Phase Space Topology and Bifurcation of Liouville Torii in the Goryatchev-Tchaplygin Top

The classical problem of a rigid body with a fixed point is considered in the case of Goryatchev-Tchaplygin. We give a complete description of its real phase space topology. All generic bifurcation of Liouville Torii is determined theoretically and numerically. We give also explicit periodic solutions of the problem.The classical problem of a rigid body with a fixed point is considered in the case of Goryatchev-Tchaplygin. We give a complete description of its real phase space topology. All generic bifurcation of Liouville Torii is determined theoretically and numerically. We give also explicit periodic solutions of the problem

The {\gamma} Dor stars as revealed by Kepler : A key to reveal deep-layer rotation in A and F stars

The {\gamma} Dor pulsating stars present high-order gravity modes, which make them important targets in the intermediate-and low-mass main-sequence region of the Hertzsprung-Russell diagram. Whilst we have only access to rotation in the envelope of the Sun, the g modes of {\gamma} Dor stars can in principle deliver us constraints on the inner layers. With the puzzling discovery of unexpectedly low rotation rates in the core of red giants, the {\gamma} Dor stars appear now as unique targets to explore internal angular momentum transport in the progenitors of red giants. Yet, the {\gamma} Dor pulsations remain hard to detect from the ground for their periods are close to 1 day. While the CoRoT space mission first revealed intriguing frequency spectra, the almost uninterrupted 4-year photometry from the Kepler mission eventually shed a new light on them. It revealed regularities in the spectra, expected to bear signature of physical processes, including rotation, in the shear layers close to the convective core. We present here the first results of our effort to derive exploitable seismic diagnosis for mid- to fast rotators among {\gamma} Dor stars. We confirm their potential to explore the rotation history of this early phase of stellar evolution.Comment: 4 pages, 1 figure, proceedings of the 22nd Los Alamos Stellar Pulsation Conference, "Wide-field variability surveys: a 21st-century perspective" held in San Pedro de Atacama, Chile, Nov. 28-Dec. 2, 201

Process modelling for Space Station experiments

Examined here is the sensitivity of a variety of space experiments to residual accelerations. In all the cases discussed the sensitivity is related to the dynamic response of a fluid. In some cases the sensitivity can be defined by the magnitude of the response of the velocity field. This response may involve motion of the fluid associated with internal density gradients, or the motion of a free liquid surface. For fluids with internal density gradients, the type of acceleration to which the experiment is sensitive will depend on whether buoyancy driven convection must be small in comparison to other types of fluid motion, or fluid motion must be suppressed or eliminated. In the latter case, the experiments are sensitive to steady and low frequency accelerations. For experiments such as the directional solidification of melts with two or more components, determination of the velocity response alone is insufficient to assess the sensitivity. The effect of the velocity on the composition and temperature field must be considered, particularly in the vicinity of the melt-crystal interface. As far as the response to transient disturbances is concerned, the sensitivity is determined by both the magnitude and frequency of the acceleration and the characteristic momentum and solute diffusion times. The microgravity environment, a numerical analysis of low gravity tolerance of the Bridgman-Stockbarger technique, and modeling crystal growth by physical vapor transport in closed ampoules are discussed

Seismic diagnostics for transport of angular momentum in stars 2. Interpreting observed rotational splittings of slowly-rotating red giant stars

Asteroseismology with the space-borne missions CoRoT and Kepler provides a powerful mean of testing the modeling of transport processes in stars. Rotational splittings are currently measured for a large number of red giant stars and can provide stringent constraints on the rotation profiles. The aim of this paper is to obtain a theoretical framework for understanding the properties of the observed rotational splittings of red giant stars with slowly rotating cores. This allows us to establish appropriate seismic diagnostics for rotation of these evolved stars. Rotational splittings for stochastically excited dipolar modes are computed adopting a first-order perturbative approach for two $1.3 M_\odot$ benchmark models assuming slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation of the rotational splittings of $\ell=1$ modes with frequency depends only on the large frequency separation, the g-mode period spacing, and the ratio of the average envelope to core rotation rates (${\cal R}$). This leds us to propose a way to infer directly ${\cal R}$ from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide a theoretical support for the use of a Lorentzian profile to measure the observed splittings for red giant stars.Comment: 15 pages, 15 figures, accepted for publication in A&

