>Magister Scientiae - MSc / This thesis reports the results of a twofold study on the recently proposed phenomenon of 'stellar pulsations' in young brown dwarfs by the seminal study of Palla and Baraffe (2005) (PB05, thereafter). The PB05 study presents results of a non-adiabatic linear stability analysis showing that young brown dwarfs should become pulsationally unstable during the deuterium burning phase of their evolution. The PB05 calculations on which this prediction is based have already been applied in a number of ground and space-based observational campaigns aimed at searching for this newly proposed putative class of potential pulsators. However, despite their significance and implications, the theoretical calculations by PB05 have not yet, to date, been subjected to independent verification in a different computational framework. To achieve this, we have generated equilibrium brown dwarf models and performed non-adiabatic linear stability calculations similar to PB05 assuming their 'frozen-in convection' approximation and the relevant input physics. The calculations performed in this thesis show, in overall, that there is a good agreement between the results from our study and those in PB05. However, there seem to be significant differences for very low mass objects as pointed out in our comparative results. We attribute this difference to our different boundary conditions. Our outer boundary condition is equivalent to the Eddington approximation in the 3-D case (e.g see Unno and Spiegel (1966)), while PB05 use a combination of different atmospheric profiles as discussed in Chabriel and Baraffe (2000). The validity of the frozen-in assumption used by PB05, which is based on the argument that the convective time scales calculated for these objects are much less than the pulsation time scales, has not been investigated. In this thesis, we have invoked a time-dependent theory of convection similar to Kuhfuss (1986) and Stellingwerf (1982) which includes turbulent pressure, turbulent diffusion and turbulent viscosity to study the pulsations. We have also investigated the effects of varying a number of free parameters in the above theoretical models. Our results show that turbulent pressure dominates in driving the pulsations in young brown dwarfs yielding growth rates much higher than in the frozen-in scenario. This is a new result that requires further analysis. The perturbation in the convective flux is found to have a damping effect on the acoustic modes. Turbulent viscosity is found to lead to damping which increases with increase in the value of the turbulent viscosity parameter and is found to have very little effect on the fundamental mode pulsation periods. Variation in the turbulent diffusion parameter has a very small effect on the fundamental mode periods and e-folding times. As a side lobe, we have determined theoretical pulsation constants for the fundamental mode and calculated the period ratios for the fundamental mode to those of the first and second harmonics. We find values of pulsation constants falling within the theoretical values calculated for variable stars shown in Cox (1980). This is explained in relation to the terms that go into the theoretical formula discussed later in this thesis. We find a correlation between the period ratios and the BDs mass and argue that such plots of the period ratios vs mass of the BDs could be useful in constraining the masses, given known periods from observations.

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Les étoiles massives sont les principaux contributeurs à l'enrichissement du milieu interstellaire. Ce sont généralement des rotateurs rapides, dotés d'une enveloppe radiative dans laquelle l'interaction de la stratification et la rotation génère une rotation différentielle. Celle-ci peut alimenter divers phénomènes de transport et l'évolution rapide de l'étoile. Nombre de ces étoiles sont par ailleurs des pulsateurs classiques. Cette thèse s'intéresse en premier lieu à l'interaction entre la rotation différentielle et les pulsations à basse fréquence dans l'étoile : celles-ci sont des modes gravito-inertiels dont la force de rappel est une combinaison de la force de Coriolis et de la poussée d'Archimède. Ils sondent les couches profondes de l'étoile, et sont étudiés suivant deux méthodes : dans la limite non-dissipative par la méthode des caractéristiques, et dans le cas dissipatif par la résolution du problème complet par une méthode spectrale. Nous mettons en évidence différentes singularités (attracteurs, latitudes critiques, résonances de corotation, piégeage en coin) et des modes réguliers. Certains modes sont excités par des instabilités baroclines, qui, si des effets non-linéaires provoquent leur saturation, permettent l'existence d'un mécanisme d'excitation nouveau dû à la rotation différentielle. Dans un second temps, nous avons associé le code de structure ESTER au code de calcul d'oscillations TOP. Ces deux codes calculent les quantités dans une étoile en deux dimensions et les modes associés en tenant compte des effets de la rotation de façon complète. Nous utilisons visibilités et taux d'amortissement des modes pour sélectionner dans le spectre synthétique les meilleurs candidats à l'identification des modes observés. Nous présentons une application au rotateur rapide Rasalhague (aOph), pour lequel de nombreuses observations sont disponibles. Nous n'avons pas obtenu une identification des modes univoque, mais le problème est maintenant mieux cerné et diverses pistes de progrès ont été identifiées. / Massive stars are the main contributors of the interstellar medium enrichment. These stars are usually fast rotators, with a radiative envelope in which the interaction between stratification and rotation gives rise to a differential rotation. This can trigger transport phenomena in the star, and affect its fast evolution. Besides, many of these stars are classical pulsators. This work focuses first on the impact of a differential rotation on the low-frequency oscillation spectrum which contains gravito-inertial modes. These modes are restored by the combination of buoyancy and Coriolis force and probe deep layers of stars. Our study is twofold : we compute the paths of characteristics in the non-dissipative limit, and solve the fully-dissipative eigenvalue problem numerically using a spectral decomposition. We find various singularities (attractors, critical latitudes, corotation resonances, wedge-trapping) and regular modes. Some of these modes are excited by baroclinic instabilities that may saturate through non-linear effects. If so, we have discovered a new excitation mechanism for these modes, driven by differential rotation. Aside of this theoretical work ; we have considered the case of Rasalhague (aOph), which is a well-known fast rotator. We studied this star by associating the ESTER structure code with the TOP oscillation code. Both of these codes use a two-dimensional structure, taking rotation effects fully into account. We use the mode damping rates and visibilities to filter the best candidates for observed modes identification out of the synthetic spectra. Even though we could not reach a satisfactory identification of the observed frequencies, we improved our understanding of the problem and identified the next steps to be taken.

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