Search

The Millennium N-body simulation and the Sloan Digital Sky Survey seventh data release (SDSS DR7) galaxy and galaxy group catalogues are compared to study the properties of galaxy groups and the distribution of galaxies in groups. We construct mock galaxy group catalogues for a Millennium semi-analytical galaxy catalogue by using the same friends-of-friends method, which was used by Tago et al to analyse the SDSS data. We analyse in detail the group luminosities, group richnesses, virial radii, sizes of groups and their rms velocities for four volume-limited samples from observations and simulations. Our results show that the spatial densities of groups agree within one order of magnitude in all samples with a rather good agreement between the mock catalogues and observations. All group property distributions have similar shapes and amplitudes for richer groups. For galaxy pairs and small groups, the group properties for observations and simulations are clearly different. In addition, the spatial distribution of galaxies in small groups is different: at the outskirts of the groups the galaxy number distributions do not agree, although the agreement is relatively good in the inner regions. Differences in the distributions are mainly due to the observational limitations in the SDSS sample and to the problems in the semi-analytical methods that produce too compact and luminous groups., Comment: 17 pages, 8 figures

We have compared numerical simulations to observations for the nearby (< 40 Mpc) groups of galaxies (Huchra & Geller 1982 and Ramella et al. 2002). The group identification is carried out using a group-finding algorithm developed by Huchra and Geller (1982). Using cosmological N-body simulation code with the LambdaCDM cosmology, we show that the dynamical properties of groups of galaxies identified from the simulation data are, in general, in a moderate, within 2sigma, agreement with the observational catalogues of groups of galaxies. As simulations offer more dynamical information than observations, we used the N-body simulation data to calculate whether the nearby groups of galaxies are gravitationally bound objects by using their virial ratio. We show that in a LambdaCDM cosmology about 20 per cent of nearby groups of galaxies, identified by the same algorithm as in the case of observations, are not bound, but merely groups in a visual sense. This is quite significant, specifically because estimations of group masses in observations are often based on an assumption that groups of galaxies found by the friends-of-friends algorithm are gravitationally bound objects. Simulations with different resolutions show the same results. We also show how the fraction of gravitationally unbound groups varies when the apparent magnitude limit of the sample and the value of the cosmological constant is changed. In general, a larger value of the Omega_Lambda generates slightly more unbound groups., 13 figures and 7 tables, Accepted 2007 September 19. Received 2007 September 19; in original form 2007 April 2

The cold dark matter (CDM) scenario generically predicts the existence of triaxial dark matter haloes which contain notable amounts of substructure. However, analytical halo models with smooth, spherically symmetric density profiles are routinely adopted in the modelling of light propagation effects through such objects. In this paper, we address the biases introduced by this procedure by comparing the surface mass densities of actual N-body haloes against the widely used analytical model suggested by Navarro, Frenk and White (1996) (NFW). We conduct our analysis in the redshift range of 0.0 - 1.5. In cluster sized haloes, we find that triaxiality can cause scatter in the surface mass density of the haloes up to sigma_+ = +60% and sigma_- = -70%, where the 1-sigma limits are relative to the analytical NFW model given value. Subhaloes can increase this scatter to sigma_+ = +70% and sigma_- = -80%. In galaxy sized haloes, the triaxial scatter can be as high as sigma_+ = +80% and sigma_- = -70%, and with subhaloes the values can change to sigma_+ = +40% and sigma_- = -80%. We present an analytical model for the surface mass density scatter as a function of distance to the halo centre, halo redshift and halo mass. The analytical description enables one to investigate the reliability of results obtained with simplified halo models. Additionally, it provides the means to add simulated surface density scatter to analytical density profiles. As an example, we discuss the impact of our results on the calculation of microlensing optical depths for MACHOs in CDM haloes.

An ensemble of Newtonian three-body models with close initial separations is investigated by following the evolution of a ‘drop’ in the homology map. The onset of chaos is revealed by the motion and the complex temporal deformation of the drop. In the state of advanced chaos, the drop spreads over almost the whole homology map, quite independently of its initial position on the map. A general quantitative measure of this process is the mean exponential rate of spreading, which bears resemblance to Kolmogorov–Sinai entropy; this is introduced and estimated in terms of the homology mapping. In a similar manner we also estimate the mean exponential rate of divergence of initially close-by trajectories. This is a close analogue to the Lyapunov exponent. These parameters measure two complementary aspects of dynamical instability, which is the basic mechanism of the onset of chaos.

ABSTRA C T We have studied the structure of chaos in three-body dynamics using the concept of intermittency, implying that violent states of a system alternate in time with quasi-regular states producing together a non-stationary and evolving pattern of unpredictable behaviour. Computer simulations are produced to demonstrate explicitly sporadic short violent bursts in quasi-regular hierarchical states of the systems. This is seen both in orbits and in the long time series generated by the system. The time series prove to be similar in shape to what is observed in various physical experiments with laboratory chaotic systems when they reveal the so-called type-III intermittency. The new effective methods of time series analysis enable us to discover a strange attractor with a fractal dimension slightly above 2. This shows that three-body dynamics has the same intrinsic qualitative structure and quantitative measure of chaos as the widely known chaotic system, the Lorenz attractor.