# A New Class of Unstable Modes of Rotating Relativistic Stars

@article{Andersson1997ANC, title={A New Class of Unstable Modes of Rotating Relativistic Stars}, author={Nils Andersson}, journal={The Astrophysical Journal}, year={1997}, volume={502}, pages={708 - 713} }

The first numerical study of axial (toroidal) pulsation modes of a slowly rotating relativistic star is presented. The calculation includes terms of first order in ϵ ≡ Ω(R3/M)1/2 ≪ 1 (R is the radius, M is the mass, and Ω is the rotation frequency of the star) and accounts for effects due to the Coriolis force. Effects due to the centrifugal flattening of the star enter at order ϵ2 and are not included in the analysis. It is shown that increased rotation tends to decrease the damping times for…

## 326 Citations

### The r-Mode Oscillations in Relativistic Rotating Stars

- Physics
- 1999

The axial mode oscillations are examined for relativistic rotating stars with uniform angular velocity. Using the slow rotation formalism and the Cowling approximation, we have derived the equations…

### Relativistic r-Modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

- Physics
- 2002

We investigate the properties of relativistic r-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the…

### Rotational Modes of Nonisentropic Stars and the Gravitational Radiation-driven Instability

- Physics
- 2000

We investigate the properties of the r-mode and the inertial mode of slowly rotating, nonisentropic, Newtonian stars by taking account of the effects of the Coriolis force and the centrifugal force.…

### Results on the spectrum of r-modes of slowly rotating, relativistic stars

- Physics
- 2002

The paper considers the spectrum of axial perturbations (‘pure r-modes’) of slowly uniformly rotating, general relativistic stars. In a first step towards a full analysis, we analyse the evolution…

### Nonlinear evolution of r-modes: The role of differential rotation

- Physics
- 2005

Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of r-modes in the nonlinear theory. We investigate…

### On the r-mode spectrum of relativistic stars: the inclusion of the radiation reaction

- Physics
- 2002

We consider both mode calculations and time-evolutions of axial r modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational…

### Inertial Modes of Slowly Rotating Isentropic Stars

- Physics
- 1999

We investigate inertial mode oscillations of slowly and uniformly rotating, isentropic, Newtonian stars. Inertial mode oscillations are induced by the Coriolis force due to the star's rotation, and…

### r modes and mutual friction in rapidly rotating superfluid neutron stars

- Physics
- 2009

We develop a new perturbative framework for studying the r modes of rotating superfluid neutron stars. Our analysis accounts for the centrifugal deformation of the star, and considers the two-fluid…

### R-mode oscillations of rapidly rotating barotropic stars in general relativity: analysis by the relativistic Cowling approximation

- Physics
- 2005

We develop a numerical scheme for obtaining the r-mode oscillations of rapidly rotating relativistic stars. In the present scheme, we neglect all metric perturbations and only take account of the…

### A Numerical Study of Normal Modes of Rotating Neutron Star Models by the Cowling Approximation

- Physics
- 1999

A numerical method of mode analysis of rapidly rotating relativistic stellar models by the Cowling approximation is applied to rotating neutron stars with realistic equations of state. For selected…

## References

SHOWING 1-10 OF 61 REFERENCES

### Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars

- Physics
- 1998

We study nonaxisymmetric perturbations of rotating relativistic stars modeled as perfect-fluid equilibria. Instability to a mode with angular dependence exp (imϕ) sets in when the frequency of the…

### On the non-radial oscillations of slowly rotating stars induced by the Lense-Thirring effect

- PhysicsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- 1991

In a star that is rotating so slowly that the distortion of its figure may be ignored, the axial modes of non-radial oscillation exhibiting resonance can be excited by the polar modes of perturbation…

### Coupled Pulsations between Polar and Axial Modes in a Slowly Rotating Relativistic Star

- Physics
- 1993

Rotational coupling between l-polar mode and (l + 1)-axial mode of axially symmetric pulsations is studied. Equations governing them in a slowly rotating relativistic star show that these oscillation…

### Normal modes of relativistic stars in slow rotation limit

- Physics
- 1993

Rotational shifts of normal frequencies in polytropic stellar models are calculated in the framework of general relativity. The stellar rotation is assumed to be slow and the first-order rotational…

### On the secular instability of axisymmetric rotating stars to gravitational radiation reaction

- Physics
- 1985

A generalization of the Eulerian variational principle derived by Ipser and Managan, for nonaxisymmetric neutral modes of axisymmetric fluid configurations, is developed. The principle provides a…

### On the Oscillation Spectra of Ultracompact Stars: an Extensive Survey of Gravitational-Wave Modes

- Physics
- 1996

An extensive survey of gravitational-wave modes for uniform density stars is presented. The study covers stars ranging in compactness from R/M=100 to the limit of stability in general relativity: R/M…

### Axial Instability of Rotating Relativistic Stars

- Physics
- 1998

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular…

### R-mode oscillations in uniformly rotating stars

- Physics
- 1982

R-mode (or quasi-toroidal mode) oscillations in uniformly and slowly rotating stars have been investigated. Perturbations of the gravitational potential have been included. Applying an adiabatic…

### Secular instability of rotating Newtonian stars.

- Physics
- 1978

The effect of gravitational radiation and of viscosity on the stability of rotating self-gravitating fluids is considered. Previous cirteria governing secular stability to radiation are shown to fail…

### On the non-radial oscillations of a star

- PhysicsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- 1991

A complete theory of the non-radial oscillations of a static spherically symmetric distribution of matter, described in terms of an energy density and an isotropic pressure, is developed, ab initio,…