User:Tohline/Apps/RotatingPolytropes/BarmodeLinearTimeDependent

Simulating the Onset of a Barmode Instability

Index of Relevant Publications

Here is a list of relevant research papers as enumerated by …

• Y. Kojima & M. Saijo (2008), Phys. Rev. D, vol. 78, Issue 12, id. 124001: Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined … Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes … CODE: Newtonian, 3D Eulerian, Cartesian, with entropy tracer; reflection symmetry through equatorial plane; <math>~\Gamma=2</math>; Poisson solved with preconditioned conjugate gradient (PCG) method MODEL(s): axisymmetric, n = 1 polytrope; j-constant rotation law with A = 1; their Table I lists four different equilibrium configurations having T/|W| = 0.256, 0.268, 0.277, 0.281.

• J. E. Tohline, R. H. Durisen & M. McCollough (1985), ApJ, 298, 220: The linear and nonlinear dynamic stability of rotating N = 3/2 polytropes

CODE: Newtonian, 3D Eulerian, 1st-order donor-cell on a cylindrical grid; π-symmetry plus reflection symmetry through equatorial plane; <math>~\Gamma=5/3</math>; Poisson solved with FFT + Buneman cyclic reduction MODEL(s): Constructed using Ostriker-Mark SCF method; axisymmetric, n = 3/2 polytrope; n' = 0 rotation law; four different equilibrium configurations having T/|W| = 0.28, 0.30, 0.33, 0.35.

• R. H. Durisen, R. A. Gingold, J. E. Tohline & A. P. Boss (1986), ApJ, 305, 281: Dynamic Fission Instabilities in Rapidly Rotating N = 3/2 Polytropes: A Comparison of Results from Finite-Difference and Smoothed Particle Hydrodynamics Codes
• H. A. Williams & J. E. Tohline (1987), ApJ, 315, 594: Linear and Nonlinear Dynamic Instability of Rotating Polytropes

CODE: Same as in Tohline, Durisen & McCollough (1985), above. MODEL(s): Constructed using Ostriker-Mark SCF method; axisymmetric, n' = 0 rotation law; five different equilibrium configurations having (see column 1 of their Table 1) n = 0.8, 1.0, 1.3, 1.5, 1.8, all having T/|W| = 0.310.

• H. A. Williams & J. E. Tohline (1988), ApJ, 334, 449: Circumstellar Ring Formation in Rapidly Rotating Protostars

Two of the models that were studied in Williams & Tohline (1987) — specifically, the models having n = 0.8 and 1.8 — … are shown as they evolve to extremely nonlinear amplitudes: the end result in both cases is … The models shed a fraction of their mass and angular momentum, producing a ring which surrounds a more centrally condensed object … The central object is a triaxial figure that is rotating about its shortest axis.

• J. L. Houser, J. M. Centrella & S. C. Smith (1994), PRL, 72, 1314: Gravitational radiation from nonaxisymmetric instability in a rotating star
• S. C. Smith, J. L. Houser & J. M. Centrella (1995), ApJ, 458, 236: Simulations of Nonaxisymmetric Instability in a Rotating Star: A Comparison between Eulerian and Smooth Particle Hydrodynamics
• J. L. Houser & J. M. Centrella (1996), Phys. Rev. D, 54, 7278: Gravitational radiation from rotational instabilites in compact stellar cores with stiff equations of state
• J. Toman, J. N. Imamura, B. J. Pickett & R. H. Durisen (1998), ApJ, 497, 370: Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes
• K. C. B. New, J. M. Centrella & J. E. Tohline (2000), Phys. Rev. D, 62, 064019: Gravitational waves from long-duration simulations of the dynamical bar instability
• M. Shibata, T. W. Baumgarte & S. L. Shapiro (2000), ApJ, 542, 453: The Bar-Mode Instability in Differentially Rotating Neutron Stars: Simulations in Full General Relativity
• Y.-T. Liu & L. Lindblom (2001), MNRAS, 324, 1063: Models of rapidly rotating neutron stars: remnants of accretion-induced collapse
• M. Saijo, M. Shibata, T. W. Baumgarte & S. L. Shapiro (2001), ApJ, 548, 919: Dynamical Bar Instability in Rotating Stars: Effect of General Relativity
• J. M. Centrella, K. C. B. New, L. L. Lowe & J. D. Brown (2001), ApJ, 550, L193: Dynamical Rotational Instability at Low T/W
• Y.-T. Liu (2002), Phys. Rev. D, 65, 124003: Dynamical instability of new-born neutron stars as sources of gravitational radiation
• M. Saijo, T. W. Baumgarte & S. L. Shapiro (2003), ApJ, 595, 352: One-armed Spiral Instability in Differentially Rotating Stars
• S. Ou & J. E. Tohline (2006), ApJ, 651, 1068: Unexpected Dynamical Instabilities in Differentially Rotating Neutron Stars
• L. Baiotti, R. De Pietri, G. M. Manco & L. Rezzolla (2007), Phys. Rev. D, 75, 044023: Accurate simulations of the dynamical bar-mode instability in full general relativity
• P. Cerda-Duran, V. Quilos & J. A. Font (2007), Comp. Phys. Comm., 177, 288: AMR simulations of the low T/|W| bar-mode instability of neutron stars
• S. Ou, J. E. Tohline & P. M. Motl (2007), ApJ, 665, 1074: Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars
• M. Saijo & Y. Kojima (2008), Phys. Rev. D, 77, 063002: Faraday resonance in dynamical bar instability of differentially rotating stars

Additional references identified through the above set of references:

• M. Saijo (2018), Phys. Rev. D, 98, 024003: Determining the stiffness of the equation of state using low T/W dynamical instabilities in differentially rotating stars

We investigate the nature of low T/W dynamical instabilities in various ranges of the stiffness of the equation of state in differentially rotating stars … We analyze these instabilities in both a linear perturbation analysis and a three-dimensional hydrodynamical simulation … the nature of the eigenfunction that oscillates between corotation and the surface for an unstable star requires reinterpretation of pulsation modes in differentially rotating stars.

See Also

• Our discussion of Rotating White Dwarfs: Example Equilibria
• Fission Theory of Binary Star Formation

© 2014 - 2021 by Joel E. Tohline |   H_Book Home   |   YouTube   | Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS | Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation