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Title: Phase-space mixing and the merging of cusps
Authors: Dehnen, Walter
First Published: 1-Jul-2005
Publisher: Oxford University Press (OUP), Royal Astronomical Society
Citation: Monthly Notices of the Royal Astronomical Society, 2005, 360 (3), pp.892-900
Abstract: Collisionless stellar systems are driven towards equilibrium by mixing of phase-space elements. I show that the excess-mass functionGraphic[where Graphic is the coarse-grained distribution function] always decreases on mixing. D(f) gives the excess mass from values of Graphic. This novel form of the mixing theorem extends the maximum phase-space density argument to all values of f. The excess-mass function can be computed from N-body simulations and is additive: the excess mass of a combination of non-overlapping systems is the sum of their individual D(f). I propose a novel interpretation for the coarse-grained distribution function, which avoids conceptual problems with the mixing theorem. As an example application, I show that for self-gravitating cusps (ρ ∝r−γ as r→ 0) the excess mass D∝f−2(3-γ)/(6-γ) as f→ 8, i.e. steeper cusps are less mixed than shallower ones, independent of the shape of surfaces of constant density or details of the distribution function (e.g. anisotropy). This property, together with the additivity of D(f) and the mixing theorem, implies that a merger remnant cannot have a cusp steeper than the steepest of its progenitors. Furthermore, I argue that the cusp of the remnant should not be shallower either, implying that the steepest cusp always survives.
DOI Link: 10.1111/j.1365-2966.2005.09099.x
Type: Article
Rights: This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society, Copyright 2005 RAS Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
Appears in Collections:Published Articles, Dept. of Physics and Astronomy

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