Theoretical power spectra of mixed modes in low mass red giant stars

CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit significant amplitude, both in the core and at the surface of the stars. It opens the possibility of probing the internal structure from their inner-most layers up to their surface along their evolution on the red giant branch as well as on the red-clump. Our objective is primarily to provide physical insight into the physical mechanism responsible for mixed-modes amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red giants spectra along with their evolution. The study of energetic aspects of these oscillations is also of great importance to predict the mode parameters in the power spectrum. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in the determination of the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed-modes

Noise and thermal stability of vibrating micro-gyrometers preamplifiers

The preamplifier is a critical component of gyrometer's electronics. Indeed the resolution of the sensor is limited by its signal to noise ratio, and the gyrometer's thermal stability is limited by its gain drift. In this paper, five different kinds of preamplifiers are presented and compared. Finally, the design of an integrated preamplifier is shown in order to increase the gain stability while reducing its noise and size.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

A new seismic analysis of Alpha Centauri

Models of alpha Cen A & B have been computed using the masses determined by Pourbaix et al. (2002) and the data derived from the spectroscopic analysis of Neuforge and Magain (1997). The seismological data obtained by Bouchy and Carrier (2001, 2002) do help improve our knowledge of the evolutionary status of the system. All the constraints are satisfied with a model which gives an age of about 6 Gyr for the binary.Comment: to be published in Astronomy and Astrophysic

The underlying physical meaning of the νmax−νc\nu_{\rm max}-\nu_{\rm c} relation

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum ($\nu_{\rm max}$) of solar-like oscillations and the cut-off frequency ($\nu_{\rm c}$). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called \emph{plateau} of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between $\nu_{\rm max}$ and $\nu_{\rm c}$, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.Comment: 8 pages, 11 figures. Accepted in A&

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

The CoRoT target HD 49933: 2- Comparison of theoretical mode amplitudes with observations

From the seismic data obtained by CoRoT for the star HD 49933 it is possible, as for the Sun, to constrain models of the excitation of acoustic modes by turbulent convection. We compare a stochastic excitation model described in Paper I (arXiv:0910.4027) with the asteroseismology data for HD 49933, a star that is rather metal poor and significantly hotter than the Sun. Using the mode linewidths measured by CoRoT for HD 49933 and the theoretical mode excitation rates computed in Paper I, we derive the expected surface velocity amplitudes of the acoustic modes detected in HD 49933. Using a calibrated quasi-adiabatic approximation relating the mode amplitudes in intensity to those in velocity, we derive the expected values of the mode amplitude in intensity. Our amplitude calculations are within 1-sigma error bars of the mode surface velocity spectrum derived with the HARPS spectrograph. The same is found with the mode amplitudes in intensity derived for HD 49933 from the CoRoT data. On the other hand, at high frequency, our calculations significantly depart from the CoRoT and HARPS measurements. We show that assuming a solar metal abundance rather than the actual metal abundance of the star would result in a larger discrepancy with the seismic data. Furthermore, calculations that assume the ``new'' solar chemical mixture are in better agreement with the seismic data than those that assume the ``old'' solar chemical mixture. These results validate, in the case of a star significantly hotter than the Sun and Alpha Cen A, the main assumptions in the model of stochastic excitation. However, the discrepancies seen at high frequency highlight some deficiencies of the modelling, whose origin remains to be understood.Comment: 8 pages, 3 figures (B-W and color), accepted for publication in Astronomy & Astrophysics. Corrected typo in Eq. (4). Updated references. Language improvement

Pratiques du titrement dans les villes en développement : trois cas d'étude (Inde, Ethiopie, Mauritanie) : rapport de recherche présenté dans le cadre de l'appel à projets "La sécurisation du droit de propriété dans les pays en voie de développement"

Les trois cas d’études en Inde, en Ethiopie et en Mauritanie ont permis de voir comment est appréhendé un même cadre référentiel qui pose la sécurisation foncière au coeur de la lutte contre la pauvreté. Plusieurs types de villes (petites, secondaires, capitales) et formes d’urbain (zone centrale, quartiers périurbains, urbain diffus) ont permis de souligner quelques uns des enjeux que représente la titrisation dans les Suds. Le contexte urbain joue fortement. L’impact des politiques de titrement foncier dépend réellement de la taille de la ville et des formes urbaines. L’urbanisation généralisée et rapide dans les trois pays étudiés, longtemps considérés comme étant à dominante rurale, implique l’adaptation et la création de nouveaux régimes fonciers. Dans nos différents cas d’étude, l’accès au sol urbain fait émerger de nouveaux besoins en termes de réglementation foncière, de nouveaux types de reconnaissance, mais aussi et surtout de nouvelles pratiques de sécurisation se tissent entre les habitants et les autorités et entre habitants. La présente étude a fait ressortir l’importance de la circulation à l’échelle internationale de politiques urbaines et « bonnes pratiques », pensées depuis Washington par les Institutions internationales, et réappropriées de façon tout à fait originale localement. La comparaison des trois cas a mis en lumière l’importance des pratiques habitantes, qui, en Ethiopie, en Inde et en Mauritanie, exploitent et construisent des opportunités offertes par les normes juridiques relatives à l’accès à la propriété, plus qu’elles arrivent à en bénéficier pleinement et simplement. Bien souvent, les réformes appuyées par les bailleurs de fond ne font que se surimposer à des juridictions foncières déjà complexes, souvent coûteuses à respecter pour les habitants qui optent pour des pratiques plus informelles. La réforme sur le papier n’est que rarement suivie par la réforme en action

Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles package, use csh to unpack (on Unix machine), to be published in Phys. Rev. Let

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

Vibrational Instability of Metal-Poor Low-Mass Main-Sequence Stars

We find that low-degree low-order g-modes become unstable in metal-poor low-mass stars due to the $\varepsilon$-mechanism of the pp-chain. Since the outer convection zone of these stars is limited only to the very outer layers, the uncertainty in the treatment of convection does not affect the result significantly. The decrease in metallicity leads to decrease in opacity and hence increase in luminosity of a star. This makes the star compact and results in decrease in the density contrast, which is favorable to the $\varepsilon$-mechanism instability. We find also instability for high order g-modes of metal-poor low-mass stars by the convective blocking mechanism. Since the effective temperature and the luminosity of metal-poor stars are significantly higher than those of Pop I stars, the stars showing $\gamma$ Dor-type pulsation are substantially less massive than in the case of Pop I stars. We demonstrate that those modes are unstable for about $1\,M_\odot$ stars in the metal-poor case.Comment: 4 pages, 4 figures, To be published in Astrophysics and Space Science Proceedings series (ASSP). Proceedings of the "20th Stellar Pulsation Conference Series: Impact of new instrumentation and new insights in stellar pulsations", 5-9 September 2011, Granada, Spai