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Astron. Astrophys. 341, 842-852 (1999)

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The dynamical tide in a rotating [FORMULA] main sequence star

A study of g- and r-mode resonances

M.G. Witte and G.J. Savonije

Astronomical Institute `Anton Pannekoek', University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands (e-mail: marnix@astro.uva.nl; gertjan@astro.uva.nl)

Received 21 July 1998 / Accepted 4 November 1998

Abstract

We study the linear, but fully non-adiabatic tidal response of a uniformly rotating, somewhat evolved ([FORMULA]), 10 [FORMULA] main sequence star to the dominant [FORMULA] components of its binary companion's tidal potential. This is done numerically with a 2D implicit finite difference scheme. We assume the spin vector of the 10 [FORMULA] star to be aligned perpendicular to the orbital plane and calculate the frequency [FORMULA] and width of the resonances with the prograde and retrograde gravity (g) modes as well as the resonances with quasi-toroidal rotational (r) modes for varying rotation rates [FORMULA] of the main sequence star. For all applied forcing frequencies we determine the rate of tidal energy and angular momentum exchange with the companion. In a rotating star tidal energy is transferred from [FORMULA] g-modes to g-modes of higher spherical degree ([FORMULA]) by the Coriolis force. These latter modes have shorter wavelength and are damped more heavily, so that the [FORMULA] resonant tidal interaction tends to be reduced for large rotation rates [FORMULA]. On the other hand, the density of potential resonances (a broad l spectrum) increases. We find several inertially excited unstable [FORMULA] g-modes, but not more than one (retrograde) unstable [FORMULA] g-mode and that only for rapid rotation. Our numerical results can be applied to study the tidal evolution of eccentric binaries containing early type B-star components.

Key words: stars: rotation – stars: oscillations – stars: binaries: close – hydrodynamics

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© European Southern Observatory (ESO) 1999

Online publication: December 16, 1998
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