How general is the global density slope-anisotropy inequality?
نویسندگان
چکیده
منابع مشابه
The velocity anisotropy - density slope relation
One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection between velocity anisotropy and density slope, the α − β relation. The first (phase-space density v.s. radius) has already been analysed through several diffe...
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We identify a universal relation between the radial density slope α(r) and the velocity anisotropy β(r) for equilibrated structures. This relation holds for a variety of systems, including disk galaxy mergers, spherical collapses, cold dark matter (CDM) halos both with and without cooling. We argue that the shape of the relation is reasonable from fundamental principles when the dark matter or ...
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Dark matter (DM) halos formed in CDM cosmologies seem to be characterized by a power law phasespace density profile. The density of the DM halos is often fitted by the NFW profile but a better fit is provided by the Sersic fitting formula. These relations are empirically derived from cosmological simulations of structure formation but have not yet been explained on a first principle basis. Here...
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Let Mg be the moduli space of stable curves of genus g ≥ 2. Let ∆i be the irreducible component of the boundary of Mg such that general points of ∆i correspond to stable curves with one node of type i. Let M 0 g be the set of stable curves that have at most one node of type i > 0. Let δi be the class of ∆i in Pic(Mg)⊗Q and λ the Hodge class onMg. In this paper, we will prove a sharp slope inequ...
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For a wide class of self-gravitating systems, we show that if the density is cusped like r −γ near the center, then the limiting value of the anisotropy parameter β = 1 − v 2 T /(2v 2 r) at the center may not be greater than γ/2. Here, v 2 r and v 2 T are the radial and tangential velocity second moments. This follows from the non-negativity of the phase space density. We compare this theorem t...
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ژورنال
عنوان ژورنال: Monthly Notices of the Royal Astronomical Society
سال: 2010
ISSN: 0035-8711
DOI: 10.1111/j.1365-2966.2010.17184.x