Numerical tests of dynamical friction in gravitational inhomogeneous systems

Popolo, A. Del

doi:10.1051/0004-6361:20030665

Cited by 11 publications

(13 citation statements)

References 40 publications

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“…It is, however, still unclear how the inhomogeneity of the system distribution affects the satellite dynamics. Whereas Del Popolo (2003), Del Popolo & Gambera (1998) and Maoz (1993) show that dynamical friction increases the steeper the density profile is, Just & Peñarrubia (2002), following the theoretical scheme proposed by Binney (1977), hereinafter B77, find a negligible effect on the satellite orbit due to the symmetry of the inhomogeneous terms of dynamical friction.…”

Section: Introductionmentioning

confidence: 98%

Dynamical friction in flattened systems: a numerical test of Binney's approach

Peñarrubia

Just

Kroupa

2004

Monthly Notices of the Royal Astronomical Society

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We carry out a set of self‐consistent N‐body calculations to investigate how important the velocity anisotropy in non‐spherical dark matter haloes is for dynamical friction. For this purpose, we allow satellite galaxies to orbit within flattened and live dark matter haloes (DMHs) and compare the resulting orbit evolution with a semi‐analytic code. This code solves the equation of motion of the same satellite orbits with mass loss and assumes the same DMH, but either employs Chandrasekhar's dynamical friction formula, which does not incorporate the velocity anisotropy, or Binney's description of dynamical friction in anisotropic systems. In the numerical and the two semi‐analytic models, the satellites are given different initial orbital inclinations and orbital eccentricities, whereas the parent galaxy is composed of a DMH with aspect ratio qh= 0.6. We find that Binney's approach successfully describes the overall satellite decay and orbital inclination decrease for the whole set of orbits, with an averaged discrepancy of less than 4 per cent in orbital radius during the first three orbits. If Chandrasekhar's expression is used instead, the discrepancy increases to 20 per cent. Binney's treatment therefore appears to provide a significantly improved treatment of dynamical friction in anisotropic systems. The velocity anisotropy of the DMH velocity distribution function leads to a significant decrease with time of the inclination of non‐polar satellite orbits. But, at the same time, it reduces the difference in decay times between polar and coplanar orbits evident in a flattened DMH when the anisotropic DMH velocity distribution function is not taken into account explicitly. Our N‐body calculations furthermore indicate that polar orbits survive about 1.6 times longer than coplanar orbits and that the orbital eccentricity e remains close to its initial value if satellites decay slowly towards the galaxy centre. However, orbits of rapidly decaying satellites modelled with the semi‐analytic code show a strong orbital circularization () not present in the N‐body computations.

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Section: Introductionmentioning

confidence: 98%

Dynamical friction in flattened systems: a numerical test of Binney's approach

Peñarrubia

Just

Kroupa

2004

Monthly Notices of the Royal Astronomical Society

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“…Maoz (1993) and follow-up papers (Sánchez-Salcedo 1999;Dominguez-Teneiro & Gómez-Flechoso 1998) used the fluctuation-dissipation theory with approximations similar to those presented here to derive the energy loss due to dynamical friction. Del Popolo &Gambera (1999) andDel Popolo (2003) compute the corrections due to a density enhancement spherically symmetric with respect to the massive body, which may be used to estimate the shielding effect on the friction force.…”

Section: Introductionmentioning

confidence: 99%

Large scale inhomogeneity and local dynamical friction

Just¹,

Peñarrubia

2005

A&A

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Abstract.We investigate the effect of a density gradient on Chandrasekhar's dynamical friction formula based on the method of 2-body encounters in the local approximation. We apply these generalizations to the orbit evolution of satellite galaxies in Dark Matter haloes. We find from the analysis that the main influence occurs through a position-dependent maximum impact parameter in the Coulomb logarithm, which is determined by the local scale-length of the density distribution. We also show that for eccentric orbits the explicit dependence of the Coulomb logarithm on position yields significant differences for the standard homogeneous force. Including the velocity dependence of the Coulomb logarithm yields ambigous results. The orbital fits in the first few periods are further improved, but the deviations at later times are much larger. The additional force induced by the density gradient, the inhomogeneous force, is not antiparallel to the satellite motion and can exceed 10% of the homogeneous friction force in magnitude. However, due to the symmetry properties of the inhomogeneous force, there is a deformation and no secular effect on the orbit at the first order. Therefore the inhomogeneous force can be safely neglected for the orbital evolution of satellite galaxies. For the homogeneous force we compare numerical N-body calculations with semi-analytical orbits to determine quantitatively the accuracy of the generalized formulae of the Coulomb logarithm in the Chandrasekhar approach. With the local scale-length as the maximum impact parameter we find a significant improvement of the orbital fits and a better interpretation of the quantitative value of the Coulomb logarithm.

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“…Chandrasekhar & von Neumann (1943) attempted to derive this force from a purely stochastic formalism in the case where the system is infinite and homogeneous and the stars have a Maxwellian velocity distribution. Their calculations were extended by Del Popolo & Gambera (1999); Del Popolo (2003) to an inhomogeneous medium with a density decaying as ρ ∼ r −p , assuming again that the velocity distribution of the stars is Maxwellian. In order to treat in a self-consistent manner more general situations of spatial inhomogeneity, and take into account collective effects, the formalism developed in the present paper is necessary.…”

Section: D3 An Ilustration Of Dynamical Friction In a Mestel Discmentioning

confidence: 99%

“…Kandrup (1983); Bekenstein & Maoz (1992); Maoz (1993); Nelson & Tremaine (1999); Chavanis (2008) reconsidered the interaction of a test particle with a background stochastic force in the context of the fluctuation-dissipation theorem, and showed that the friction force depends on the global structure of the system. This was also investigated in Del Popolo & Gambera (1999); Del Popolo (2003) which extended Chandrasekhar & von Neumann (1943)'s analysis to the case where the background particles are inhomogeneously distributed with a density profile decaying as ρ ∼ r −p . Kinetic theories for spatially inhomogeneous systems were developed in Severne & Haggerty (1976); Parisot & Severne (1979); Kandrup (1981); Chavanis (2008Chavanis ( , 2013 using position-velocity variables.…”

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confidence: 99%

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Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems

Heyvaerts

Fouvry

Chavanis

2017

Monthly Notices of the Royal Astronomical Society

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General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding particles and their self-consistent dressing by collective gravitational interactions. The associated Fokker-Planck equation is shown to be fully consistent with the corresponding inhomogeneous Balescu-Lenard equation and, in the weak self-gravitating limit, to the inhomogeneous Landau equation. Hence it provides an alternative derivation to both and demonstrates their equivalence. The corresponding stochastic Langevin equations are presented: they can be a practical alternative to numerically solving the inhomogeneous Fokker-Planck and Balescu-Lenard equations. The present formalism allows for a self-consistent description of the secular evolution of different populations covering a spectrum of masses, with a proper accounting of the induced secular mass segregation, which should be of interest to various astrophysical contexts, from galactic centers to protostellar discs.

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Numerical tests of dynamical friction in gravitational inhomogeneous systems

Abstract: Abstract. In this paper,

Cited by 11 publications

References 40 publications

Dynamical friction in flattened systems: a numerical test of Binney's approach

Dynamical friction in flattened systems: a numerical test of Binney's approach

Large scale inhomogeneity and local dynamical friction

Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems

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