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Paper IPM / Astronomy / 12135  


Abstract:  
The impact of the combination 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 wish to decipher the solution of this problem in the context of rmodes 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 but of infinite electrical conductivity and analyze propagation of modal perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the m=2 rmode oscillation is influenced by the magnetic field when the Lehnert number (ratio of Alfvén speed to rotation speed) exceeds a value proportional to the onefourth power of the Ekman number (nondimensional 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 10^{14} G are necessary to perturb the rmodes instability.
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