r-Mode Movie: Part II


Properties of r-Modes in Rotating Magnetic Neutron Stars

University of Illinois at Urbana-Champaign

Introduction: r-Mode Instabilities

The instability of r-mode oscillations in rapidly rotating neutron stars has attracted attention as a potential mechanism for producing high frequency, almost periodic gravitational waves. The analyses carried so far have shown the existence of these modes and have considered damping by shear and bulk viscosity. However, the magnetohydrodynamic coupling of the modes with a stellar magnetic field and its role in the damping of the instability has not been fully investigated yet. Here we visualize the secular higher-order kinematical effects which will produce toroidal fluid drifts.

The evolution of the r-mode instability is likely to be accompanied by secular kinematic effects which will produce differential rotation with large scale drifts of fluid elements, mostly in the azimuthal direction. The interaction of these secular velocity fields with a pre-existing neutron star magnetic field could result in the generation of intense and large scale toroidal fields. We also have assessed the impact of the generation of large magnetic fields on the gravitational wave detectability of r-mode unstable neutron stars. Our results indicate that the signal to noise ratio in the detection of gravitational waves from the r-mode instability might be considerably decreased if the latter develops in neutron stars with initial magnetic fields larger than 1010 G.


Exact Nonlinear Solution as Seen in the Pattern Frame


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    • In this movie we show both the magnetic field lines and velocity vectors in the pattern frame. The alfven speed VA = 0.3WR, where W is the angular velocity of the rotating star and R is the radius. The dimensionless amplitude a = 0.3. The field lines and velocity vectors are stationary in this frame. We rotate the viewer around the star to show its full character.



    Exact Nonlinear Solution as Seen in the Corotating Frame


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    • Here we animate a set of magnetic field lines and velocity vectors in the fast mode. For this and all subsequent movies, the alfven speed VA = 0.3WR and the dimensionless amplitude a = 0.3.


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    • In this movie, we animate a set of magnetic field lines and Lagrangian test particles in the fast mode. Note that the particles near the pole drift westward, while the particles near the equator drift eastward.


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    • Here we animate a set of magnetic field lines and velocity vectors in the slow mode.


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    • In this movie, we animate a set of magnetic field lines and Lagrangian test particles in the slow mode.



    Velocity Field: Second-Order Correction

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    • In this movie we show the time evolution of a set of vertical magnetic field lines arranged on a cylindrical surface centered about the star's axis of rotation. This evolution is due to the first-order velocity perturbation only. Note the twisting of the magnetic field lines. In this and the next movie, the alfven speed VA = 0.3WR and dimensionless amplitude a = 0.3.


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    • Here we show the time evolution of the same field lines subject to both the first- and second-order velocity perturbations. The second-order correction to the velocity field is in the azimuthal direction. Note that the twisting of the magnetic field lines is less severe than that of the first-order velocity perturbation only.


    Magnetic Field Lines: r-Mode Oscillation and Back-Reaction

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    • In this movie we show the time evolution of a set of vertical magnetic field lines arranged as rings circling the surface of the star. We then rotate the viewer around the star to see its full character. Note that in the full evolution movie, the field lines begin to reverse the direction of their motion due to the back-reaction.

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    • This movie is the same as the previous one, except that the time evolution is five times faster than before. Notice that the magnetic field lines eventually reverse the direction of their motion due to the back-reaction.

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    • Here we plot the total energy, total magnetic energy, and total kinetic energy as a function of time.



    Scientific visualization by


    Undergraduate Research Team
    Departments of Physics and Astronomy
    University of Illinois at Urbana-Champaign

    last updated 4/26/03 by rlc
    Center for Theoretical Astrophysics---University of Illinois at Urbana-Champaign
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