The Structure of Invariant Tori in a 3d Galactic Potential

Katsanikas, Matthaios; Patsis, P. A.

doi:10.1142/s0218127411028520

Cited by 35 publications

(49 citation statements)

References 29 publications

(40 reference statements)

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“…We can conclude from the inspection of these figures all orbits seem to be regular orbits, because they are represented by an tori in the surface of sections (Katsanikas & Patsis 2011). In order to crosscheck the results, we have computed the Lyapunov Asymptotic Exponent for the selected orbits.…”

Section: Lyapunov Asymptotic Exponentsmentioning

confidence: 99%

Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

Taani¹,

Vallejo

2017

Publ. Astron. Soc. Aust.

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We describe the dynamical behavior of isolated old (≥ 1 Gyr) objects-like Neutron Stars (NSs). These isolated NSs are evolved under smooth, time-independent, 3-D gravitational potentials, axisymmetric and with a triaxial dark halo. We analysed the geometry of the dynamics and applied the Poincaré section method for comparing the influence of different birth velocity distributions. The inspection of the maximal asymptotic Lyapunov (λ) exponent shows that the dynamical behaviors of the selected orbits are nearly the same as the regular orbits with two degrees of freedom, both in axisymmetric and triaxial when (φ, q z )= (0,0). Conversely, a few chaotic trajectories are found with a rotated triaxial halo when (φ, q z )= (90, 1.5). The tube orbits preserve the direction of their circulation around either the long or short axis as appeared in the triaxial potential, even when every initial condition leads to different orientations. The Poincaré section method shows that there are 2-D invariant tori and invariant curves (islands) around stable periodic orbits that bound to the surface of 3-D tori. The regularity of the several prototypical orbits offer the means to identify the phase space regions with localized motions and to determine their environment in different models, because they can occupy significant parts of phase-space depending on the potential. This is of particular importance in Galactic Dynamics.

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Section: Lyapunov Asymptotic Exponentsmentioning

confidence: 99%

Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

Taani¹,

Vallejo

2017

Publ. Astron. Soc. Aust.

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“…This technique has been used by several authors (e.g. Katsanikas & Patsis (2011)) to analyze the structure of phase space in the neighborhood of stable periodic orbits in a 3D potential, and the properties of the invariant tori in the 4D spaces of section, under different galactic potentials. We use it here to study the 3-D NS trajectories and their 2-D projections.…”

Section: Ns Orbits In the Galaxymentioning

confidence: 99%

“…Caldwell & Ostriker (1981), Ofek (2009), Katsanikas & Patsis (2011)). In particular, Paczyński (1990) (hereafter P90) simulated the motion of NSs in connection with the galactic origin of gamma ray bursts and calculated the NS space density distribution.…”

Section: Introductionmentioning

confidence: 99%

Modeling the spatial distribution of neutron stars in the Galaxy

Taani

Naso

Wei

et al. 2012

Astrophys Space Sci

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In this paper we investigate the space and velocity distributions of old neutron stars (aged 10 9 to 10 10 yr) in our Galaxy. Galactic old Neutron Stars (NSs) population fills a torus-like area extending to a few tens kiloparsecs above the galactic plane. The initial velocity distribution of NSs is not well known, in this work we adopt a three component initial distribution, as given by the contribution of kick velocities, circular velocities and Maxwellian velocities. For the spatial initial distribution we use a Γ function. We then use Monte Carlo simulations to follow the evolution of the NSs under the influence of the Paczyński Galactic gravitational potential. Our calculations show that NS orbits have a very large Galactic radial expansion and that their radial distribution peak is quite close to their progenitors' one. We also study the NS vertical distribution and find that it can well be described by a double exponential low. Finally, we investigate the correlation of the vertical and radial distribution and study the radial dependence of scale-heights.

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“…In Fig. 2 we observe that as the orbit evolves on the rotational torus projected on the r, P r , P θ surface, the colors representing P φ vary smoothly [31]. This means that the orbit is regular.…”

Section: Examples For S =mentioning

confidence: 88%

Dynamics of a spinning particle in a linear in spin Hamiltonian approximation

et al. 2016

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We investigate for order and chaos the dynamical system of a spinning test particle of mass m moving in the spacetime background of a Kerr black hole of mass M . This system is approximated in our investigation by the linear in spin Hamiltonian function provided in [E. Barausse, and A. Buonanno, Phys.Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincaré section. Various topological structures coming from the non-integrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin S/(m M ) = 10 −4 of the particle and below, the impact of the non-integrability of the system on the motion of the particle seems to be negligible.

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The Structure of Invariant Tori in a 3d Galactic Potential

Cited by 35 publications

References 29 publications

Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

Modeling the spatial distribution of neutron stars in the Galaxy

Dynamics of a spinning particle in a linear in spin Hamiltonian approximation

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