Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

Kandrup, Henry E.

doi:10.1086/158709

Cited by 80 publications

(137 citation statements)

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“…We follow the treatment presented in the paper of Colpi & Pallavicini (1998), which contains the Chandrasekhar work as a special limit (e.g., Kandrup 1983). In this formulation of the perturbative approach (extension of previous works of e.g., Kandrup 1981;Seguin & Dupraz 1994, 1996 the authors recollect and extend several important results in order to overcome the limitation of the Chandrasekhar formula that allow one to analytically follow the gravitational wake influence, the tidal deformation, and the shift of the barycentre of the primary galaxy.…”

Section: The Dynamical Frictionmentioning

confidence: 99%

Orbital evolution of the Carina dwarf galaxy and self-consistent determination of star formation history

Pasetto

Grebel

Berczik

et al. 2010

A&A

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We present a new study of the evolution of the Carina dwarf galaxy that includes a simultaneous derivation of its orbit and star formation history. The structure of the galaxy is constrained through orbital parameters derived from the observed distance, proper motions, radial velocity, and star formation history. The different orbits admitted by the large proper motion errors are investigated in relation to the tidal force exerted by an external potential representing the Milky Way. Our analysis is performed with the aid of fully consistent N-body simulations that are able to follow the dynamics and the stellar evolution of the dwarf system in order to determine the star formation history of Carina self-consistently. We also find a star formation history characterized by several bursts, partially matching the observational expectation. We find also compatible results between dynamical projected quantities and the observational constraints. The possibility of a past interaction between Carina and the Magellanic Clouds is also separately considered and deemed unlikely.

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Section: The Dynamical Frictionmentioning

confidence: 99%

Orbital evolution of the Carina dwarf galaxy and self-consistent determination of star formation history

Pasetto

Grebel

Berczik

et al. 2010

A&A

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“…In TLR, dynamical friction is viewed as a direct manifestation of the fluctuation-dissipation theorem 117,118 . In this interpretation, the fluctuations of the two-body force between the massive perturber M BH and any particle m * add collectively to give a non-vanishing drag.…”

Section: Dynamical Frictionmentioning

confidence: 99%

<I>A Special Section on</I> Computational Astrophysics

Colpi

Dotti

2011

adv sci lett

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Binary black holes occupy a special place in our quest for understanding the evolution of galaxies along cosmic history. If massive black holes grow at the center of (pre-)galactic structures that experience a sequence of merger episodes, then dual black holes form as inescapable outcome of galaxy assembly, and can in principle be detected as powerful dual quasars. But, if the black holes reach coalescence, during their inspiral inside the galaxy remnant, then they become the loudest sources of gravitational waves ever in the universe. The Laser Interferometer Space Antenna is being developed to reveal these waves that carry information on the mass and spin of these binary black holes out to very large look-back times. Nature seems to provide a pathway for the formation of these exotic binaries, and a number of key questions need to be addressed: How do massive black holes pair in a merger? Depending on the properties of the underlying galaxies, do black holes always form a close Keplerian binary? If a binary forms, does hardening proceed down to the domain controlled by gravitational wave back reaction? What is the role played by gas and/or stars in braking the black holes, and on which timescale does coalescence occur? Can the black holes accrete on flight and shine during their pathway to coalescence? After outlining key observational facts on dual/binary black holes, we review the progress made in tracing their dynamics in the habitat of a gas-rich merger down to the smallest scales ever probed with the help of powerful numerical simulations. N-Body/hydrodynamical codes have proven to be vital tools for studying their evolution, and progress in this field is expected to grow rapidly in the effort to describe, in full realism, the physics of stars and gas around the black holes, starting from the cosmological large scale of a merger. If detected in the new window provided by the upcoming gravitational wave experiments, binary black holes will provide a deep view into the process of hierarchical clustering which is at the heart of the current paradigm of galaxy formation. They will also be exquisite probes for testing General Relativity, as the theory of gravity. The waveforms emitted during the inspiral, coalescence and ringdown phase carry in their shape the sign of a dynamically evolving space-time and the proof of the existence of an horizon.

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“…A third possibility is to use a projection operator formalism, e.g. [33]. An interest of this approach is that it takes into account non Markovian effects and spatial delocalization.…”

Section: F the Landau Equationmentioning

confidence: 99%

Hamiltonian and Brownian systems with long-range interactions: II. Kinetic equations and stability analysis

Chavanis¹

2006

Physica A: Statistical Mechanics and its Applications

204

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We discuss the kinetic theory of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system described by the Liouville equation from the canonical description of a stochastically forced Brownian system described by the FokkerPlanck equation. We show that the mean-field approximation is exact in a proper thermodynamic limit. For N → +∞, a Hamiltonian system is described by the Vlasov equation. In this collisionless regime, coherent structures can emerge from a process of violent relaxation. These metaequilibrium states, or quasi-stationary states (QSS), are stable stationary solutions of the Vlasov equation. To order 1/N , the collision term of a homogeneous system has the form of the Lenard-Balescu operator. It reduces to the Landau operator when collective effects are neglected. The statistical equilibrium state (Boltzmann) is obtained on a collisional timescale of order N or larger (when the Lenard-Balescu operator cancels out). We also consider the stochastic motion of a test particle in a bath of field particles and derive the general form of the Fokker-Planck equation describing the evolution of the velocity distribution of the test particle. The diffusion coefficient is anisotropic and depends on the velocity of the test particle. For Brownian systems, in the N → +∞ limit, the kinetic equation is a non-local Kramers equation. In the strong friction limit ξ → +∞, or for large times t ≫ ξ −1 , it reduces to a non-local Smoluchowski equation. We give explicit results for self-gravitating systems, two-dimensional vortices and for the HMF model. We also introduce a generalized class of stochastic processes and derive the corresponding generalized Fokker-Planck equations. We discuss how a notion of generalized thermodynamics can emerge in complex systems displaying anomalous diffusion.

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Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

Cited by 80 publications

References 0 publications

Orbital evolution of the Carina dwarf galaxy and self-consistent determination of star formation history

Orbital evolution of the Carina dwarf galaxy and self-consistent determination of star formation history

<I>A Special Section on</I> Computational Astrophysics

Hamiltonian and Brownian systems with long-range interactions: II. Kinetic equations and stability analysis

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