Nonlinear evolution of the r-modes in neutron stars.
TL;DR: The evolution of a neutron-star r-mode driven unstable by gravitational radiation is studied here using numerical solutions of the full nonlinear fluid equations to study the nonlinear evolution of the mode.
Abstract: The evolution of a neutron-star $r$-mode driven unstable by gravitational radiation is studied here using numerical solutions of the full nonlinear fluid equations. The dimensionless amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about $40%$ of its initial angular momentum and $50%$ of its rotational kinetic energy before the mode is damped. The nonlinear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and poles of the star.
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TL;DR: In this article, it was shown that only sources spinning at frequencies above a few hundred Hertz can be unstable to r-modes and derived a more stringent universal r-mode spindown limit on their gravitational wave signal, exploiting the fact that the rmode saturation amplitude is insensitive to the structural properties of individual sources.
Abstract: Neutron stars undergoing r-mode oscillation emit gravitational radiation that might be detected on earth. For known millisecond pulsars the observed spindown rate imposes an upper limit on the possible gravitational wave signal of these sources. Taking into account the physics of r-mode evolution, we show that only sources spinning at frequencies above a few hundred Hertz can be unstable to r-modes, and we derive a more stringent universal r-mode spindown limit on their gravitational wave signal, exploiting the fact that the r-mode saturation amplitude is insensitive to the structural properties of individual sources. We find that this refined bound limits the gravitational wave strain from millisecond pulsars to values below the detection sensitivity of next-generation detectors. Young sources are therefore a more promising option for the detection of gravitational waves emitted by r-modes and to probe the interior composition of compact stars in the near future.
44 citations
TL;DR: In this paper, the authors describe two aspects of the physics of hybrid stars that have a sharp interface between a core of quark matter and a mantle of nuclear matter, and propose a mechanism for the damping of density oscillations, including r-modes, in hybrid stars with sharp interface.
Abstract: We describe two aspects of the physics of hybrid stars that have a sharp interface between a core of quark matter and a mantle of nuclear matter.
Firstly, we analyze the mass-radius relation. We describe a generic "Constant Speed of Sound" (CSS) parameterization of the quark matter equation of state (EoS), in which the speed of sound is independent of density. In terms of the three parameters of the CSS EoS we obtain the phase diagram of possible forms of the hybrid star mass-radius relation, and we show how observational constraints on the maximum mass and typical radius of neutron stars can be expressed as constraints on the CSS parameters.
Secondly, we propose a mechanism for the damping of density oscillations, including r-modes, in hybrid stars with a sharp interface. The dissipation arises from the periodic conversion between quark matter and nuclear matter induced by the pressure oscillations in the star. We find the damping grows nonlinearly with the amplitude of the oscillation and is powerful enough to saturate an r-mode at very low saturation amplitude, of order $10^{-10}$, which is compatible with currently-available observations of neutron star spin frequencies and temperatures.
43 citations
Cites background from "Nonlinear evolution of the r-modes ..."
... saturating unstable r-modes at a sat . 10 810 7 [39,34,40]. Previously proposed mechanisms have problems to achieve this. Suprathermal bulk viscosity and hydrodynamic oscillations both give a sat ˘1 [41,42]. The nonlinear coupling of the r-mode to viscously damped daughter modes could give a sat ˘10 6 to 10 3 [43,44]. The recently proposed vortex-fluxtube cutting mechanism [45] might give sufficiently sma...
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TL;DR: In this article, the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star were discussed.
Abstract: The loss of angular momentum owing to unstable r-modes in hot young neutron stars has been proposed as a mechanism for achieving the spin rates inferred for young pulsars. One factor that could have a significant effect on the action of the r-mode instability is fallback of supernova remnant material. The associated accretion torque could potentially counteract any gravitational-wave-induced spin-down, and accretion heating could affect the viscous damping rates and hence the instability. We discuss the effects of various external agents on the r-mode instability scenario within a simple model of supernova fallback on to a hot young magnetized neutron star. We find that the outcome depends strongly on the strength of the magnetic field of the star. Our model is capable of generating spin rates for young neutron stars that accord well with initial spin rates inferred from pulsar observations. The combined action of r-mode instability and fallback appears to cause the spin rates of neutron stars born with very different spin rates to converge, on a time-scale of approximately 1 year. The results suggest that stars with magnetic fields ?1013 G could emit a detectable gravitational wave signal for perhaps several years after the supernova event. Stars with higher fields (magnetars) are unlikely to emit a detectable gravitational wave signal via the r-mode instability. The model also suggests that the r-mode instability could be extremely effective in preventing young neutron stars from going dynamically unstable to the bar-mode.
41 citations
TL;DR: In this article, the authors investigated the role of differential rotation in the evolution of the instability of a newly born, hot, rapidly-rotating neutron star and showed that the amplitude of the mode saturates a few hundred seconds after the mode instability sets in.
Abstract: Recent work has shown that differential rotation, producing large scale drifts of fluid elements along stellar latitudes, is an unavoidable feature of $r$-modes in the nonlinear theory. We investigate the role of this differential rotation in the evolution of the $l=2$ $r$-mode instability of a newly born, hot, rapidly-rotating neutron star. It is shown that the amplitude of the $r$-mode saturates a few hundred seconds after the mode instability sets in. The saturation amplitude depends on the amount of differential rotation at the time the instability becomes active and can take values much smaller than unity. It is also shown that, independently of the saturation amplitude of the mode, the star spins down to rotation rates that are comparable to the inferred initial rotation rates of the fastest pulsars associated with supernova remnants. Finally, it is shown that, when the drift of fluid elements at the time the instability sets in is significant, most of the initial angular momentum of the star is transferred to the $r$-mode and, consequently, almost none is carried away by gravitational-radiation.
40 citations
TL;DR: In this article, a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes, is investigated.
Abstract: The differential rotation of r-modes is investigated within the nonlinear theory up to second order in the mode amplitude in the case of a slowly rotating, Newtonian, barotropic, perfect-fluid star. We find a nonlinear extension of the linear r-mode, which represents differential rotation that produces large scale drifts of fluid elements along stellar latitudes. This solution includes a piece induced by first-order quantities and another one that is a pure second-order effect. Since the latter is stratified on cylinders, it cannot cancel differential rotation induced by first-order quantities, which is not stratified on cylinders. It is shown that, unlike the situation in the linearized theory, r-modes do not preserve the vorticity of fluid elements at second order. It is also shown that the physical angular momentum and energy of the perturbation are, in general, different from the corresponding canonical quantities.
38 citations