Radial orbit instability as a dissipation-induced phenomenon

Maréchal, Lionel; Perez, Jérôme

doi:10.1111/j.1365-2966.2010.16663.x

Cited by 10 publications

(10 citation statements)

References 29 publications

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“…Using the energy approach, Maréchal & Perez (2010) argue that instability in sufficiently anisotropic systems can be induced by dissipation inevitably present in the real stellar systems. The energy approach claims that if the second order variation of energy due to the perturbation, H (2) , is negative, then the system may be unstable.…”

Section: Discussionmentioning

confidence: 99%

“…A distinct approach is suggested by Maréchal & Perez (2010), who give an example of dissipation-induced ROI. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

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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“…Analytical studies are usually involved (e.g. [79][80][81][82]), and the stability properties of anisotropic systems are very often investigated thanks to numerical simulations (e.g. [83][84][85]), which is far beyond the scope of this work.…”

Section: Stable Distribution Functionsmentioning

confidence: 99%

Anatomy of Eddington-like inversion methods in the context of dark matter searches

Lacroix

Stref

Lavalle

2018

J. Cosmol. Astropart. Phys.

114

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Irrespective of the dark matter (DM) candidate, several potentially observable signatures derive from the velocity distribution of DM in halos, in particular in the Milky Way (MW) halo. Examples include direct searches for weakly-interacting massive particles (WIMPs), p-wave suppressed or Sommerfeld-enhanced annihilation signals, microlensing events of primordial black holes (PBHs), etc. Most current predictions are based on the Maxwellian approximation which is not only theoretically inconsistent in bounded systems, but also not supported by cosmological simulations. A more consistent method sometimes used in calculations for direct WIMP searches relies on the so-called Eddington inversion method, which relates the DM phase-space distribution function (DF) to its mass density profile and the total gravitational potential of the system. Originally built upon the isotropy assumption, this method can be extended to anisotropic systems. We investigate these inversion methods in the context of Galactic DM searches, motivated by the fact that the MW is a strongly constrained system, and should be even more so with the ongoing Gaia survey. We still draw conclusions that apply to the general case. In particular, we illustrate how neglecting the radial boundary of the DM halo leads to theoretical inconsistencies. We also show that several realistic configurations of the DM halo and the MW baryonic content entail ill-defined DFs, significantly restricting the configuration space over which these inversion methods can apply. We propose consistent solutions to these issues. Finally, we compute several observables inferred from constrained Galactic mass models relevant to DM searches (WIMPs or PBHs), e.g. moments and inverse moments of the DM speed and relative speed distributions.

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“…For example, by use of such methods, much attention has been paid to the case of radially anisotropic systems, where the radial orbit instability leads to the presence of bars, which are of obvious interest from the point of view of the morphology of galaxies (e.g. Polyachenko 1989;Allen, Palmer, & Papaloizou 1990;Carpintero & Muzzio 1995;Cincotta, Nunez, & Muzzio 1996;Trenti & Bertin 2006;MacMillan, Widrow, & Henriksen 2006;Buyle et al 2007;Bellovary et al 2008;Barnes, Lanzel, & Williams 2009;Maréchal & Perez 2010;Gajda, Lokas, & Wojtak 2015;Polyachenko & Shukhman 2017).…”

Section: Introductionmentioning

confidence: 99%

l = 1: Weinberg’s weakly damped mode in an N-body model of a spherical stellar system

Heggie

Breen

Varri

2020

Monthly Notices of the Royal Astronomical Society

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Spherical stellar systems such as King models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever application of the matrix method of linear stability, that they may be nearly unstable, in the sense of possessing weakly damped modes of oscillation. He also demonstrated the presence of such a mode in an N -body model by endowing it with initial conditions generated from his perturbative solution. In the present paper we provide evidence for the presence of this same mode in N -body simulations of the King W 0 = 5 model, in which the initial conditions are generated by the usual Monte Carlo sampling of the King distribution function. It is shown that the oscillation of the density centre correlates with variations in the structure of the system out to a radius of about 1 virial radius, but anticorrelates with variations beyond that radius. Though the oscillations appear to be continually reexcited (presumably by the motions of the particles) we show by calculation of power spectra that Weinberg's estimate of the period (strictly, 2π divided by the real part of the eigenfrequency) lies within the range where the power is largest. In addition, however, the power spectrum displays another very prominent feature at shorter periods, around 5 crossing times.

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Radial orbit instability as a dissipation-induced phenomenon

Cited by 10 publications

References 29 publications

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

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

Anatomy of Eddington-like inversion methods in the context of dark matter searches

l = 1: Weinberg’s weakly damped mode in an N-body model of a spherical stellar system

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