29 research outputs found

### Phase-space shapes of clusters and rich groups of galaxies

Clusters and groups of galaxies are highly aspherical, with shapes
approximated by nearly prolate ellipsoids of revolution. An equally fundamental
property is the shape of these objects in velocity space which is the
anisotropy of the global velocity dispersion tensor. Here we make use of
kinematical data comprising around 600 nearby clusters and rich groups of
galaxies from the SDSS to place constraints on the phase-space shapes of these
objects, i.e. their shapes in both position and velocity space. We show that
the line of sight velocity dispersion normalised by a mass dependent velocity
scale correlates with the apparent elongation, with circular (elongated)
clusters exhibiting an excessive (decremental) normalised velocity dispersion.
This correlation holds for dynamically young or old clusters and, therefore, it
originates from projecting their intrinsic phase-space shapes rather than from
dynamical evolution. It signifies that clusters are preferentially prolate not
only in position space, but also in velocity space. The distribution of the
axial ratios in position space is found to be well approximated by a Gaussian
with a mean 0.66+/-0.01 and a dispersion 0.07+/-0.008. The velocity ellipsoids
representing the shapes in velocity space are more spherical, with a mean axial
ratio of 0.78+/-0.03. This finding has important implications for mass
measurements based on the line of sight velocity dispersion profiles in
individual clusters. For typical axial ratios of the velocity ellipsoids in the
analysed cluster sample, systematic errors on the mass estimates inferred from
the line of sight velocity dispersions become comparable to statistical
uncertainties for galaxy clusters with as few as 40 spectroscopic redshifts.Comment: 9 pages, 7 figures; published in A&A; typo in eq. 5 correcte

### 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

### Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations

We compare the DARKexp differential energy distribution, N(E) \propto
\exp(\phi_0-E)-1, obtained from statistical mechanical considerations, to the
results of N-body simulations of dark matter halos. We first demonstrate that
if DARKexp halos had anisotropic velocity distributions similar to those of
N-body simulated halos, their density and energy distributions could not be
distinguished from those of isotropic DARKexp halos. We next carry out the
comparison in two ways, using (1) the actual energy distribution extracted from
simulations, and (2) N-body fitting formula for the density distribution as
well as N(E) computed from the density using the isotropic Eddington formula.
Both the methods independently agree that DARKexp N(E) with \phi_0\approx 4-5
is an excellent match to N-body N(E). Our results suggest (but do not prove)
that statistical mechanical principles of maximum entropy can be used to
explain the equilibrated final product of N-body simulations.Comment: 17 pages, 7 figures; ApJ, in pres

### Radial velocity moments of dark matter haloes

Using cosmological N-body simulations we study the radial velocity
distribution in dark matter haloes focusing on the lowest-order even moments,
dispersion and kurtosis. We determine the properties of ten massive haloes in
the simulation box approximating their density distribution by the NFW formula
characterized by the virial mass and concentration. We also calculate the
velocity anisotropy parameter of the haloes and find it mildly radial and
increasing with distance from the halo centre. The radial velocity dispersion
of the haloes shows a characteristic profile with a maximum, while the radial
kurtosis profile decreases with distance starting from a value close to
Gaussian near the centre. We therefore confirm that dark matter haloes possess
intrinsically non-Gaussian, flat-topped velocity distributions. We find that
the radial velocity moments of the simulated haloes are quite well reproduced
by the solutions of the Jeans equations obtained for the halo parameters with
the anisotropy measured in the simulations. We also study the radial velocity
moments for a composite cluster made of ten haloes out to ten virial radii. In
this region the velocity dispersion decreases systematically to reach the value
of the background, while kurtosis increases from below to above the Gaussian
value of 3 signifying a transition from a flat-topped to a strongly peaked
velocity distribution with respect to the Gaussian, which can be interpreted as
the dominance of ordered flow with a small dispersion. We illustrate the
transition by showing explicitly the velocity distribution of the composite
cluster in a few radial bins.Comment: 5 pages, 4 figures, minor changes, accepted for publication in MNRAS
Letter

### Velocity moments of dark matter haloes

Using cosmological N-body simulations we study the line-of-sight velocity
distribution of dark matter haloes focusing on the lowest-order even moments,
dispersion and kurtosis, and their application to estimate the mass profiles of
cosmological structures. For each of the ten massive haloes selected from the
simulation box we determine the virial mass, concentration and the anisotropy
parameter. In order to emulate observations from each halo we choose randomly
300 particles and project their velocities and positions along the line of
sight and on the surface of the sky, respectively. After removing interlopers
we calculate the profiles of the line-of-sight velocity moments and fit them
with the solutions of the Jeans equations. The estimates of virial mass,
concentration parameter and velocity anisotropy obtained in this way are in
good agreement with the values found from the full 3D analysis.Comment: 2 pages, 1 figure, poster contribution to the proceedings of the
XXIst IAP Colloquium "Mass Profiles and Shapes of Cosmological Structures",
Paris 4-9 July 2005, Editors: G. Mamon, F. Combes, C. Deffayet, B. Fort, EDP
Sciences, in pres

### Mass distribution in nearby Abell clusters

We study the mass distribution in six nearby (z<0.06) relaxed Abell clusters
of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of
dark matter in galaxy clusters we approximate their total density distribution
by the NFW formula characterized by virial mass and concentration. We also
assume that the anisotropy of galactic orbits is reasonably well described by a
constant and that galaxy distribution traces that of the total density. Using
the velocity and position data for 120-420 galaxies per cluster we calculate,
after removal of interlopers, the profiles of the lowest-order even velocity
moments, dispersion and kurtosis. We then reproduce the velocity moments by
jointly fitting the moments to the solutions of the Jeans equations. Including
the kurtosis in the analysis allows us to break the degeneracy between the mass
distribution and anisotropy and constrain the anisotropy as well as the virial
mass and concentration. The method is tested in detail on mock data extracted
from N-body simulations of dark matter haloes. We find that the best-fitting
galactic orbits are remarkably close to isotropic in most clusters. Using the
fitted pairs of mass and concentration parameters for the six clusters we
conclude that the trend of decreasing concentration for higher masses found in
cosmological N-body simulations is consistent with the data. By scaling the
individual cluster data by mass we combine them to create a composite cluster
with 1465 galaxies and perform a similar analysis on such sample. The estimated
concentration parameter then lies in the range 1.5 < c < 14 and the anisotropy
parameter in the range -1.1 < \beta < 0.5 at the 95 percent confidence level.Comment: 11 pages, 9 figures, final version accepted for publication in MNRA

### A new method to measure the mass of galaxy clusters

The mass measurement of galaxy clusters is an important tool for the
determination of cosmological parameters describing the matter and energy
content of the Universe. However, the standard methods rely on various
assumptions about the shape or the level of equilibrium of the cluster. We
present a novel method of measuring cluster masses. It is complementary to most
of the other methods, since it only uses kinematical information from outside
the virialized cluster. Our method identifies objects, as galaxy sheets or
filaments, in the cluster outer region, and infers the cluster mass by modeling
how the massive cluster perturbs the motion of the structures from the Hubble
flow. At the same time, this technique allows to constrain the
three-dimensional orientation of the detected structures with a good accuracy.
We use a cosmological numerical simulation to test the method. We then apply
the method to the Coma cluster, where we find two galaxy sheets, and measure
the mass of Coma to be Mvir=(9.2\pm2.4)10^{14} Msol, in good agreement with
previous measurements obtained with the standard methods.Comment: 10 pages, 12 figures, submitted to MNRA