An r-mode in a magnetic rotating spherical layer: application to neutron stars
Article first published online: 21 NOV 2011
© 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS
Monthly Notices of the Royal Astronomical Society
Volume 419, Issue 4, pages 2893–2899, February 2012
How to Cite
Abbassi, S., Rieutord, M. and Rezania, V. (2012), An r-mode in a magnetic rotating spherical layer: application to neutron stars. Monthly Notices of the Royal Astronomical Society, 419: 2893–2899. doi: 10.1111/j.1365-2966.2011.19930.x
- Issue published online: 9 JAN 2012
- Article first published online: 21 NOV 2011
- Accepted 2011 September 30. Received 2011 September 29; in original form 2011 August 6
- stars: magnetic fields;
- stars: oscillations
The combined impact of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfvén and inertial waves. Neutron stars are a place where both effects may be at work. We aim to solve this problem in the context of the r-mode instability in neutron stars, as it appears when these modes are coupled to gravitational radiation.
We consider a rotating spherical shell filled with a viscous fluid of infinite electrical conductivity and analyse propagation of model perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the m= 2 r-mode oscillation is influenced by the magnetic field when the Lehnert number (the ratio of Alfvén speed to rotation speed) exceeds a value proportional to the one-fourth power of the Ekman number (a non-dimensional measure of viscosity). This scaling is interpreted as the coincidence of the width of internal shear layers of inertial modes and the wavelength of the Alfvén waves. Applied to the case of rotating magnetic neutron stars, we find that dipolar magnetic fields above 1014 G are necessary to perturb the r-mode instability.