Radial Orbit Instability: Review and Perspectives

Maréchal, Lionel; Perez, Jérôme

doi:10.1080/00411450.2011.654750

Cited by 11 publications

(8 citation statements)

References 39 publications

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“…the velocity distribution is dominated by orbits with low values of the angular momentum J) are prone to the so-called as radial-orbit instability, (hereafter ROI, e.g. see Polyachenko 1992b;Binney & Tremaine 2008;Maréchal & Perez 2011;Bertin 2014). The origin of this process, despite the the large efforts made from both the analytical (e.g.…”

Section: Introductionmentioning

confidence: 99%

Discreteness effects, N-body chaos and the onset of radial-orbit instability

Cintio

Casetti

2020

Monthly Notices of the Royal Astronomical Society

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We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called γ−models with Osipkov-Merritt velocity anisotropy, by means of N −body simulations. In particular, we analyze the effect of self-consistent N −body chaos on the onset of radial-orbit instability (ROI). We find that degree of chaoticity of the system associated to its largest Lyapunov exponent Λ max has no appreciable relation with the stability of the model for fixed density profile and different values of radial velocity anisotropy. However, by studying the distribution of the Lyapunov exponents λ m of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger λ m .

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Section: Introductionmentioning

confidence: 99%

Discreteness effects, N-body chaos and the onset of radial-orbit instability

Cintio

Casetti

2020

Monthly Notices of the Royal Astronomical Society

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“…Such instability is commonly referred to as radial-orbit instability, (hereafter ROI, e.g. see Polyachenko 1992;Binney & Tremaine 2008;Maréchal & Perez 2011;Bertin 2014).…”

Section: Introductionmentioning

confidence: 99%

Radially anisotropic systems with r−α forces – II: radial-orbit instability

Cintio

Ciotti

Nipoti

2017

Monthly Notices of the Royal Astronomical Society

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We continue to investigate the dynamics of collisionless systems of particles interacting via additive r −α interparticle forces. Here we focus on the dependence of the radial-orbit instability on the force exponent α. By means of direct N -body simulations we study the stability of equilibrium radially anisotropic Osipkov-Merritt spherical models with Hernquist density profile and with 1 ≤ α < 3. We determine, as a function of α, the minimum value for stability of the anisotropy radius r as and of the maximum value of the associated stability indicator ξ s . We find that, for decreasing α, r as decreases and ξ s increases, i.e. longer-range forces are more robust against radial-orbit instability. The isotropic systems are found to be stable for all the explored values of α. The end products of unstable systems are all markedly triaxial with minor-to-major axial ratio > 0.3, so they are never flatter than an E7 system.

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“…A comprehensive modern review on ROI can be found in ⋆ E-mail: epolyach@inasan.ru † E-mail: shukhman@iszf.irk.ru Maréchal & Perez (2012), who also suggest a new symplectic method for exploring stability of equilibrium gravitating systems. Antonov (1973) presents a first formal proof of ROI for purely radial motion using the Lyapunov method.…”

Section: Introductionmentioning

confidence: 99%

Radial orbit instability in systems of highly eccentric orbits: Antonov problem reviewed

Polyachenko

Shukhman

2017

Monthly Notices of the Royal Astronomical Society

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Stationary stellar systems with radially elongated orbits are subject to radial orbit instability -an important phenomenon that structures galaxies. Antonov (1973) presented a formal proof of the instability for spherical systems in the limit of purely radial orbits. However, such spheres have highly inhomogeneous density distributions with singularity ∼ 1/r 2 , resulting in an inconsistency in the proof. The proof can be refined, if one considers an orbital distribution close to purely radial, but not entirely radial, which allows to avoid the central singularity. For this purpose we employ nonsingular analogs of generalised polytropes elaborated recently in our work in order to derive and solve new integral equations adopted for calculation of unstable eigenmodes in systems with nearly radial orbits. In addition, we establish a link between our and Antonov's approaches and uncover the meaning of infinite entities in the purely radial case. Maximum growth rates tend to infinity as the system becomes more and more radially anisotropic. The instability takes place both for even and odd spherical harmonics, with all unstable modes developing rapidly, i.e. having eigenfrequencies comparable to or greater than typical orbital frequencies. This invalidates orbital approximation in the case of systems with all orbits very close to purely radial.

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Radial Orbit Instability: Review and Perspectives

Cited by 11 publications

References 39 publications

Discreteness effects, N-body chaos and the onset of radial-orbit instability

Discreteness effects, N-body chaos and the onset of radial-orbit instability

Radially anisotropic systems with r−α forces – II: radial-orbit instability

Radial orbit instability in systems of highly eccentric orbits: Antonov problem reviewed

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