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

Brink, Jeandrew and Teukolsky, Saul A. and Wasserman, Ira (2005) Nonlinear coupling network to simulate the development of the r mode instability in neutron stars. II. Dynamics. Physical Review D, 71 (6). Art. No. 064029. ISSN 2470-0010. doi:10.1103/PhysRevD.71.064029.

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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 10^9 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 10^6  K to 10^9  K, is considered. Exponential growth of the r mode is found to cease at small amplitudes ≈10^(−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^(−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.

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Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2005 The American Physical Society. Received 25 October 2004; published 31 March 2005. Thanks to Larry Kidder for helping with parallelization of the code and numerous other technical details. This research is supported in part by NSF Grant No. AST-0307273, No. PHY-9900672, and No. PHY-0312072 at Cornell University.
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Issue or Number:6
Record Number:CaltechAUTHORS:20180606-090026723
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86823
Deposited By: Tony Diaz
Deposited On:06 Jun 2018 16:39
Last Modified:15 Nov 2021 20:42

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