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Saturation of the r-Mode Instability

Arras, Phil and Flanagan, Eanna E. and Morsink, Sharon M. and Schenk, A. Katrin and Teukolsky, Saul A. and Wasserman, Ira (2003) Saturation of the r-Mode Instability. Astrophysical Journal, 591 (2). pp. 1129-1151. ISSN 0004-637X. doi:10.1086/374657.

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Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because of the emission of gravitational radiation. As a result, the stellar rotational energy is converted into both gravitational waves and r-mode energy. The saturation level for the r-mode energy is a fundamental parameter needed to determine how fast the neutron star spins down, as well as whether gravitational waves will be detectable. In this paper we study saturation by nonlinear transfer of energy to the sea of stellar "inertial" oscillation modes that arise in rotating stars with negligible buoyancy and elastic restoring forces. We present detailed calculations of stellar inertial modes in the WKB limit, their linear damping by bulk and shear viscosity, and the nonlinear coupling forces among these modes. The saturation amplitude is derived in the extreme limits of strong or weak driving by radiation reaction, as compared to the damping rate of low-order inertial modes. In the weak driving case, energy can be stably transferred to a small number of modes, which damp the energy as heat or neutrinos. In the strong driving case, we show that a turbulent cascade develops, with a constant flux of energy to large wavenumbers and small frequencies where it is damped by shear viscosity. We find that the saturation energy is extremely small, at least 4 orders of magnitude smaller than that found by previous investigators. We show that the large saturation energy found in the simulations of Lindblom and coworkers is an artifact of their unphysically large radiation reaction force. In most physical situations of interest, for either nascent, rapidly rotating neutron stars or neutron stars being spun up by accretion in low-mass X-ray binaries (LMXBs), the strong driving limit is appropriate and the saturation energy is roughly E_(r-mode)/(0.5Mr^2_+Ω^2) sime 0.1γgr/Ω ≃ 10^(-6)(ν_(spin)/10^3 Hz)^5, where M and r* are the stellar mass and radius, respectively, γ_(gr) is the driving rate by gravitational radiation, Ω is the angular velocity of the star, and ν_(spin) is the spin frequency. At such a low saturation amplitude, the characteristic time for the star to exit the region of r-mode instability is ≳ 10^3-10^4 yr, depending sensitively on the instability curve. Although our saturation amplitude is smaller than that found by previous investigators, it is still sufficiently large to explain the observed period clustering in LMXBs. We find that the r-mode signal from both newly born neutron stars and LMXBs in the spin-down phase of Levin's limit cycle will be detectable by enhanced LIGO detectors out to ~100-200 kpc.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Morsink, Sharon M.0000-0003-4357-0575
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2003. The American Astronomical Society. Received 2002 February 18; accepted 2003 February 4. It is a pleasure to acknowledge many useful conversations on stellar oscillations with Yanqin Wu. P. A. would also like to thank Chris Matzner, Chris Thompson, and Maxim Lyutikov. Part of this work was completed when two of us (P. A. and S. M.) were at the Institute for Theoretical Physics at the Spin and Magnetism in Young Neutron Stars workshop. We thank Lars Bildsten for his gracious hospitality and for a number of useful conversations and John Friedman, Curt Cutler, and Peter Goldreich for useful comments on the manuscript. P. A. is supported by an NSERC Fellowship. This work was supported in part by NSF grants PHY 99-00672 and PHY 00-84729 at Cornell University. E. E. F. was supported by NSF grants PHY 97-22189 and PHY 01-40209 and by the Alfred P. Sloan Foundation. S. M. received support from NSERC.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
NSFPHY 99-00672
NSFPHY 00-84729
NSFPHY 97-22189
NSFPHY 01-40209
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:gravitational waves; stars: neutron; stars: oscillations; turbulence
Issue or Number:2
Record Number:CaltechAUTHORS:20180605-155948780
Persistent URL:
Official Citation:Phil Arras et al 2003 ApJ 591 1129
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86811
Deposited By: George Porter
Deposited On:06 Jun 2018 15:01
Last Modified:15 Nov 2021 20:42

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