Transport and mixing in the radiation zones of rotating stars: I-Hydrodynamical processes

The purpose of this paper is to improve the modelization of the rotational mixing which occurs in stellar radiation zones, through the combined action of the thermally driven meridional circulation and of the turbulence generated by the shear of differential rotation. The turbulence is assumed to be anisotropic, due to the stratification, with stronger transport in the horizontal directions than in the vertical. The main difference with the former treatments by Zahn (1992) and Maeder & Zahn (1998) is that we expand here the departures from spherical symmetry to higher order, and include explicitly the differential rotation in latitude, to first order. This allows us to treat simultaneously the bulk of a radiation zone and its tachocline(s). Moreover, we take fully into account the non-stationarity of the problem, which will enable us to tackle the rapid phases of evolution. The system of partial differential equations, which govern the transport of angular momentum, heat and chemical elements, is written in a form which makes it ready to implement in a stellar evolution code. Here the effect of a magnetic field is deliberately ignored; it will be included in forthcoming papers.Comment: 16 pages, no figures, accepted for publication in A&

Remarks on twisted noncommutative quantum field theory

We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.Comment: 13 pages, v2: minor correction

Influence of the Tachocline on Solar Evolution

Recently helioseismic observations have revealed the presence of a shear layer at the base of the convective zone related to the transition from differential rotation in the convection zone to almost uniform rotation in the radiative interior, the tachocline. At present, this layer extends only over a few percent of the solar radius and no definitive explanations have been given for this thiness. Following Spiegel and Zahn (1992, Astron. Astrophys.), who invoke anisotropic turbulence to stop the spread of the tachocline deeper in the radiative zone as the Sun evolves, we give some justifications for their hypothesis by taking into account recent results on rotating shear instability (Richard and Zahn 1999, Astron. Astrophys.). We study the impact of the macroscopic motions present in this layer on the Sun's structure and evolution by introducing a macroscopic diffusivity $D_T$ in updated solar models. We find that a time dependent treatment of the tachocline significantly improves the agreement between computed and observed surface chemical species, such as the $^7$Li and modify the internal structure of the Sun (Brun, Turck-Chi\`eze and Zahn, 1999, in Astrophys. J.).Comment: to appear in Annals of the New York Academy of Sciences, vol 898. Postscript file, 9 pages and 5 figures New Email Address for A. S. Brun: [email protected]

Noncommutative Electrodynamics with covariant coordinates

We study Noncommutative Electrodynamics using the concept of covariant coordinates. We propose a scheme for interpreting the formalism and construct two basic examples, a constant field and a plane wave. Superposing these two, we find a modification of the dispersion relation. Our results differ from those obtained via the Seiberg-Witten map.Comment: 5 pages, published versio

Standard Solar models in the Light of New Helioseismic Constraints II. Mixing Below the Convective Zone

In previous work, we have shown that recent updated standard solar models cannot reproduce the radial profile of the sound speed at the base of the convective zone (CZ) and fail to predict the Li7 depletion. In parallel, helioseismology has shown that the transition from differential rotation in the CZ to almost uniform rotation in the radiative solar interior occurs in a shallow layer called the tachocline. This layer is presumably the seat of large scale circulation and of turbulent motions. Here, we introduce a macroscopic transport term in the structure equations, which is based on a hydrodynamical description of the tachocline proposed by Spiegel and Zahn, and we calculate the mixing induced within this layer. We discuss the influence of different parameters that represent the tachocline thickness, the Brunt-Vaissala frequency at the base of the CZ, and the time dependence of this mixing process along the Sun's evolution. We show that the introduction of such a process inhibits the microscopic diffusion by about 25%. Starting from models including a pre-main sequence evolution, we obtain: a) a good agreement with the observed photospheric chemical abundance of light elements such as He3, He4, Li7 and Be9, b) a smooth composition gradient at the base of the CZ, and c) a significant improvement of the sound speed square difference between the seismic sun and the models in this transition region, when we allow the phostospheric heavy element abundance to adjust, within the observational incertitude, due to the action of this mixing process. The impact on neutrino predictions is also discussed.Comment: 15 pages, 7 figures, to be published in ApJ (used emulateapj style for latex2e). New email for A. S. Brun: [email protected]

Dynamical Tide in Solar-Type Binaries

Circularization of late-type main-sequence binaries is usually attributed to turbulent convection, while that of early-type binaries is explained by resonant excitation of g modes. We show that the latter mechanism operates in solar-type stars also and is at least as effective as convection, despite inefficient damping of g modes in the radiative core. The maximum period at which this mechanism can circularize a binary composed of solar-type stars in 10 Gyr is as low as 3 days, if the modes are damped by radiative diffusion only and g-mode resonances are fixed; or as high as 6 days, if one allows for evolution of the resonances and for nonlinear damping near inner turning points. Even the larger theoretical period falls short of the observed transition period by a factor two.Comment: 17 pages, 2 postscript figures, uses aaspp4.sty. Submitted to Ap