Nonlinear coupling network to simulate the development of the r mode instability in neutron stars. II. Dynamics

Journal Article · Tue Mar 15 00:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.064029· OSTI ID:20708906

Brink, Jeandrew; Teukolsky, Saul A; Wasserman, Ira ^[1]

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1. Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853 (United States)

Two mechanisms for nonlinear mode saturation of the r mode in neutron stars have been suggested: the parametric instability mechanism involving a small number of modes and the formation of a nearly continuous Kolmogorov-type cascade. Using a network of oscillators constructed from the eigenmodes of a perfect fluid incompressible star, we investigate the transition between the two regimes numerically. Our network includes the 4995 inertial modes up to n{<=}30 with 146 998 direct couplings to the r mode and 1 306 999 couplings with detuning <0.002 (out of a total of approximately 10{sup 9} possible couplings). The lowest parametric instability thresholds for a range of temperatures are calculated and it is found that the r mode becomes unstable to modes with 13<n<15. In the undriven, undamped, Hamiltonian version of the network the rate to achieve equipartition is found to be amplitude dependent, reminiscent of the Fermi-Pasta-Ulam problem. More realistic models driven unstable by gravitational radiation and damped by shear viscosity are explored next. A range of damping rates, corresponding to temperatures 10{sup 6} K to 10{sup 9} K, is considered. Exponential growth of the r mode is found to cease at small amplitudes {approx_equal}10{sup -4}. For strongly damped, low temperature models, a few modes dominate the dynamics. The behavior of the r mode is complicated, but its amplitude is still no larger than about 10{sup -4} on average. For high temperature, weakly damped models the r mode feeds energy into a sea of oscillators that achieve approximate equipartition. In this case the r-mode amplitude settles to a value for which the rate to achieve equipartition is approximately the linear instability growth rate.

• OSTI ID: 20708906
• Journal Information: Physical Review. D, Particles Fields, Vol. 71, Issue 6; Other Information: DOI: 10.1103/PhysRevD.71.064029; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COSMOLOGY
COUPLING
DAMPING
EIGENFUNCTIONS
EIGENVALUES
GRAVITATIONAL RADIATION
GRAVITATIONAL WAVES
HAMILTONIANS
IDEAL FLOW
INSTABILITY GROWTH RATES
NEUTRON STARS
NONLINEAR PROBLEMS
OSCILLATORS
PARAMETRIC INSTABILITIES
PULSATIONS
SHEAR
VISCOSITY