A Universal density slope - velocity anisotropy relation for relaxed structures

By S. Hansen, B. Moore. 2004

168 citations recorded by the source corpus.

Abstract 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, and 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 stars are assumed to obey Tsallis statistics, and in that case we fit the α–β relation with just one free parameter. One can use this result to close the Jeans equations, for example to construct mass models of elliptical galaxies from observational data or to tune dark matter structures directly to detection experiments. We also predict the asymptotic central slope and anisotropy of CDM halos to be approximately −1 and 0.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ff0ab2ad8cd234fe62609861b08e720e7f4c38d3

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Citations in the corpus

Galactic Searches for Dark Matter (2012, background): “f the velocity anisotropy prole. Though it does qualitatively provide the correct behavior for , the slope of the rise of is much steeper than what is seen on average in simulated dark matter halos. Hansen and Moore (2006) more accurately quantify the relation between the anisotropy and the log-slop”
CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z = 0.44 galaxy cluster MACS J1206.2-0847 (2013, background): “…betweenβ(r) and the logarithmic derivative of the total mass density profile,γ(r), for all, passive, and SF member galaxies (top, middle, and bottom panel, respectively), within 1 σ confidence regions (shaded regions), and the theoreticalγ-β relation of Hansen & Moore (2006) (dashed line).”
Formation of Galaxy Clusters (2012, background): “Another interestingfinding is that the velocity anisotropy correlates with the slope of the density profile (Hansen & Moore 2006), albeit with significant scatter (Lemze et al. 2011).”
Dark matter direct detection with non-Maxwellian velocity structure (2009, background): “It is well established that numerically simulated dark matter halos exhibit significant velocity anisotropy and global departures from a Maxwell-Boltzmann distribution [17, 18, 19, 20].”
MAMPOSSt: Modelling Anisotropy and Mass Profiles of Observed Spherical Systems – I. Gaussian 3D velocities (2012, methodology): “…= Min [ 1, (r/rβ) 1/3 ] is another model that fits well the anisotropy ofΛCDM haloes withrβ = rv (Diemand, Moore, & Stadel 2004), while the last two rows describe the anisotropy that varies linearly with the slope of the density profile (Hansen & Moore 2006), since the kernel depends on the…”
A lower bound on the mass of dark matter particles (2008, background): “This assumption seems to be correct for the DM particles, since numerical simulations of DM structures of different scales show that the velocity anisotropy β(r) ≡ 1 − σ θ+σ 2 φ 2σ r tends to be zero towards the central region [97–101].”
Hunting for the Dark Matter Wake Induced by the Large Magellanic Cloud (2019, methodology): “We build two MW models with different forms for the ra- dial anisotropic profile, β(r): 1) Model 1 assumes an isotropic DM halo (β = 0); and 2) Model 2 assumes a radially varying profile (Hansen & Moore 2006): β(r) = −0.5− 0.2α(r) ; α(r) = dln ρ(r) dln r .”
The diversity and similarity of simulated cold dark matter haloes (2008, methodology): “The relation recently proposed by Hansen & Moore (2006) works reasonably well in the inner regions (r r−2), but fails at larger radii.”
Dark matter response to galaxy formation (2009, background): “Hansen & Moore (2006) suggested that there might be a “universal” relation between these parameters in dissipationaless haloes.”