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 paper, the authors investigate the dredge-up and mixing during the merger of two white dwarfs with different chemical compositions by conducting hydrodynamic simulations of binary mergers for three representative mass ratios.
Abstract: We present the results of an investigation of the dredge-up and mixing during the merger of two white dwarfs with different chemical compositions by conducting hydrodynamic simulations of binary mergers for three representative mass ratios. In all the simulations, the total mass of the two white dwarfs is $\lesssim1.0~{\rm M_\odot}$. Mergers involving a CO and a He white dwarf have been suggested as a possible formation channel for R Coronae Borealis type stars, and we are interested in testing if such mergers lead to conditions and outcomes in agreement with observations. Even if the conditions during the merger and subsequent nucleosynthesis favor the production of $^{18}{\mathrm O}$, the merger must avoid dredging up large amounts of $^{16}{\mathrm O}$, or else it will be difficult to produce sufficient $^{18}{\mathrm O}$ to explain the oxygen ratio observed to be of order unity. We performed a total of 9 simulations using two different grid-based hydrodynamics codes using fixed and adaptive meshes, and one smooth particle hydrodynamics (SPH) code. We find that in most of the simulations, $>10^{-2}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ is indeed dredged up during the merger. However, in SPH simulations where the accretor is a hybrid He/CO white dwarf with a $\sim 0.1~{\rm M_\odot}$ layer of helium on top, we find that no $^{16}{\mathrm O}$ is being dredged up, while in the $q=0.8$ simulation $<10^{-4}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ has been brought up, making a WD binary consisting of a hybrid CO/He WD and a companion He WD an excellent candidate for the progenitor of RCB stars.
17 citations
TL;DR: In this article, the coupling coefficients between the r-modes are computed in the weakly nonlinear regime of fluid dynamics and the properties of these coupling coefficients and the types of resonances possible are discussed.
Abstract: The r-modes of neutron stars can be driven to instability by gravitational radiation. While linear perturbation theory predicts the existence of this instability, linear theory cannot provide any information about the nonlinear development of the instability. The subject of this paper is the weakly nonlinear regime of fluid dynamics. In the weakly nonlinear regime, the nonlinear fluid equations are approximated by an infinite set of oscillators that are coupled together so that terms quadratic in the mode amplitudes are kept in the equations of motion. In this paper, the coupling coefficients between the r-modes are computed. The stellar model assumed is a polytropic model in which a source of buoyancy is included so that the Schwarzschild discriminant is nonzero. The properties of these coupling coefficients and the types of resonances possible are discussed in this paper. It is shown that no exact resonance involving the unstable l = m = 2 r-mode occurs and that only a small number of modes have a dimensionless coupling constant larger than unity. However, an infinite number of resonant mode triplets exist that couple indirectly to the unstable r-mode. All couplings in this paper involve the l > |m| r-modes that only exist if the star is slowly rotating. This work is complementary to that of Schenk and coworkers in 2002, who consider rapidly rotating stars that are neutral to convection.
16 citations
TL;DR: In this paper, the authors studied the evolution of isolated stars synthetically, considering the influence of {it r-}mode instability on the spin-down of the stars, and they showed that the cooling of these color superconducting stars is very slow, and the stars can remain high temperature within million years differing completely from previous understanding.
Abstract: We studied the evolution of isolated strange stars synthetically, considering the influence of {\it r-}mode instability. Our results show that the cooling of strange stars with non-ultra strong magnetic fields is delayed by the heating due to the {\it r-}modes damping during million years, while the spin-down of the stars is dominated by gravitational radiation. Especially for the strange stars in a possible existing color-flavor locked phase, the effect of the {\it r-}mode instability on the evolution of the stars becomes extremely important since the viscosity, the neutrino emissivity, and the specific heat involving paring quarks are blocked. It leads to the cooling of these color superconducting stars is very slow, and the stars can remain high temperature within million years differing completely from previous understanding. In this case, a strange star in color-flavor locked phase can be located at the bottom of its {\it r-}mode instability window for a long time, but does not spin down to a very low frequency within hours.
16 citations
TL;DR: In this paper, the authors investigated the influence of the differential rotation on the long-term evolution of isolated NSs and NSs in low-mass X-ray binaries, where the viscous damping of the r-modes and its resultant effects were taken into account.
Abstract: In a second-order r-mode theory, Sa and Tome found that the r-mode oscillation in neutron stars (NSs) could induce stellar differential rotation, which naturally leads to a saturated state of the oscillation. Based on a consideration of the coupling of the r-modes and the stellar spin and thermal evolution, we carefully investigate the influences of the differential rotation on the long-term evolution of isolated NSs and NSs in low-mass X-ray binaries, where the viscous damping of the r-modes and its resultant effects are taken into account. The numerical results show that, for both kinds of NSs, the differential rotation can significantly prolong the duration of the r-modes. As a result, the stars can keep nearly a constant temperature and constant angular velocity for over a thousand years. Moreover, the persistent radiation of a quasi-monochromatic gravitational wave would also be predicted due to the long-term steady r-mode oscillation and stellar rotation. This increases the detectability of gravitational waves from both young isolated and old accreting NSs.
16 citations
TL;DR: In this paper, the authors studied the evolution of isolated strange stars (SSs) synthetically, considering the influence of r-mode instability on the cooling of SSs with non-ultrastrong magnetic fields.
Abstract: We studied the evolution of isolated strange stars (SSs) synthetically, considering the influence of r-mode instability. Our results show that the cooling of SSs with non-ultrastrong magnetic fields is delayed by heating due to r-mode damping for millions of years, while the spin-down of the stars is dominated by gravitational radiation (GR). Especially for the SSs in a possible existing colour-flavour locked (CFL) phase, the effect of r-mode instability on the evolution of stars becomes extremely important because the viscosity, neutrino emissivity and specific heat involving pairing quarks are blocked. It leads to the cooling of these colour superconducting stars being very slow and the stars can remain at high temperature for millions of years, which differs completely from previous understanding. In this case, an SS in CFL phase can be located at the bottom of its r-mode instability window for a long time, but does not spin-down to a very low frequency for hours.
15 citations