Orbital anisotropy in cosmological haloes revisited

Abstract

The velocity anisotropy of particles inside dark matter (DM) haloes is an important physical quantity, which is required for the accurate modelling of mass profiles of galaxies and clusters of galaxies. It is typically measured using the ratio of the radialto-tangential velocity dispersions at a given distance from the halo centre. However, this measure is insufficient to describe the dynamics of realistic haloes, which are not spherical and are typically quite elongated. Studying the velocity distribution in massive DM haloes in cosmological simulations, we find that in the inner parts of the haloes the local velocity ellipsoids are strongly aligned with the major axis of the halo, the alignment being stronger for more relaxed haloes. In the outer regions of the haloes, the alignment becomes gradually weaker and the orientation is more random. These two distinct regions of different degree of the alignment coincide with two characteristic regimes of the DM density profile: a shallow inner cusp and a steep outer profile that are separated by a characteristic radius at which the density declines as ρ ∝ r −2 . This alignment of the local velocity ellipsoids requires reinterpretation of features found in measurements based on the spherically averaged ratio of the radial-to-tangential velocity dispersions. In particular, we show that the velocity distribution in the central halo regions is highly anisotropic. For cluster-size haloes with mass 10 14 − 10 15 h −1 M ⊙ , the velocity anisotropy along the major axis is nearly independent of radius and is equal to β = 1 − σ 2 perp /σ 2 radial ≈ 0.4, which is significantly larger than the previously estimated spherically averaged velocity anisotropy. The alignment of density and velocity anisotropies, and the radial trends may also have some implications for the mass modelling based on kinematical data of such objects as galaxy clusters or dwarf spheroidals, where the orbital anisotropy is a key element in an unbiased mass inference.

The impact of galaxy formation on satellite kinematics and redshift-space distortions

“…iv) Finally, we explored a description of velocities in which the anisotropy of the intra-halo velocity distribution is preserved. The anisotropy of the velocity dispersion has been shown to be key to interpret and model kinematic mass data (Wojtak et al 2013;Kafle et al 2014) and can thus lead to further corrections in the amplitude of fingers of god, especially if the anisotropy depends on the properties of the galaxy samples. To construct these galaxy samples we preserve the radial component of the intra-halo velocity of each galaxy, and randomize the direction of the tangential component.…”

Globular clusters formed within dark haloes I: present-day abundance, distribution, and kinematics

“…Unless explicitly mentioned, we focus on our fiducial tagging model, although the results presented do not depend significantly on this assumption. Dark matter halos within ΛCDM have radially biased orbits (Wojtak et al 2009(Wojtak et al , 2013 with apocentres that are significantly larger than the pericentres. Numerical simulations have shown that subhalos (and therefore satellite galaxies inhabiting those subhalos) inherit such elliptical orbits (Sales et al 2007;Iannuzzi & Dolag 2012), an effect that contributes to the disruption and lowering of star formation in satellites, even for those seemingly today in the outskirts of groups and clusters.…”

On the dark matter profile in Sculptor: breaking the β degeneracy with Virial shape parameters

“…Unfortunately, the method presented here also depends on the assumption that the velocity ellipsoid is spherical. This introduces an additional bias to the anisotropy parameter as discussed in Wojtak et al (2013) for tracers in cluster sized haloes. Replacing the Jeans equations with the Virial equations enables us to include information on the shape of the LOS velocity distribution without reference to β , the anisotropy between the shape of the radial and tangential distributions.…”