### Abstract

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with differential rotation. We perform fully relativistic three-dimensional simulations of compact stars with M/R ≥ 0.1, where M is the total gravitational mass and R the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index Γ = 2. As in Newtonian theory, we find that stars above a critical value of β ≡ T/W (where T is the rotational kinetic energy and W the gravitational binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation profile, the critical value of β = β_{dGR} is ∼0.24-0.25, only slightly smaller than the well-known Newtonian value ∼0.27 for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of differential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large β subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large β ≳ β_{dGR} do not develop spiral arms or eject mass but adjust to form dynamically stable ellipsoidal-like configurations. If the bar-mode instability is triggered in supernova collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies.

Original language | English (US) |
---|---|

Pages (from-to) | 453-463 |

Number of pages | 11 |

Journal | Astrophysical Journal |

Volume | 542 |

Issue number | 1 PART 1 |

State | Published - Oct 10 2000 |

### Keywords

- Dense matter
- Relativity
- Stars: neutron
- Stars: rotation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

## Fingerprint Dive into the research topics of 'The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity'. Together they form a unique fingerprint.

## Cite this

*Astrophysical Journal*,

*542*(1 PART 1), 453-463.