A theoretical study of stellar pulsations in young brown dwarfs
Onchong'a, Okeng'o Geoffrey
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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.