Saturation of the r-Mode Instability

By Philipp Arras, E. Flanagan, S. Morsink, A. Schenk, Saul A. Teukolsky, I. Wasserman. 2002

163 citations recorded by the source corpus.

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 Er-mode/(0.5MrΩ2) ≃ 0.1γgr/Ω ≃ 10-6(νspin/103 Hz)5, where M and r* are the stellar mass and radius, respectively, γgr is the driving rate by gravitational radiation, Ω is the angular velocity of the star, and νspin 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 ≳103-104 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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/00349055fb82379ddbdfad838ed28acee6b4e67e

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Citations in the corpus

Toward Gravitational Wave Signals from Realistic Core-Collapse Supernova Models (2003, background): “Neither do R-modes appear now as a likely energy drain (Arras et al. 2003).”
The Spin Periods and Rotational Profiles of Neutron Stars at Birth (2005, background): “With this, we estimate Ṗ ¼ 1 2 M I P2: ð8Þ Because of the low saturation level, e 0:1 (Arras et al. 2003), and the extreme spin-frequency dependence, r-modes can lead to a factor-of-2 increase within a matter of days in the period of neutron stars that spin close to breakup but will require…”
Presupernova Evolution of Differentially Rotating Massive Stars Including Magnetic Fields (2004, background): “However, Arras et al. (2003) found that the r-mode waves saturate at amplitudes lower than obtained in previous numerical calculations (Lindblom et al. 2001) that assumed an unrealistically large driving force.”
The Masses and Spins of Neutron Stars and Stellar-Mass Black Holes (2014, background): “Stars with more modest initial spin periods may take thousands of years to spin down substantially [136,137].”
The Progenitor Stars of Gamma-Ray Bursts (2005, background): “Gravitational radiation by the r-mode instability does not slow a 1 ms pulsar to a period of 10 ms in a few centuries (Arras et al. 2003) and the dissipation of the rotational energy of a 1 ms pulsar by means other than gravity waves or neutrinos would give much more energy than is observed in a…”
Viscosity and Rotation in Core-Collapse Supernovae (2004, background): “Gravitational radiation (e.g., Ostriker & Gunn 1969), magnetic dipole radiation (e.g., Pacini 1967, 1968; Gunn & Ostriker 1969; Lindblom et al. 2001; Arras et al. 2003), magnetocentrifugal winds (Thompson 2003; Thompson et al. 2004), and late-time fallback (see Woosley & Heger 2003 and references…”
Detecting gravitational wave emission from the known accreting neutron stars (2008, background): “However for all other sources the required amplitude is below the Arras et al. (2003) limit.”