The Ariki-Terasoma-Yamada tensor space and the blob-algebra

We show that the Ariki-Terasoma-Yamada tensor module and its permutation submodules $M(\lambda)$ are modules for the blob algebra when the Ariki-Koike algebra is a Hecke algebra of type $B$. We show that $M(\lambda)$ and the standard modules $\Delta(\lambda)$ have the same dimensions, the same localization and similar restriction properties and are equal in the Grothendieck group. Still we find that the universal property for $\Delta(\lambda)$ fails for $M(\lambda)$, making $M(\lambda)$ and $\Delta(\lambda)$ different modules in general. Finally, we prove that $M(\lambda)$ is isomorphic to the dual Specht module for the Ariki-Koike algebra.Comment: Improved version

Cluster temperatures and non-extensive thermo-statistics

We propose a novel component to the understanding of the temperature structure of galaxy clusters which does not rely on any heating or cooling mechanism. The new ingredient is the use of non-extensive thermo-statistics which is based on the natural generalization of entropy for systems with long-range interactions. Such interactions include gravity and attraction or repulsion due to charges. We explain that there is growing theoretical indications for the need of this generalization for large cosmological structures. The observed pseudo temperature is generally different from the true thermodynamic temperature, and we clarify the connection between the two. We explain that this distinction is most important in the central part of the cluster where the density profile is most shallow. We show that the observed pseudo temperature may differ up to a factor 2/5 from the true thermodynamic temperature, either larger or smaller. In general the M-T and L-T relations will be affected, and the central DM slope derived through hydrostatic equilibrium may be either more shallow or steeper. We show how the true temperature can be extracted correctly either from the spectrum or from the shape of the Doppler broadening of spectral lines.Comment: 11 pages, 1 figur

The behaviour of shape and velocity anisotropy in dark matter haloes

Dark matter haloes from cosmological N-body simulations typically have triaxial shapes and anisotropic velocity distributions. Recently it has been shown that the velocity anisotropy, beta, of cosmological haloes and major merger remnants depends on direction in such a way that beta is largest along the major axis and smallest along the minor axis. In this work we use a wide range of non-cosmological N-body simulations to examine halo shapes and direction-dependence of velocity anisotropy profiles. For each of our simulated haloes we define 48 cones pointing in different directions, and from the particles inside each cone we compute velocity anisotropy profiles. We find that elongated haloes can have very distinct velocity anisotropies. We group the behaviour of haloes into three different categories, that range from spherically symmetric profiles to a much more complex behaviour, where significant differences are found for beta along the major and minor axes. We encourage future studies of velocity anisotropies in haloes from cosmological simulations to calculate beta-profiles in cones, since it reveals information, which is hidden from a spherically averaged profile. Finally, we show that spherically averaged profiles often obey a linear relation between beta and the logarithmic density slope in the inner parts of haloes, but this relation is not necessarily obeyed, when properties are calculated in cones.Comment: 23 pages, 14 figures. Accepted for publication in JCA

Asymmetric velocity anisotropies in remnants of collisionless mergers

Dark matter haloes in cosmological N-body simulations are affected by processes such as mergers, accretion and the gravitational interaction with baryonic matter. Typically the analysis of dark matter haloes is performed in spherical or elliptical bins and the velocity distributions are often assumed to be constant within those bins. However, the velocity anisotropy, which describes differences between the radial and tangential velocity dispersion, has recently been show to have a strong dependence on direction in the triaxial halos formed in cosmological simulations. In this study we derive properties of particles in cones parallel or perpendicular to the collision axis of merger remnants. We find that the velocity anisotropy has a strong dependence on direction. The finding that the direction-dependence of the velocity anisotropy of a halo depends on the merger history, explains the existence of such trends in cosmological simulations. It also explains why a large diversity is seen in the velocity anisotropy profiles in the outer parts of high-resolution simulations of cosmological haloes.Comment: 19 pages, 15 figures, Resubmitted to JCAP after referee comment