Growth of Velocity Dispersions for Collapsing Spherical Stellar Systems

Hozumi, Shunsuke; Fujiwara, Takanori; Kan-ya, Yukitoshi

doi:10.1093/pasj/48.3.503

Cited by 9 publications

(24 citation statements)

References 14 publications

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“…Thus for axisymmetric cold distributions, of initial aspect ratio < 3/4, any sensible simulation particle number will adequately reproduce the Lin-Mestel-Shu flow. The time-evolution of axis-ratio of collapsing triaxial systems with N = 10 5 particles performed by Hozumi et al (1996) shows growth of surface modes (pancaking) in agreement with (11). The initial axis ratios of their systems were ξo/r(0) ≃ 0.01 and 0.005, or three times the Poisson noise level for this number of particles.…”

Section: Small Deviationssupporting

confidence: 75%

Scaling up tides in numerical models of galaxy and halo formation

Boily¹,

Athanassoula²,

Kroupa³

2002

Monthly Notices of the Royal Astronomical Society

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The purpose of this article is to show that when dynamically cold, dissipationless self‐gravitating systems collapse, their evolution is a strong function of the symmetry in the initial distribution. We explore with a set of pressureless homogeneous fluids the time evolution of ellipsoidal distributions and map the depth of potential achieved during relaxation as function of initial ellipsoid axis ratios. We then perform a series of N‐body numerical simulations and contrast their evolution with the fluid solutions. We verify an analytic relation between collapse factor 𝒞 and particle number N in spherical symmetry, such that 𝒞∝N1/3. We sought a similar relation for axisymmetric configurations, and found an empirical scaling relation such that 𝒞∝N1/6 in these cases. We then show that when mass distributions do not respect spherical or axial symmetry, the ensuing gravitational collapse deepens with increasing particle number N but only slowly: 86 per cent of triaxial configurations may collapse by a factor of no more than 40 as N→∞. For N≈105 and larger, violent relaxation develops fully under the Lin–Mestel–Shu instability such that numerical N‐body solutions now resolve the different initial morphologies adequately.

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Section: Small Deviationssupporting

confidence: 75%

Scaling up tides in numerical models of galaxy and halo formation

Boily¹,

Athanassoula²,

Kroupa³

2002

Monthly Notices of the Royal Astronomical Society

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“…The splitting scheme was applied for the first time in astronomy in early 1980's, to one dimensional systems (Fujiwara 1981), galactic disks (Watanabe et al 1981;Nishida et al 1981) and spherical systems (Fujiwara 1983). Nevertheless, it has been almost forgotten since then except for a few contributions (e.g., Hozumi, Fujiwara, & Kan-Ya 1996;Hozumi, Burkert, & Fujiwara 2000) that include a recent preliminary investigation of the algorithm in full 6dimensional phase-space (Yoshikawa, Yoshida, & Umemura 2013).…”

Section: Introductionmentioning

confidence: 99%

“…In this respect, the Hénon sphere (Hénon 1964) is particularly suited for our purpose since it is known to preserve well its spherical nature during the course of dynamics even when being simulated with a N -body technique and, in particular, it is not prone to radial orbit instability (see, e.g., van Albada 1982;Hozumi, Fujiwara, & Kan-Ya 1996;Roy & Perez 2004;Barnes, Lanzel, & Williams 2009). In this configuration, the initial phase-space distribution function is isotropic and Gaussian distributed in velocity space and given by…”

Section: Introductionmentioning

confidence: 99%

Vlasov versus N-body: the Hénon sphere

Colombi¹,

Sousbie²,

Peirani³

et al. 2015

Monthly Notices of the Royal Astronomical Society

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We perform a detailed comparison of the phase-space density traced by the particle distribution in Gadget simulations to the result obtained with a spherical Vlasov solver using the splitting algorithm. The systems considered are apodized Hénon spheres with two values of the virial ratio, R 0.1 and 0.5. After checking that spherical symmetry is well preserved by the N -body simulations, visual and quantitative comparisons are performed. In particular we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether N -body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the Nbody and the Vlasov codes, namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase-space grid in the second case, we find a spectacular agreement between both methods, even in regions of phase-space where nontrivial physical instabilities develop. However, in the colder case, R = 0.1, it was not possible to prove actual numerical convergence of the N -body results after a number of dynamical times, even with N = 10 8 particles.

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“…This raises issues with the growth of velocity anisotropies near the time of maximum contraction in studies with lower resolution. Aarseth, Lin & Papaloizou (1988) and Hozumi, Fujiwara & Kan‐Ya (1996) have argued that the tangential velocity dispersion grows faster than the radial component at the bounce. Tangential velocities will arise from the growth of fragmentation modes (McGlynn 1984; Aarseth et al 1988).…”

Section: Introductionmentioning

confidence: 99%

On the equilibrium morphology of systems drawn from spherical collapse experiments

Boily¹,

Athanassoula²

2006

Monthly Notices of the Royal Astronomical Society

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We present a purely theoretical study of the morphological evolution of self‐gravitating systems formed through the dissipationless collapse of N‐point sources. We explore the effects of resolution in mass and length on the growth of triaxial structures formed by an instability triggered by an excess of radial orbits. We point out that as resolution increases, the equilibria shift, from mildly prolate, to oblate. A number of particles N≃ 100 000 or larger is required for convergence of axial aspect ratios. An upper bound for the softening, ε≈ 1/256, is also identified. We then study the properties of a set of equilibria formed from scale‐free cold initial mass distributions, ρ∝r−γ; 0 ≤γ≤ 2. Oblateness is enhanced for initially more peaked structures (larger values of γ). We map the run of density in space and find no evidence for a power‐law inner structure when γ≤ 3/2 down to a mass fraction ≲0.1 per cent of the total. However, when 3/2 < γ≤ 2, the mass profile in equilibrium is well matched by a power law of index ≈γ out to a mass fraction ≈ 10 per cent. We interpret this in terms of less‐effective violent relaxation for more peaked profiles when more phase mixing takes place at the centre. We map out the velocity field of the equilibria and note that at small radii the velocity coarse‐grained distribution function (DF) is Maxwellian to a very good approximation. We extend our study to non‐scale‐free initial conditions and finite but subvirial kinetic energy. For cold collapses, the equilibria are again oblate, as the scale‐free models. With increasing kinetic energy, the equilibria first shift to prolate morphology and then to spherical symmetry.

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Growth of Velocity Dispersions for Collapsing Spherical Stellar Systems

Cited by 9 publications

References 14 publications

Scaling up tides in numerical models of galaxy and halo formation

Scaling up tides in numerical models of galaxy and halo formation

Vlasov versus N-body: the Hénon sphere

On the equilibrium morphology of systems drawn from spherical collapse experiments

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