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

Observational constraints on the inflaton potential combined with flow-equations in inflaton space

Direct observations provide constraints on the first two derivatives of the inflaton potential in slow roll models. We discuss how present day observations, combined with the flow equations in slow roll parameter space, provide a non-trivial constraint on the third derivative of the inflaton potential. We find a lower bound on the third derivative of the inflaton potential V'''/V > -0.2. We also show that unless the third derivative of the inflaton potential is unreasonably large, then one predicts the tensor to scalar ratio, r, to be bounded from below r > 3 * 10^{-6}.Comment: 4 pages, 2 figures. Important sign mistake corrected. Conclusions, abstract and discussion change

Analytical derivation of the radial distribution function in spherical dark matter halos

The velocity distribution of dark matter near the Earth is important for an accurate analysis of the signals in terrestrial detectors. This distribution is typically extracted from numerical simulations. Here we address the possibility of deriving the velocity distribution function analytically. We derive a differential equation which is a function of radius and the radial component of the velocity. Under various assumptions this can be solved, and we compare the solution with the results from controlled numerical simulations. Our findings complement the previously derived tangential velocity distribution. We hereby demonstrate that the entire distribution function, below 0.7 v_esc, can be derived analytically for spherical and equilibrated dark matter structures.Comment: 6 pages, 5 figures, submitted to MNRA

Effect of asphericity in caustic mass estimates of galaxy clusters

The caustic technique for measuring mass profiles of galaxy clusters relies on the assumption of spherical symmetry. When applied to aspherical galaxy clusters, the method yields mass estimates affected by the cluster orientation. Here we employ mock redshift catalogues generated from cosmological simulations to study the effect of clusters intrinsic shape and surrounding filamentary structures on the caustic mass estimates. To this end, we develop a new method for removing perturbations from large-scale structures, modelled as the two-halo term, in a caustic analysis of stacked cluster data. We find that the cluster masses inferred from kinematical data of ~10^14 Msun clusters observed along the major axis are larger than masses from those observed along the minor axis by a factor of 1.7 within the virial radius, increasing to 1.8 within three virial radii. This discrepancy increases by 20% for the most massive clusters. In addition a smaller but still significant mass discrepancy arises when filamentary structures are present near a galaxy cluster. We find that the mean cluster mass from random sightlines is unbiased at all radii and their scatter ranges from 0.14 to 0.17 within one and three virial radii, with a 40% increase for the most massive clusters. We provide tables which estimate the caustic mass bias given observational constraints on the cluster orientation.Comment: 19 pages, 9 figures, 6 tables, accepted for publication in MNRA