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Symmetry breaking in nonlinear growth of bar instability

Published online by Cambridge University Press:  30 September 2008

M. Saijo*
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK
Y. Kojima
Affiliation:
Department of Physics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
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Abstract

We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. The numerical results also indicate that the vertical oscillation amplifies another waves with odd azimuthal wave-numbers in the horizontal plane like Faraday resonance. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.

Type
Research Article
Copyright
© EAS, EDP Sciences, 2008

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References

Baiotti, L., De Pietri, R., Manca, G.M., & Rezzolla, L., 2007, PRD, 75, 044023 CrossRef
Chandrasekhar, S., 1969, Ellipsoidal Figures of Equilibrium (Yale Univ. Press, New York), Chap. 5
Drazin, P.G., & Reid, W.H., 1981, Hydrodynamic Stability (Cambridge Univ. Press., Cambridge), Sect. 48
Miles, J., & Hederson, D., 1990, Ann. Rev. Fluid Mech., 22, 143 CrossRef
Saijo, M., & Kojima, Y., 2007, in preparation