Mathematics
Scientific paper
May 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phdt.........2w&link_type=abstract
PhDT, Katholieke Universiteit Leuven, Belgium
Mathematics
5
Binaries: Close, Tides, Oscillations, Resonances, Orbital Evolution, Methods: Analytical
Scientific paper
In this dissertation, we mainly investigate resonances of dynamic tides with free oscillation modes in components of close binaries and we examine the effects of such resonances on the dynamic evolution of these systems. When the forcing frequency of a dynamic tide is close to an eigenfrequency of a free oscillation mode of the tidally distorted star, the oscillation mode is resonantly excited. For the study of such resonances, we use perturbation methods. These methods have the advantage to yield semi-analytical solutions, which allow one to discriminate between the effects of the various acting factors. We have solved the perturbation problems by means of mathematical techniques that are appropriate for the treatment of singular perturbation problems: boundary-layer techniques and multiple scale expansion procedures. We first consider the resonantly excited oscillation mode in the isentropic (adiabatic) approximation. We show that it is unlikely that a g+-mode with an observed orbital period of 4.23 days is resonantly excited in the star 51 Pegasi by a Jupiter-mass planet. Still in the isentropic approximation, we show that for sufficiently long orbital periods, the classical formula for the apsidal motion in close binaries derived by Sterne (1939) is equivalent with the formula derived in the frame of the theory of dynamic tides. For orbital periods of the order of a few days, the classical formula can lead to apsidal motions that are several tens of percents slower than the apsidal motions determined within the frame of the theory of dynamic tides. Next, we examine the influence of the nonadiabatic effects associated with the energy generation and the radiative energy flux on the resonantly excited oscillation mode. The nonadiabatic effects induce a phase shift between the tidal displacement and the tide-generating potential which leads to time-dependent variations of the orbital elements and the star's angular velocity. In particular, we show that, due to multiple resonanes, circularisation of the orbit and synchronisation of the rotation in binaries with short orbital periods can occur on time scales shorter than the star's nuclear time scale.
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