# Dynamical bar‐mode instability of differentially rotating stars: effects of equations of state and velocity profiles

@article{Shibata2003DynamicalBI,
title={Dynamical bar‐mode instability of differentially rotating stars: effects of equations of state and velocity profiles},
author={Masaru Shibata and Shigeyuki Karino and Yoshiharu Eriguchi},
journal={Monthly Notices of the Royal Astronomical Society},
year={2003},
volume={343},
pages={619-626}
}
• Published 16 April 2003
• Physics
• Monthly Notices of the Royal Astronomical Society
As an extension of our previous work, we investigate the dynamical instability against nonaxisymmetric bar-mode deformations of differentially rotating stars in Newtonian gravity by varying the equations of state and velocity profiles. We performed the numerical simulation and the follow-up linear stability analysis by adopting polytropic equations of state with polytropic indices n = 1, 3/2 and 5/2, and with two types of angular velocity profiles (the so-called j-constant-like and Kepler-like…

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## References

SHOWING 1-10 OF 23 REFERENCES
Dynamical instability of differentially rotating stars
• Physics
• 2002
We study the dynamical instability against bar-mode deformation of differentially rotating stars. We performed numerical simulation and linear perturbation analysis adopting polytropic equations of
R-mode oscillations of rapidly rotating Newtonian stars: A new numerical scheme and its application to the spin evolution of neutron stars
We have developed a new numerical scheme to solve r-mode oscillations of {\it rapidly rotating polytropic stars} in Newtonian gravity. In this scheme, Euler perturbations of the density, three
R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars
• Physics
• 2001
For analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of differential rotation, because viscosity is not strong enough for differentially rotating
Gravitational radiation from rotational instabilites in compact stellar cores with stiff equations of state.
• Physics, Medicine
Physical review. D, Particles and fields
• 1996
3D numerical simulations of the dynamical instability in rapidly rotating stars initially modeled as polytropes, finding that this instability may operate in a stellar core that has expended its nuclear fuel and is prevented from further collapse due to centrifugal forces.
Numerical Study on the Hydrodynamic Instability of Binary Stars in the First Post Newtonian Approximation of General Relativity
• Physics
• 1997
We present numerical results on the hydrodynamic stability of coalescing binary stars in the first post Newtonian (lPN) approximation of general relativity. We pay particular attention to the
A Survey of the Principal Modes of Nonaxisymmetric Instability in Self-Gravitating Accretion Disk Models
• Physics
• 1997
We present a survey of the three principal nonaxisymmetric modes of instability (the so-called P-, I-, and J-modes) that have been found in rotating, self-gravitating, accretion disk models. The
Linear and nonlinear dynamic instability of rotating polytropes
• Physics
• 1987
A three-dimensional hydrodynamic computer program is used to study the growth of nonaxisymmetric structures in rapidly rotating, self-gravitating polytropes. Models with polytropic index n = 0.8,
Dynamical instability of new-born neutron stars as sources of gravitational radiation
The dynamical instability of new-born neutron stars is studied by evolving the linearized hydrodynamical equations. The neutron stars considered in this paper are those produced by the accretion
Gravitational radiation from rapidly rotating nascent neutron stars
• Physics
• 1995
We study the secular evolution and gravitational wave signature of a newly formed, rapidly rotating neutron star. The neutron star may arise from core collapse in a massive star or from the
Models of rapidly rotating neutron stars: remnants of accretion-induced collapse
• Physics
• 2001
Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion induced collapse of rapidly rotating white dwarfs. The models are