Hydrodynamical stellar models including rotation, internal gravity waves and atomic diffusion. I. Formalism and tests on Pop I dwarfs

In this paper, we develop a formalism in order to incorporate the contribution of internal gravity waves to the transport of angular momentum and chemicals over long time-scales in stars. We show that the development of a double peaked shear layer acts as a filter for waves, and how the asymmetry of this filter produces momentum extraction from the core when it is rotating faster than the surface. Using only this filtered flux, it is possible to follow the contribution of internal waves over long (evolutionary) time-scales. We then present the evolution of the internal rotation profile using this formalism for stars which are spun down via magnetic torquing. We show that waves tend to slow down the core, creating a "slow" front that may then propagate from the core to the surface. Further spin down of the surface leads to the formation of a new front. Finally we show how this momentum transport reduces rotational mixing in a 1.2Msun, Z=0.02 model, leading to a surface lithium abundance in agreement with observations in the Hyades.Comment: 14 pages, accepted for publication in A&

From Canonical to Enhanced Extra Mixing in Low-Mass Red Giants: Tidally Locked Binaries

Stellar models which incorporate simple diffusion or shear induced mixing are used to describe canonical extra mixing in low mass red giants of low and solar metallicity. These models are able to simultaneously explain the observed Li and CN abundance changes along upper red giant branch (RGB) in field low-metallicity stars and match photometry, rotation and carbon isotopic ratios for stars in the old open cluster M67. The shear mixing model requires that main sequence (MS) progenitors of upper RGB stars possessed rapidly rotating radiative cores and that specific angular momentum was conserved in each of their mass shells during their evolution. We surmise that solar-type stars will not experience canonical extra mixing on the RGB because their more efficient MS spin-down resulted in solid-body rotation, as revealed by helioseismological data for the Sun. Thus, RGB stars in the old, high metallicity cluster NGC 6791 should show no evidence for mixing in their carbon isotopic ratios. We develop the idea that canonical extra mixing in a giant component of a binary system may be switched to its enhanced mode with much faster and somewhat deeper mixing as a result of the giant's tidal spin-up. This scenario can explain photometric and composition peculiarities of RS CVn binaries. The tidally enforced enhanced extra mixing might contribute to the star-to-star abundance variations of O, Na and Al in globular clusters. This idea may be tested with observations of carbon isotopic ratios and CN abundances in RS CVn binaries.Comment: 47 pages, 19 figures, accepted for publication in Ap

Bohr-Sommerfeld conditions for several commuting Hamiltonians

The goal of this paper is to find the quantization conditions of Bohr-Sommerfeld of k quantum Hamiltonians acting on the euclidian space of dimension n, depending on a small parameter h, and which commute to each other. That is we determine, around a regular energy level E of the euclidian space of dimension k the principal term of the asymptotics in h of the eigenvalues of the operators that are associated to a common eigenfunction. Thus we localize the so-called joint spectrum of the operators. Under the assumption that the classical Hamiltonian flow of the joint principal symbol is periodic with constant periods on the energy level of E(a submanifold of codimension k) we prove that the part of the joint spectrum lying in a small neighbourhood of E is localized near a lattice of size h determined in terms of actions and Maslov indices. The multiplicity of the spectrum is also determined.Comment: 18 pages, LaTe