PLATO: PSF modelling using a microscanning technique

The PLATO space mission is designed to detect telluric planets in the habitable zone of solar type stars, and simultaneously characterise the host star using ultra high precision photometry. The photometry will be performed on board using weighted masks. However, to reach the required precision, corrections will have to be performed by the ground segment and will rely on precise knowledge of the instrument PSF (Point Spread Function). We here propose to model the PSF using a microscanning method.Comment: 2 pages, conference proceedings of the CoRoT Symposium 3, KASC 7, appears in EPJ conference 201

Analysis of low gravity tolerance of model experiments for space station: Preliminary results for directional solidification

It has become clear from measurements of the acceleration environment in the Spacelab that the residual gravity levels on board a spacecraft in low Earth orbit can be significant and should be of concern to experimenters who wish to take advantage of the low gravity conditions on future Spacelab missions and on board the Space Station. The basic goals are to better understand the low gravity tolerance of three classes of materials science experiments: crystal growth from a melt, a vapor, and a solution. The results of the research will provide guidance toward the determination of the sensitivity of the low gravity environment, the design of the laboratory facilites, and the timelining of materials science experiments. To data, analyses of the effects of microgravity environment were, with a few exceptions, restricted to order of magnitude estimates. Preliminary results obtained from numerical models of the effects of residual steady and time dependent acceleration are reported on: heat, mass, and momentum transport during the growth of a dilute alloy by the Bridgman-Stockbarger technique, and the response of a simple fluid physics experiment involving buoyant convection in a square cavity

Angular momentum redistribution by mixed modes in evolved low-mass stars. I. Theoretical formalism

Seismic observations by the space-borne mission \emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews \& McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_\odot$ benchmark model, representative of observed CoRoT and \emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.Comment: Accepted in A&A, 11 pages, and 6 figure

Angular momentum redistribution by mixed modes in evolved low-mass stars. II. Spin-down of the core of red giants induced by mixed modes

The detection of mixed modes in subgiants and red giants by the CoRoT and \emph{Kepler} space-borne missions allows us to investigate the internal structure of evolved low-mass stars. In particular, the measurement of the mean core rotation rate as a function of the evolution places stringent constraints on the physical mechanisms responsible for the angular momentum redistribution in stars. It showed that the current stellar evolution codes including the modelling of rotation fail to reproduce the observations. An additional physical process that efficiently extracts angular momentum from the core is thus necessary. Our aim is to assess the ability of mixed modes to do this. To this end, we developed a formalism that provides a modelling of the wave fluxes in both the mean angular momentum and the mean energy equations in a companion paper. In this article, mode amplitudes are modelled based on recent asteroseismic observations, and a quantitative estimate of the angular momentum transfer is obtained. This is performed for a benchmark model of 1.3 $M_{\odot}$ at three evolutionary stages, representative of the evolved pulsating stars observed by CoRoT and Kepler. We show that mixed modes extract angular momentum from the innermost regions of subgiants and red giants. However, this transport of angular momentum from the core is unlikely to counterbalance the effect of the core contraction in subgiants and early red giants. In contrast, for more evolved red giants, mixed modes are found efficient enough to balance and exceed the effect of the core contraction, in particular in the hydrogen-burning shell. Our results thus indicate that mixed modes are a promising candidate to explain the observed spin-down of the core of evolved red giants, but that an other mechanism is to be invoked for subgiants and early red giants.Comment: Accepted in A&A, 7 pages, 8 figure