Escape from the vicinity of fractal basin boundaries of a star cluster

Ernst, A.; Just, A.; Spurzem, Rainer; Porth, Oliver

doi:10.1111/j.1365-2966.2007.12640.x

Cited by 24 publications

(28 citation statements)

References 54 publications

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“…In particular, for an axisymmetric galactic field, the tidal potential differs from the one obtained here only by the z-term (Chandrasekhar 1942;Heggie & Hut 2003). This case is often considered, for example, by referring to a globular cluster in a circular orbit on the (axisymmetric) disk of our Galaxy (see Heggie & Ramamani 1995;Ernst et al 2008), for which È T is then formulated in terms of the Oort constants.…”

Section: The Tidal Potentialmentioning

confidence: 90%

The Construction of Nonspherical Models of Quasi‐Relaxed Stellar Systems

Bertin

Varri

2008

Astrophysical Journal

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Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical conditions, but including explicitly the ingredients that lead to departures from spherical symmetry. In particular, we focus on the effects of the tidal field associated with the hosting galaxy. We then take a stellar system on a circular orbit inside a galaxy represented as a ''frozen'' external field. The equilibrium distribution function is obtained from the one describing the spherical case by replacing the energy integral with the relevant Jacobi integral in the presence of the external tidal field. Then the construction of the model requires the investigation of a singular perturbation problem for an elliptic partial differential equation with a free boundary, for which we provide a method of solution to any desired order, with explicit solutions to 2 orders. We outline the relevant parameter space, thus opening the way to a systematic study of the properties of a two-parameter family of physically justified nonspherical models of quasi-relaxed stellar systems. The general method developed here can also be used to construct models for which the nonspherical shape is due to internal rotation. Eventually, the models will be a useful tool to investigate whether the shapes of globular clusters are primarily determined by internal rotation, by external tides, or by pressure anisotropy.

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Section: The Tidal Potentialmentioning

confidence: 90%

The Construction of Nonspherical Models of Quasi‐Relaxed Stellar Systems

Bertin

Varri

2008

Astrophysical Journal

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“…the splitting angle between them may be zero. A comparison of Figure 5 and Figure 6 reveals that, in contrast to the system studied in Ernst et al (2008), the phase-spatial extent of the chaotic saddle for the present system is tiny as compared to the squared Lagrangian radius. For this reason we did not calculate the chaotic saddle for the system studied in the present work.…”

Section: Basins Of Escapementioning

confidence: 99%

“…Regarding aspect (iii), it must be noted that, for eJ > eJ,crit, the reason may be the fact that particles can leak out through exits in the equipotential surfaces (as in the upper right panel of Figure 2 of Ernst et al 2008).…”

Section: Poincaré Surfaces Of Sectionmentioning

confidence: 99%

“…Then we integrate the initial condition forwards in time and plot a dot at each consequent (="piercing point through the surface of section") with y = 0 when vy 0. These values of the Jacobi energy correspond to the relative deviations from the critical Jacobi energy (eJ,crit − eJ )/eJ,crit = 0.1, 0.01 and 0.001 as in Ernst et al (2008).…”

Section: Poincaré Surfaces Of Sectionmentioning

confidence: 99%

“…The problem of escape from Hamiltonian systems is a classical problem in dynamical astronomy and nonlinear dynamics (e.g. Contopoulos 1990;Contopoulos & Kaufmann 1992;Contopoulos et al 1993Contopoulos et al , 2012Siopis et al 1996;Navarro & Henrard 2001;Schneider et al 2002;Ernst et al 2008). However, it is far email: aernst@ari.uni-heidelberg.de † email: tpeters@physik.uzh.ch less studied than the closely related situation of chaotic scattering, where a body from infinity approaches and scatters off a complex potential.…”

Section: Introductionmentioning

confidence: 99%

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Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar

Ernst¹,

Peters²

2014

Monthly Notices of the Royal Astronomical Society

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We investigate the dynamics in the close vicinity of and within the critical area in a 2D effective galactic potential with a bar of Zotos. We have calculated Poincaré surfaces of section and the basins of escape. In both the Poincaré surfaces of section and the basins of escape we find numerical evidence for the existence of a separatrix which hinders orbits from escaping out of the bar region. We present numerical evidence for the similarity between spiral arms of barred spiral galaxies and tidal tails of star clusters.

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Roche volume filling and the dissolution of open star clusters

et al. 2015

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From direct N -body simulations we find that the dynamical evolution of star clusters is strongly influenced by the Roche volume filling factor. We present a parameter study of the dissolution of open star clusters with different Roche volume filling factors and different particle numbers. We study both Roche volume underfilling and overfilling models and compare with the Roche volume filling case. We find that in the Roche volume overfilling limit of our simulations twobody relaxation is no longer the dominant dissolution mechanism but the changing cluster potential. We call this mechnism "mass-loss driven dissolution" in contrast to "two-body relaxation driven dissolution" which occurs in the Roche volume underfilling regime. We have measured scaling exponents of the dissolution time with the two-body relaxation time. In this experimental study we find a decreasing scaling exponent with increasing Roche volume filling factor. The evolution of the escaper number in the Roche volume overfilling limit can be described by a log-logistic differential equation. We report the finding of a resonance condition which may play a role for the evolution of star clusters and may be calibrated by the main periodic orbit in the large island of retrograde quasiperiodic orbits in the Poincaré surfaces of section. We also report on the existence of a stability curve which may be of relevance with respect to the structure of star clusters.

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Escape from the vicinity of fractal basin boundaries of a star cluster

Cited by 24 publications

References 54 publications

The Construction of Nonspherical Models of Quasi‐Relaxed Stellar Systems

The Construction of Nonspherical Models of Quasi‐Relaxed Stellar Systems

Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar

Roche volume filling and the dissolution of open star clusters

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