Linear Stability Analysis of Differentially Rotating Polytropes: New Results for the<i>m</i> = 2<i>f</i>‐Mode Dynamical Instability

Karino, Shotaro; Eriguchi, Yoshiharu

doi:10.1086/375768

Cited by 28 publications

(23 citation statements)

References 32 publications

(38 reference statements)

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“…Interestingly, the resulting number β c (M * = 0) = 0.266 is in very good agreement with the value of β c = 0.266 obtained in Newtonian gravity [13] through a linear stability analysis for a sequence of equilibrium models with the same polytropic index and degree of differential rotation as used here. This agreement represents an additional confirmation of the accuracy and robustness of our extrapolation method in determining the position of the threshold.…”

Section: 9supporting

confidence: 85%

Dynamical non-axisymmetric instabilities in rotating relativistic stars

Manca

Baiotti

Pietri

et al. 2007

Class. Quantum Grav.

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We present new results on dynamical instabilities in rapidly rotating relativistic stars. In particular, using numerical simulations in full general relativity, we analyse the effects that the stellar compactness has on the threshold for the onset of the dynamical bar-mode instability, as well as on the appearance of other dynamical instabilities. By using an extrapolation technique developed and tested in our previous study (Baiotti L et al 2007 Phys. Rev. D 75 044023), we explicitly determine the threshold for a wide range of compactnesses using four sequences of models of constant baryonic mass comprising a total of 59 stellar models. Our calculation of the threshold is in good agreement with the Newtonian prediction and improves the previous post-Newtonian estimates. In addition, we find that for stars with sufficiently large mass and compactness, the m = 3 deformation is the fastest growing one. For all of the models considered, the non-axisymmetric instability is suppressed on a dynamical timescale with an m = 1 deformation dominating the final stages of the instability. These results, together with those presented in Baiotti L et al (2007 Phys. Rev. D 75 044023), suggest that an m = 1 deformation represents a general and latetime feature of non-axisymmetric dynamical instabilities both in full general relativity and in Newtonian gravity.

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Section: 9supporting

confidence: 85%

Dynamical non-axisymmetric instabilities in rotating relativistic stars

Manca

Baiotti

Pietri

et al. 2007

Class. Quantum Grav.

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“…the m = 2 instability which takes place when β is larger than the threshold β c [7]. Previous results for the onset of the classical bar-mode instability have already shown that the critical value β c for the onset of the instability is not a universal quantity and it is strongly influenced by the rotational profile [15,16], by relativistic effects [6,7], and, in a quantitative way, by the compactness [17].…”

Section: Introductionmentioning

confidence: 92%

“…For all these models (except for G2.25M0.5b0.255 and G2.25M1.0b0.255) it is indeed possible to extract the main features of the m = 2 mode using the trial function detailed in Eq. (16). As in [11], we decided to quantify the properties of the bar-mode instability by means of a non-linear fit, using the trial dependence of Eq.…”

Section: B General Features Of the Evolution Above The Threshold Formentioning

confidence: 99%

Stiffness effects on the dynamics of the bar-mode instability of neutron stars in full general relativity

et al. 2015

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We present results on the effect of the stiffness of the equation of state on the dynamical barmode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change in the threshold for the emergence of the instability for a range of the adiabatic Γ index from 2.0 to 3.0, including two values chosen to mimic more realistic equations of state at high densities.PACS numbers: 04.25. 04.40.Dg, 95.30.Lz, 97.60.Jd

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“…The dynamical bar-instability usually develops when the ratio β = T /W is high enough, e.g. β > ∼ 0.25 -0.27 [4,18], where T is the rotational kinetic energy and W is the gravitational binding energy (however, for extreme degrees of differential rotation a bar-instability may also develop for stars with very low β [19][20][21]; moreover, an m = 1 one-armed spiral mode may also become dynamically unstable for stars with a very soft equation of state and a high degree of differential rotation [31,32]). A hot, proto-neutron star formed a few milliseconds after core bounce may not have a sufficiently high value of β to trigger the dynamical barinstability immediately.…”

Section: Introductionmentioning

confidence: 99%

Magnetic braking in differentially rotating, relativistic stars

Liu

Shapiro

2004

Phys. Rev. D

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We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars, according to general relativity. The remnant of a binary neutron star merger or supernova core collapse may produce such a "hypermassive" neutron star. Although a hypermassive neutron star may be stable on a dynamical timescale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we treat the slowrotation, weak-magnetic field limit in which Erot ≪ Emag ≪ W , where Erot is the rotational kinetic energy, Emag is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the MHD equations in both Newtonian gravitation and general relativity. For an initially uniform magnetic field parallel to the rotation axis in which we neglect viscosity, the Newtonian case can be solved analytically, but the other cases we consider require a numerical integration. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfvén timescales ("phase mixing"). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.

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Linear Stability Analysis of Differentially Rotating Polytropes: New Results for them = 2f‐Mode Dynamical Instability

Cited by 28 publications

References 32 publications

Dynamical non-axisymmetric instabilities in rotating relativistic stars

Dynamical non-axisymmetric instabilities in rotating relativistic stars

Stiffness effects on the dynamics of the bar-mode instability of neutron stars in full general relativity

Magnetic braking in differentially rotating, relativistic stars

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