T. Bernatowitz and E. Zinner (AIP: Sunnyside, NY), in press; also available at http://www.maths.monash.edu.au/~boothroy

Shock waves for radiative hyperbolic--elliptic systems

The present paper deals with the following hyperbolic--elliptic coupled system, modelling dynamics of a gas in presence of radiation, $u_{t}+ f(u)_{x} +Lq_{x}=0, -q_{xx} + Rq +G\cdot u_{x}=0,$ where $u\in\R^{n}$, $q\in\R$ and $R>0$, $G$, $L\in\R^{n}$. The flux function $f : \R^n\to\R^n$ is smooth and such that $\nabla f$ has $n$ distinct real eigenvalues for any $u$. The problem of existence of admissible radiative shock wave is considered, i.e. existence of a solution of the form $(u,q)(x,t):=(U,Q)(x-st)$, such that $(U,Q)(\pm\infty)=(u_\pm,0)$, and $u_\pm\in\R^n$, $s\in\R$ define a shock wave for the reduced hyperbolic system, obtained by formally putting L=0. It is proved that, if $u_-$ is such that $\nabla\lambda_{k}(u_-)\cdot r_{k}(u_-)\neq 0$,(where $\lambda_k$ denotes the $k$-th eigenvalue of $\nabla f$ and $r_k$ a corresponding right eigenvector) and $(\ell_{k}(u_{-})\cdot L) (G\cdot r_{k}(u_{-})) >0$, then there exists a neighborhood $\mathcal U$ of $u_-$ such that for any $u_+\in{\mathcal U}$, $s\in\R$ such that the triple $(u_{-},u_{+};s)$ defines a shock wave for the reduced hyperbolic system, there exists a (unique up to shift) admissible radiative shock wave for the complete hyperbolic--elliptic system. Additionally, we are able to prove that the profile $(U,Q)$ gains smoothness when the size of the shock $|u_+-u_-|$ is small enough, as previously proved for the Burgers' flux case. Finally, the general case of nonconvex fluxes is also treated, showing similar results of existence and regularity for the profiles.Comment: 32 page