Constraining Omega using weak gravitational lensing by clusters

The morphology of galaxy clusters reflects the epoch at which they formed and hence depends on the value of the mean cosmological density, Omega. Recent studies have shown that the distribution of dark matter in clusters can be mapped from analysis of the small distortions in the shapes of background galaxies induced by weak gravitational lensing in the cluster potential. We construct new statistics to quantify the morphology of clusters which are insensitive to limitations in the mass reconstruction procedure. By simulating weak gravitational lensing in artificial clusters grown in numerical simulations of the formation of clusters in three different cosmologies, we obtain distributions of a quadrupole statistic which measures global deviations from spherical symmetry in a cluster. These distributions are very sensitive to the value of Omega_0 and, as a result, lensing observations of a small number of clusters should be sufficient to place broad constraints on Omega_{0} and certainly to distinguish between the extreme values of 0.2 and 1.Comment: Submitted to MNRAS. Compressed postscript also available at ftp://star-ftp.dur.ac.uk/pub/preprints/wcf2.ps.g

Extending the halo mass resolution of NN-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.Comment: 11 pages, 7 Figure

Massive dark matter haloes around bright isolated galaxies in the 2dFGRS

We identify a large sample of isolated bright galaxies and their fainter satellites in the 2dF Galaxy Redshift Survey (2dFGRS). We analyse the dynamics of ensembles of these galaxies selected according to luminosity and morphological type by stacking the positions of their satellites and estimating the velocity dispersion of the combined set. We test our methodology using realistic mock catalogues constructed from cosmological simulations. The method returns an unbiased estimate of the velocity dispersion provided that the isolation criterion is strict enough to avoid contamination and that the scatter in halo mass at fixed primary luminosity is small. Using a maximum likelihood estimator that accounts for interlopers, we determine the satellite velocity dispersion within a projected radius of 175 h−1kpc. The dispersion increases with the luminosity of the primary and is larger for elliptical galaxies than for spiral galaxies of similar bJ luminosity. Calibrating the mass-velocity dispersion relation using our mock catalogues, we find a dynamical mass within 175 h−1kpc of for elliptical galaxies and for spiral galaxies. Finally, we compare our results with recent studies and investigate their limitations using our mock catalogue

Evolution of galactic planes of satellites in the eagle simulation

We study the formation of planes of dwarf galaxies around Milky Way (MW)-mass haloes in the EAGLE galaxy formation simulation. We focus on satellite systems similar to the one in the MW: spatially thin or with a large fraction of members orbiting in the same plane. To characterize the latter, we introduce a robust method to identify the subsets of satellites that have the most coplanar orbits. Out of the 11 MW classical dwarf satellites, 8 have highly clustered orbital planes whose poles are contained within a 22° opening angle centred around (l, b) = (182°, −2°). This configuration stands out when compared to both isotropic and typical ΛCDM satellite distributions. Purely flattened satellite systems are short-lived chance associations and persist for less than 1Gyr⁠. In contrast, satellite subsets that share roughly the same orbital plane are longer lived, with half of the MW-like systems being at least 4Gyr old. On average, satellite systems were flatter in the past, with a minimum in their minor-to-major axes ratio about 9Gyr ago, which is the typical infall time of the classical satellites. MW-like satellite distributions have on average always been flatter than the overall population of satellites in MW-mass haloes and, in particular, they correspond to systems with a high degree of anisotropic accretion of satellites. We also show that torques induced by the aspherical mass distribution of the host halo channel some satellite orbits into the host’s equatorial plane, enhancing the fraction of satellites with coplanar orbits. In fact, the orbital poles of coplanar satellites are tightly aligned with the minor axis of the host halo

Using the Evolution of Clusters to Constrain Omega

The population of rich galaxy clusters evolves much more rapidly in a universe with critical density than one with low density, thus offering the possibility of determining the cosmological density parameter, Omega_0. We quantify this evolution using the Press-Schechter formalism which we extend to flat models with a cosmological constant. Using new large N-body simulations, we verify that this formalism accurately predicts the abundance of rich clusters as a function of redshift in various cosmologies. We normalise the models by comparing them to the local abundance of clusters as a function of their X-ray temperature which we rederive from data compiled by Henry & Arnaud. This gives values of the rms density fluctuation in spheres of radius 8 Mpc/h of sigma_8 = (0.50+/- 0.04) Omega_0^{-0.47+0.10 Omega_0} if Lambda_0=0 and sigma_8 = (0.50 +/- 0.04) Omega_0^{-0.53+0.13 Omega_0} if Lambda_0=1-Omega_0. These values depend very weakly on the shape of the power spectrum. We then examine how the distributions of mass, X-ray temperature and Sunyaev-Zel'dovich decrement evolve as a function of Omega_0. We present the expected distributions at z=0.33 and z=0.5 and the predicted number counts of the largest clusters. We find that even at z=0.33, these distributions depend very strongly on Omega_0 and only weakly on Lambda_0. For example, at this redshift, we expect 20 times as many clusters per comoving volume with M>3.5 10^{14} Msol/h and 5 times as many clusters with kT>5 keV if Omega_0=0.3 than if Omega_0=1. The splitting in the integrated counts is enhanced by the larger volume element in low Omega_0 models. There is therefore a real prospect of estimating Omega_0 from forthcoming surveys of intermediate redshift clusters that will determine their masses, X-ray temperatures or SZ decrements.Comment: Compressed postscript also available at ftp://star-ftp.dur.ac.uk/pub/preprints/ecf.ps.g