Velocity Distributions from Nonextensive Thermodynamics

Barnes, Eric I.; Williams, Liliya L. R.; Babul, Arif; Dalcanton, Julianne J.

doi:10.1086/509871

Cited by 9 publications

(11 citation statements)

References 22 publications

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“…Some analytical studies suggest that secondary infall and accretion can determine the density profile shape (Avila-Rees et al 1998). Barnes et al (2005a) argue that the density profile, and in particular its radially changing slope, is the result of a mild aspect of the radial orbit instability.…”

Section: Introductionmentioning

confidence: 96%

Semianalytical Dark Matter Halos and the Jeans Equation

Austin

Williams

Barnes

et al. 2005

ApJ

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Although N-body studies of dark matter halos show that the density profiles, ρ(r), are not simple power-laws, the quantity ρ/σ 3 , where σ(r) is the velocity dispersion, is in fact a featureless power-law over ∼ 3 decades in radius. In the first part of the paper we demonstrate, using the semi-analytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of ρ/σ 3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N-body and semi-analytic approaches, we argue that the scale-free nature of ρ/σ 3 cannot be the result of hierarchical merging, rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use ρ/σ 3 ∝ r −α as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique "periodic" solution with α = 1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of ρ ∼ r −0.78 , and ρ ∼ r −3.44 , respectively.

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Section: Introductionmentioning

confidence: 96%

Semianalytical Dark Matter Halos and the Jeans Equation

Austin

Williams

Barnes

et al. 2005

ApJ

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“…Some of these issues have been addressed in terms of modifications of the extent of the relaxation process, so-called incomplete violent relaxation (Stiavelli & Bertin 1987), relaxation in a finite volume (Hjorth & Madsen 1991), or explicit scattering processes (Spergel & Hernquist 1992). Another approach has been to propose a change in the entropy functional to be optimized, applicable to non-extensive systems (Tsallis 1988;Plastino & Plastino 1993), although this has been demonstrated not to work (Barnes et al 2007;Féron & Hjorth 2008).…”

Section: Introductionmentioning

confidence: 99%

Statistical Mechanics of Collisionless Orbits. I. Origin of Central Cusps in Dark-Matter Halos

Hjorth

Williams

2010

ApJ

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We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible microstates is computed in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirling's approximation. Combined, the two modifications predict that the relaxed parts of collisionless self-gravitating systems, such as dark-matter halos, have a differential energy distribution N (ε) ∝ [exp(φ 0 − ε) − 1], dubbed "DARKexp". Such systems have central power-law density cusps ρ(r) ∝ r −1 , which suggests a statistical mechanical origin of cusps in simulated dark-matter halos.

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“…2 2 For example, while it is clear from N ‐body simulations that the action of 1/ r 2 gravitational forces in a cold dark matter (CDM) universe leads to dark matter haloes with approximately Navarro–Frenk–White (NFW) density profiles, there is a clear drive to provide simple, analytic models to demonstrate that we understand the underlying physics of these profiles (Taylor & Navarro 2001; Barnes et al 2007a,b). …”

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confidence: 99%

Galaxy formation spanning cosmic history

Benson

Bower

2010

Monthly Notices of the Royal Astronomical Society

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Over the past several decades, galaxy formation theory has met with significant successes. In order to test current theories thoroughly we require predictions for as yet unprobed regimes. To this end, we describe a new implementation of the GALFORM semi-analytic model of galaxy formation. Our motivation is the success of the model described by Bower et al. in explaining many aspects of galaxy formation. Despite this success, the Bower et al. model fails to match some observational constraints, and certain aspects of its physical implementation are not as realistic as we would like. The model described in this work includes substantially updated physics, taking into account developments in our understanding over the past decade, and removes certain limiting assumptions made by these (and most other) semi-analytic models. This allows it to be exploited reliably in high-redshift and low-mass regimes. Furthermore, we have performed an exhaustive search of model parameter space to find a particular set of model parameters which produce results in good agreement with a wide range of observational data (luminosity functions, galaxy sizes and dynamics, clustering, colours, metal content) over a wide range of redshifts. This model represents a solid basis on which to perform calculations of galaxy formation in as yet unprobed regimes.

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Velocity Distributions from Nonextensive Thermodynamics

Cited by 9 publications

References 22 publications

Semianalytical Dark Matter Halos and the Jeans Equation

Semianalytical Dark Matter Halos and the Jeans Equation

Statistical Mechanics of Collisionless Orbits. I. Origin of Central Cusps in Dark-Matter Halos

Galaxy formation spanning cosmic history

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