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Register a new userViscous Boundary Layer Damping of R-Modes in Neutron Stars
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Authors
Lars Bildsten
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Recent work has raised the exciting possibility that r-modes (Rossby waves) in rotating neutron star cores might be strong gravitational wave sources. We estimate the effect of a solid crust on their viscous damping rate and show that the dissipation rate in the viscous boundary layer between the oscillating fluid and the nearly static crust is >10^5 times higher than that from the shear throughout the interior. This increases the minimum frequency for the onset of the gravitational r-mode instability to at least 500 Hz when the core temperature is less than 10^10 K. It eliminates the conflict of the r-mode instability with the accretion-driven spin-up scenario for millisecond radio pulsars and makes it unlikely that the r-mode instability is active in accreting neutron stars. For newborn neutron stars, the formation of a solid crust shortly after birth affects their gravitational wave spin-down and hence detectability by ground-based interferometric gravitational wave detectors.
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Superfluid hydrodynamics affects the spin-evolution of mature neutron stars, and may be key to explaining timing irregularities such as pulsar glitches. However, most models for this phenomenon exclude the global instability required to trigger the event. In this paper we discuss a mechanism that may fill this gap. We establish that small scale inertial r-modes become unstable in a superfluid neutron star that exhibits a rotational lag, expected to build up due to vortex pinning as the star spins down. Somewhat counterintuitively, this instability arises due to the (under normal circumstances dissipative) vortex-mediated mutual friction. We explore the nature of the superfluid instability for a simple incompressible model, allowing for entrainment coupling between the two fluid components. Our results recover a previously discussed dynamical instability in systems where the two components are strongly coupled. In addition, we demonstrate for the first time that the system is secularly unstable (with a growth time that scales with the mutual friction) throughout much of parameter space. Interestingly, large scale r-modes are also affected by this new aspect of the instability. We analyse the damping effect of shear viscosity, which should be particularly efficient at small scales, arguing that it will not be sufficient to completely suppress the instability in astrophysical systems.
R-modes in neutron stars with crusts are damped by viscous friction at the crust-core boundary. The magnitude of this damping, evaluated by Bildsten and Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the maximum spin frequency for a neutron star spun up by accretion in a Low-Mass X-ray binary (LMXB). In this paper we explore the mechanical coupling between the core r-modes and the elastic crust, using a toy model of a constant density neutron star with a constant shear modulus crust. We find that, at spin frequencies in excess of ~50 Hz, the r-modes strongly penetrate the crust. This reduces the relative motion (slippage) between the crust and the core compared to the rigid crust limit. We therefore revise down, by as much as a factor of 10^2-10^3, the damping rate computed by BU, significantly reducing the maximal possible spin frequency of neutron star with a solid crust. The dependence of the crust-core slippage on the spin frequency is complicated, and is very sensitive to the physical thickness of the crust. If the crust is sufficiently thick, the curve of the critical spin frequency for the onset of the r-mode instability becomes multi-valued for some temperatures; this is related to the avoided crossings between the r-mode and the higher-order torsional modes in the crust. The critical frequencies are comparable to the observed spins of neutron stars in LMXBs and millisecond pulsars.
We study how the frequencies and damping times of oscillations of a newly born, hot proto-neutron star depend on the physical quantities which characterize the star quasi-stationary evolution which follows the bounce. Stellar configurations are modeled using a microscopic equation of state obtained within the Brueckner-Hartree-Fock, nuclear many-body approach, extended to the finite-temperature regime. We discuss the mode frequency behaviour as function of the lepton composition, and of the entropy gradients which prevail in the interior of the star. We find that, in the very early stages, gravitational wave emission efficiently competes with neutrino processes in dissipating the star mechanical energy residual of the gravitational collapse.
We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the stars surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.
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