A rapidly rotating, axisymmetric star can be dynamically unstable to an m=2
"bar" mode that transforms the star from a disk shape to an elongated bar. The
fate of such a bar-shaped star is uncertain. Some previous numerical studies
indicate that the bar is short lived, lasting for only a few bar-rotation
periods, while other studies suggest that the bar is relatively long lived.
This paper contains the results of a numerical simulation of a rapidly rotating
gamma=5/3 fluid star. The simulation shows that the bar shape is long lived:
once the bar is established, the star retains this shape for more than 10
bar-rotation periods, through the end of the simulation. The results are
consistent with the conjecture that a star will retain its bar shape
indefinitely on a dynamical time scale, as long as its rotation rate exceeds
the threshold for secular bar instability. The results are described in terms
of a low density neutron star, but can be scaled to represent, for example, a
burned-out stellar core that is prevented from complete collapse by centrifugal
forces. Estimates for the gravitational-wave signal indicate that a dynamically
unstable neutron star in our galaxy can be detected easily by the first
generation of ground based gravitational-wave detectors. The signal for an
unstable neutron star in the Virgo cluster might be seen by the planned
advanced detectors. The Newtonian/quadrupole approximation is used throughout
this work.Comment: Expanded version to be published in Phys. Rev. D: 13 pages, REVTeX,
13 figures, 9 TeX input file
