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, the thermal evolution of neutron stars is investigated by coupling with the evolution of the second order mode instability, which is described by a second-order model, and the heating effect due to shear viscous damping of the $\textit{r}$-modes enables us to understand the high temperature of two young pulsars (i.e., PSR B0531+21 and RX J0822-4300) in the framework of the simple $npe$ NS model.
Abstract: The thermal evolution of neutron stars (NSs) is investigated by coupling with the evolution of $\textit{r}$-mode instability that is described by a second order model.The heating effect due to shear viscous damping of the $\textit{r}$-modes enables us to understand the high temperature of two young pulsars (i.e., PSR B0531+21 and RX J0822-4300) in the framework of the simple $npe$ NS model, without superfluidity or exotic particles.Moreover, the light curves predicted by the model within an acceptable parameter regime may probably cover all of the young and middle-aged pulsars in the $\lg T_s^{\infty}-\lg t$ panel, and an artificially strong $p$ superfluidity invoked in some early works is not needed here. Additionally, by considering the radiative viscous damping of the $\textit{r}$-modes, a surprising extra cooling effect is found, which can even exceed the heating effect sometimes although plays an ignorable role in the thermal history.
01 Jan 2002
TL;DR: In this article, the authors review the relevance of a stellar magnetic field, its modifications under the action of the r-mode instability, and how the interaction between rmode oscillations and a magnetic field might limit the onset and duration of the instability.
Abstract: The instability of r-mode oscillations in rapidly rotating neutron stars has been so far a source of surprises The analyses carried to date have revealed the surprising existence of this instability and, perhaps even more surprisingly, have shown that such instability has a rather large parameter space in which it can survive against the damping produced by shear and bulk viscosity, as well as against the interaction with a solid star crust The magnetohydrodynamic coupling of the modes with a stellar magnetic field, which is likely to be present, has recently been shown to provide another surprising aspect of the instability We here review the relevance of a stellar magnetic field, its modifications under the action of the r-mode instability, and how the interaction between r-mode oscillations and a magnetic field might limit the onset and duration of the instability
01 Jan 2022
TL;DR: In this article , several macroscopic applications of the closed contour dynamics problem were studied by using theorems for differential geometry. And the first application presented is the study of the geometry of trajectories of charged particles in magnetic fields.
Abstract: AbstractIn this chapter we study several macroscopic applications of the closed contour dynamics problem by using theorems for differential geometry. A first application presented is the study of the geometry of trajectories of charged particles in magnetic fields. We present some closeness trajectories criteria based on Bonnet and Fenchel theorems.
16 Jul 2021
TL;DR: In this paper, an algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which is relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops.
Abstract: Irrotational flow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schr\"odinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for $\ensuremath{\alpha}$-particle clustering nuclei.
TL;DR: In this article, the second order perturbations of a perfect fluid non-rotating compact star were investigated in the time domain, where the radial and non-radial perturbation parameters were separately parameterized.
Abstract: This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions.
As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative order this configuration does not exhibit any gravitational radiation, we have found a new interesting gravitational signal at non-linear order, in which the radial normal modes are precisely mirrored. In addition, a resonance effect is present when the frequencies of the radial pulsations are close to the first axial w-mode. Finally, we have roughly estimated the damping times of the radial pulsations due to the non-linear gravitational emission. The coupling near the resonance results to be a very effective mechanism for extracting energy from the radial oscillations.