Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

AbstractDense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources) and blue stragglers. We investigate the secular dynamics of a binary system driven by the global tidal field of an axisymmetric stellar cluster in which the binary orbits. In a companion paper we developed a general Hamiltonian framework describing such systems. The effective (doubly-averaged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter Γ. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as Γ is varied. We find that for Γ > 1/5 the phase-space structure and the evolution of binary orbital elements are qualitatively similar to the Lidov–Kozai problem. However, this is only one of four possible regimes, because the dynamics are qualitatively changed by bifurcations at Γ = 1/5, 0, −1/5. We show how the dynamics are altered in each regime and calculate characteristics such as the secular evolution time-scale and maximum possible eccentricity. We verify the predictions of our doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular time-scale should exceed the period of the binary around the cluster by ≳10–102 (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harboured by stellar clusters.

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Secular dynamics of binaries in stellar clusters – I. General formulation and dependence on cluster potential

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1730 ◽

2019 ◽

Vol 488 (4) ◽

pp. 5489-5511 ◽

Cited By ~ 5

Author(s):

Chris Hamilton ◽

Roman R Rafikov

Keyword(s):

Binary Systems ◽

Dynamical Evolution ◽

Compact Object ◽

Companion Paper ◽

Orbital Evolution ◽

Oort Cloud ◽

Stellar Clusters ◽

Dimensional Parameter ◽

Stellar Cluster ◽

Secular Dynamics

AbstractOrbital evolution of binary systems in dense stellar clusters is important in a variety of contexts: origin of blue stragglers, progenitors of compact object mergers, millisecond pulsars, and so on. Here we consider the general problem of secular evolution of the orbital elements of a binary system driven by the smooth tidal field of an axisymmetric stellar cluster (globular, nuclear, etc.) in which the binary orbits. We derive a secular Hamiltonian (averaged over both the inner Keplerian orbit of the binary and its outer orbit within the cluster) valid to quadrupole order for an arbitrary cluster potential and explore its characteristics. This doubly averaged ‘tidal’ Hamiltonian depends on just two parameters, which fully absorb the information about the background cluster potential and the binary’s orbit within it: a dimensional parameter A setting the secular time-scale, and a dimensionless parameter Γ which determines the phase portrait of the binary’s inner orbital evolution. We examine the dependence of A and Γ on cluster potential (both spherical and axisymmetric) and on the binary orbit within the cluster. Our theory reproduces known secular results – such as Lidov–Kozai evolution and the effect of the Galactic tide on Oort Cloud comets – in appropriate limits, but is more general. It provides a universal framework for understanding dynamical evolution of various types of binaries driven by the smooth tidal field of any axisymmetric potential. In a companion paper we provide a detailed exploration of the resulting orbital dynamics.

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QUINTOM COSMOLOGY WITH GENERAL POTENTIALS

International Journal of Modern Physics D ◽

10.1142/s0218271809014625 ◽

2009 ◽

Vol 18 (04) ◽

pp. 549-557 ◽

Cited By ~ 68

Author(s):

M. R. SETARE ◽

E. N. SARIDAKIS

Keyword(s):

Dark Energy ◽

Phase Space ◽

Dynamical Evolution ◽

Space Structure ◽

Late Time ◽

Phase Space Structure ◽

Phantom Model ◽

Potential Form ◽

Homogeneous Universe

We investigate the phase space structure of the quintom paradigm in the framework of a spatially flat, open or closed isotropic and homogeneous universe. We examine the dynamical evolution under the assumption of late time dark energy domination, without specifying the explicit quintom potential form. The obtained cosmological behavior is qualitatively different than that acquired from the single phantom model.

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Explicit symplectic-like integration with corrected map for inseparable Hamiltonian

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3745 ◽

2020 ◽

Vol 501 (1) ◽

pp. 1511-1519

Author(s):

Junjie Luo ◽

Weipeng Lin ◽

Lili Yang

Keyword(s):

Phase Space ◽

Space Structure ◽

Eighth Order ◽

Time Step ◽

Extended Phase ◽

Energy Error ◽

Phase Space Structure ◽

Compact Binary ◽

Three Body

ABSTRACT Symplectic algorithms are widely used for long-term integration of astrophysical problems. However, this technique can only be easily constructed for separable Hamiltonian, as preserving the phase-space structure. Recently, for inseparable Hamiltonian, the fourth-order extended phase-space explicit symplectic-like methods have been developed by using the Yoshida’s triple product with a mid-point map, where the algorithm is more effective, stable and also more accurate, compared with the sequent permutations of momenta and position coordinates, especially for some chaotic case. However, it has been found that, for the cases such as with chaotic orbits of spinning compact binary or circular restricted three-body system, it may cause secular drift in energy error and even more the computation break down. To solve this problem, we have made further improvement on the mid-point map with a momentum-scaling correction, which turns out to behave more stably in long-term evolution and have smaller energy error than previous methods. In particular, it could obtain a comparable phase-space distance as computing from the eighth-order Runge–Kutta method with the same time-step.

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