Resonance breaking due to dissipation in planar planetary systems

We study the evolution of two planets around a star, in mean-motion resonance and undergoing tidal effect. We derive an integrable analytical model of mean-motion resonances of any order which reproduce the main features of the resonant dynamics. Using this simplified model, we obtain a criterion showing that depending on the balance of the tidal dissipation in both planets, their final period ratio may stay at the resonant value, increase above, or decrease below the resonant value. Applying this criterion to the two inner planets orbiting GJ163, we deduce that the current period ratio (2.97) could be the outcome of dissipation in the 3:1 MMR provided that the innermost planet is gaseous (slow dissipation) while the second one is rocky (faster dissipation). We perform N-body simulations with tidal dissipation to confirm the results of our analytical model. We also apply our criterion on GJ581b, c (5:2 MMR) and reproduce the current period ratio (2.4) if the inner planet is gaseous and the outer is rocky (as for GJ163). Finally, we apply our model to the Kepler mission's statistics. We show that the excess of planets pairs close to first order MMR but in external circulation, i.e., with period ratios P_out/P_in > (p+1)/p for the resonance (p+1):p, can be reproduced by tidal dissipation in the inner planet. There is no need for any other dissipative mechanism, provided that these systems left the resonance with non-negligible eccentricities.Comment: 14 pages, 9 figures, submitted for publicatio

Unit organization of the subject: child care and development with laboratory experience in nursery school, secondary level.

Thesis (Ed.M.)--Boston Universit

Planets in Mean-Motion Resonances and the System Around HD45364

In some planetary systems, the orbital periods of two of its members present a commensurability, usually known by mean-motion resonance. These resonances greatly enhance the mutual gravitational influence of the planets. As a consequence, these systems present uncommon behaviors, and their motions need to be studied with specific methods. Some features are unique and allow us a better understanding and characterization of these systems. Moreover, mean-motion resonances are a result of an early migration of the orbits in an accretion disk, so it is possible to derive constraints on their formation. Here we review the dynamics of a pair of resonant planets and explain how their orbits evolve in time. We apply our results to the HD 45365 planetary system.Comment: invited review, 17 pages, 6 figure

Dissipation in planar resonant planetary systems

Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that damps the eccentricities. However, the resonant angles appear to librate at the end of the migration process, which is often believed to be an evidence that the systems remain in resonance. Here we provide an analytical model for the dissipation in resonant planetary systems valid for low eccentricities. We confirm that dissipation accounts for an excess of pairs that lie just aside from the nominal periods ratios, as observed by the Kepler mission. In addition, by a global analysis of the phase space of the problem, we demonstrate that these final pairs are non-resonant. Indeed, the separatrices that exist in the resonant systems disappear with the dissipation, and remains only a circulation of the orbits around a single elliptical fixed point. Furthermore, the apparent libration of the resonant angles can be explained using the classical secular averaging method. We show that this artifact is only due to the severe damping of the amplitudes of the eigenmodes in the secular motion.Comment: 18 pages, 20 figures, accepted to A&

Prédiction de l’insulino-résistance par les ratios de lipoprotéines chez les adultes béninois

Des controverses subsistent sur force prédictive de l’insulino-résistance par les ratios de lipoprotéines chez les Afro-américains. L’objectif est de déterminer la force prédictive de l’insulino-résistance (IR) par les ratios triglycérides-par-HDL-cholestérol (TG/HDL-C) et cholestérol total-par-HDL-cholestérol (CT/HDL-C) chez des adultes béninois. L’étude est de type transversal, issue d’une enquête longitudinale sur le risque cardiométabolique et a inclut 416 sujets âgés de 29 à 69 ans. Les mesures anthropométriques et les dosages de la glycémie à jeun, de l’insulinémie, du CT, du HDL-C et des TG sont réalisés. L’IR est définie par le 75ème percentile des valeurs de « l’indice d’évaluation de modèle d'homéostasie pour l’insulino-résistance» (HOMA IR). Les valeurs prédictives de l’IR par les ratios TG/HDL-C et CT/HDL-C sont déterminées par les aires sous les courbes (AUC) de la « fonction d’efficacité du récepteur» (ROC). Les concentrations plasmatiques moyennes des lipides ont été en général plus élevées chez les IR que chez les non IR sauf pour les triglycérides : 0,9±0,5 mmol/L versus 0,8±0,4 mmol/L (p=0,138) chez les femmes, le cholestérol total : 4,7±1,7 mmol/L versus 4,3±1,2 mmol/L (p=0,161) et le HDL-Cholestérol : 1,2±0,5 mmol/L versus 1,34±0,5 mmol/L (p=0,105) chez les hommes. Les AUC ROC de prédiction de l’IR par le TG/HDL-C sont inférieures à 0,70 chez les femmes et les hommes, les obèses et les non obèses. L’AUC ROC de prédiction de l’IR par le CT/HDL-C est supérieure à 0,70 seulement chez les femmes : 0,71 (0,64-0,78). Le ratio TG/HDL-C n’est pas un prédicteur de l’IR dans la population d’étude alors que le ratio CT/HDL-C prédit l’IR chez les femmes seulement. Ces résultats contribueront au dépistage précoce de l’IR chez les femmes aux fins de la mise en place de mesures préventives.Mots clés : Prédiction, insulino-résistance, lipoprotéines, dyslipidémies, Bénin

Nematicity as a route to a magnetic field-induced spin density wave order; application to the high temperature cuprates

The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a spin density wave order in the presence of a magnetic field. We show that a cooperation of the nematicity and the magnetic field induces a finite coupling between the spin density wave and spin-triplet staggered flux orders. As a consequence of such a coupling, the magnon gap decreases as the magnetic field increases, and it eventually condenses beyond a critical magnetic field leading to a field-induced spin density wave order. Both commensurate and incommensurate orders are studied, and the experimental implications of our findings are discussed.Comment: 5 pages, 3 figure