Abstract
In this lecture I present the basic knowledge needed to understand the properties of the low-frequency spectrum of rotating stars. This spectrum is a mixture of inertial and gravity modes. These modes both have singularities in the limit of vanishing diffusion for a generic container. I explain the nature and the role of these singularities; I also discuss the way these modes can be computed and the actual difficulties that need to be circumvented to get sensible results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aufdenberg, J.P., Mérand, A., Coudé du Foresto, V., Absil, O., Di Folco, E., Kervella, P., Ridgway, S.T., Berger, D.H., Brummelaar,T.A.t., McAlister, H.A., Sturmann, J., Sturmann, L., Turner, N.H. First Results from the CHARA array. VII. Long-baseline interferometric measurements of Vega consistent with a pole-on, rapidly rotating star. ApJ 645, 664–675 (2006)
Cartan, E.: Sur les petites oscillations d’une masse fluide. Bull. Sci. Math. 46, 317–352, 356–369 (1922)
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford (1961)
Dintrans, B., Rieutord, M.: Oscillations of a rotating star: a non-perturbative theory. A&A 354, 86–98 (2000)
Dintrans, B., Rieutord, M., Valdettaro, L.: Gravito-inertial waves in a rotating stratified sphere or spherical shell. J. Fluid Mech. 398, 271–297 (1999)
Domiciano de Souza, A., Kervella, P., Jankov, S., Abe, L., Vakili, F., di Folco, E., Paresce, F. The spinning-top Be star Achernar from VLTI-VINCI. A&A 407, L47–L50 (2003)
Domiciano de Souza, A., Kervella, P., Jankov, S., Vakili, F., Ohishi, N., Nordgren, T.E., Abe, L.: Gravitational-darkening of Altair from interferometry. A&A 442, 567–578 (2005)
Friedlander, S., Siegmann, W.: Internal waves in a rotating stratified fluid in an arbitrary gravitational field. Geophys. Astrophys. Fluid Dyn. 19, 267–291 (1982)
Maas, L., Benielli, D., Sommeria, J., Lam, F.P.: Observation of an internal wave attractor in a confined, stably stratified fluid. Nature 388, 557–561 (1997)
Monnier, J.D., Zhao, M., Pedretti, E., Thureau, N., Ireland, M., Muirhead, P., Berger, J.P., Millan-Gabet, R., Van Belle, G., ten Brummelaar, T., McAlister, H., Ridgway, S., Turner, N., Sturmann, L., Sturmann, J., Berger, D.: Imaging the Surface of Altair. Science 317, 342–, arXiv:0706.0867 (2007)
Peterson, D., Hummel, C., Pauls, T., Armstrong, J., Benson, J., Gilbreath, G., Hindsley, R., Hutter, D., Johnston, K., Mozurkewich, D., Schmitt, H.: Resolving the effects of rotation in Altair with long-baseline interferometry. ApJ 636, 1087–1097 (2006)
Rieutord, M.: The dynamics of the radiative envelope of rapidly rotating stars. i. a spherical boussinesq model. A&A 451, 1025–1036 (2006)
Rieutord, M., Georgeot, B., Valdettaro, L.: Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum. J. Fluid Mech. 435, 103–144 (2001)
Rieutord, M., Valdettaro, L., Georgeot, B.: Analysis of singular inertial modes in a spherical shell: the slender toroidal shell model. J. Fluid Mech. 463, 345–360 (2002)
Roberts, P., Stewartson, K.: On the stability of a maclaurin spheroid of small viscosity. ApJ 137, 777–790 (1963)
Sleijpen, G., Van der Vorst, H.: A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM Rev. 42, 267–293 (2000)
Valdettaro, L., Rieutord, M., Braconnier, T., Fraysse, V.: Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and arnoldi-chebyshev algorithm. J. Comput. Appl. Math. 205, 382–393, physics/0604219 (2007)
van Belle, G.T., Ciardi, D.R., Thompson, R.R., Akeson, R.L., Lada, E.A.: Altair’s Oblateness and Rotation Velocity from Long-Baseline Interferometry. ApJ 559, 1155–1164 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Rieutord, M. (2009). Approaching the Low-Frequency Spectrum of Rotating Stars. In: Rozelot, JP., Neiner, C. (eds) The Rotation of Sun and Stars. Lecture Notes in Physics, vol 765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87831-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-87831-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87830-8
Online ISBN: 978-3-540-87831-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)