Dynamical bar instability in rotating stars

Effect of general relativity

Motoyuki Saijo, Masaru Shibata, Thomas W. Baumgarte, Stuart L. Shapiro

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

We study the dynamical stability against bar-mode deformation of rapidly and differentially rotating stars in the first post-Newtonian approximation of general relativity. We vary the compaction of the star M/R (where M is the gravitational mass and R the equatorial circumferential radius) between 0.01 and 0.05 to isolate the influence of relativistic gravitation on the instability. For compactions in this moderate range, the critical value of β ≡ T/W for the onset of the dynamical instability (where T is the rotational kinetic energy and W the gravitational binding energy) slightly decreases from ∼0.26 to ∼0.25 with increasing compaction for our choice of the differential rotational law. Combined with our earlier findings based on simulations in full general relativity for stars with higher compaction, we conclude that relativistic gravitation enhances the dynamical bar-mode instability, i.e., the onset of instability occurs for smaller values of β in relativistic gravity than in Newtonian gravity. We also find that once a triaxial structure forms after the bar-mode perturbation saturates in dynamically unstable stars, the triaxial shape is maintained, at least for several rotational periods. To check the reliability of our numerical integrations, we verify that the general relativistic Kelvin-Helmholtz circulation is well conserved, in addition to rest-mass energy, total mass energy, and linear and angular momentum. Conservation of circulation indicates that our code is not seriously affected by numerical viscosity. We determine the amplitude and frequency of the quasi-periodic gravitational waves emitted during the bar formation process using the quadrupole formula.

Original languageEnglish
Pages (from-to)919-931
Number of pages13
JournalAstrophysical Journal
Volume548
Issue number2 PART 1
DOIs
Publication statusPublished - 2001 Feb 20
Externally publishedYes

Fingerprint

relativity
compaction
stars
gravitation
gravity
energy
gravitational binding energy
angular momentum
kinetic energy
numerical integration
viscosity
gravitational waves
perturbation
conservation
quadrupoles
effect
momentum
radii
simulation
approximation

Keywords

  • Gravitation
  • Hydrodynamics
  • Instabilities
  • Relativity
  • Stars: neutron
  • Stars: rotation

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

Saijo, M., Shibata, M., Baumgarte, T. W., & Shapiro, S. L. (2001). Dynamical bar instability in rotating stars: Effect of general relativity. Astrophysical Journal, 548(2 PART 1), 919-931. https://doi.org/10.1086/319016

Dynamical bar instability in rotating stars : Effect of general relativity. / Saijo, Motoyuki; Shibata, Masaru; Baumgarte, Thomas W.; Shapiro, Stuart L.

In: Astrophysical Journal, Vol. 548, No. 2 PART 1, 20.02.2001, p. 919-931.

Research output: Contribution to journalArticle

Saijo, M, Shibata, M, Baumgarte, TW & Shapiro, SL 2001, 'Dynamical bar instability in rotating stars: Effect of general relativity', Astrophysical Journal, vol. 548, no. 2 PART 1, pp. 919-931. https://doi.org/10.1086/319016
Saijo M, Shibata M, Baumgarte TW, Shapiro SL. Dynamical bar instability in rotating stars: Effect of general relativity. Astrophysical Journal. 2001 Feb 20;548(2 PART 1):919-931. https://doi.org/10.1086/319016
Saijo, Motoyuki ; Shibata, Masaru ; Baumgarte, Thomas W. ; Shapiro, Stuart L. / Dynamical bar instability in rotating stars : Effect of general relativity. In: Astrophysical Journal. 2001 ; Vol. 548, No. 2 PART 1. pp. 919-931.
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