Ecole doctorale de Physique de la région Parisienne (ED107)

Chapitre 4
Inertial modes in slowly rotating
stars : An evolutionary description
Sommaire
Abstract
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2 Equations and numbers . . . . . . . . . . . . . . . . . . . . . . . 107
4.3 Mass conservation, boundary conditions and approximations 115
4.4 Test and calibration of the code . . . . . . . . . . . . . . . . . . 117
4.5 Differential rotation . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.6 Strong Cowling approximation in GR . . . . . . . . . . . . . . 133
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.8 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Loïc Villain and Silvano Bonazzola
Laboratoire Univers et THéories
(F.R.E. 2462 du CNRS) / Observatoire de Paris,
F-92195 Meudon Cedex, France.
Phys. Rev. D 66 : 123001 (2002).
We present a new hydrocode based on spectral methods using spherical coordinates.
The first version of this code aims at studying time evolution of inertial modes in slowly
rotating neutron stars. In this paper, we introduce the anelastic approximation, developed
in atmospheric physics, using the mass conservation equation to discard acoustic waves.
We describe our algorithms and some tests of the linear version of the code, and also some
preliminary linear results. We show, in the Newtonian framework with a differentially rotating
background, as in the relativistic case with the strong Cowling approximation, that
the main part of the velocity quickly concentrates near the equator of the star. Thus, our
time evolution approach gives results analogous to those obtained by Karino, Yoshida,