Bifurcations sets of the Sretensky axial symmetric gyrostat

In this paper, we perform an adapted Deprit coordinate transformation and we analyse the flow evolution on the phase space for the axial symmetric gyrostat in the Sretensky case .We give a complete description of thegeneric bifurcations of the common level sets of the first integrals. A numerical investigation of these bifurcations is considered.In this paper, we perform an adapted Deprit coordinate transformation and we analyse the flow evolution on the phase space for the axial symmetric gyrostat in the Sretensky case .We give a complete description of thegeneric bifurcations of the common level sets of the first integrals. A numerical investigation of these bifurcations is considered

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

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

Seismic diagnostics for transport of angular momentum in stars 1. Rotational splittings from the PMS to the RGB

Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles. Our aim is to obtain seismic constraints on the internal transport and surface loss of angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes. We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of $1.3 M_{\odot}$ models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch. Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars.Comment: 15 pages, 13 figures, accepted for publication in A&

KIC 10080943: a binary star with two γ Doradus/δ Scuti hybrid pulsators. Analysis of the g modes

We use 4 yr of Kepler photometry to study the non-eclipsing spectroscopic binary KIC 10080943. We find both components to be γ Doradus/δ Scuti hybrids, which pulsate in both p and g modes. We present an analysis of the g modes, which is complicated by the fact that the two sets of l = 1 modes partially overlap in the frequency spectrum. Nevertheless, it is possible to disentangle them by identifying rotationally split doublets from one component and triplets from the other. The identification is helped by the presence of additive combina- tion frequencies in the spectrum that involve the doublets but not the triplets. The rotational splittings of the multiplets imply core rotation periods of about 11 and 7 d in the two stars. One of the stars also shows evidence of l = 2 modes

Third order nonlinear optical response of self-assembled molecular corners

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