On the Dynamical Origin of Bias in Clusters of Galaxies

Monthly Notices of the Royal Astronomical Society, 2000

We have used a combination of high resolution cosmological N-body simulations and semi-analytic modelling of galaxy formation to investigate the processes that determine the spatial distribution of galaxies in cold dark matter (CDM) models and its relation to the spatial distribution of dark matter. The galaxy distribution depends sensitively on the efficiency with which galaxies form in halos of different mass. In small mass halos, galaxy formation is inhibited by the reheating of cooled gas by feedback processes, whereas in large mass halos, it is inhibited by the long cooling time of the gas. As a result, the mass-to-light ratio of halos has a deep minimum at the halo mass, ∼ 10 12 M ⊙ , associated with L * galaxies, where galaxy formation is most efficient. This dependence of galaxy formation efficiency on halo mass leads to a scale-dependent bias in the distribution of galaxies relative to the distribution of mass. On large scales, the bias in the galaxy distribution is related in a simple way to the bias in the distribution of massive halos. On small scales, the correlation function is determined by the interplay between various effects including the spatial exclusion of dark matter halos, the distribution function of the number of galaxies occupying a single dark matter halo and, to a lesser extent, dynamical friction. Remarkably, these processes conspire to produce a correlation function in a flat, Ω 0 = 0.3, CDM model that is close to a power-law over nearly four orders of magnitude in amplitude. This model agrees well with the correlation function of galaxies measured in the APM survey. On small scales, the model galaxies are less strongly clustered than the dark matter, whereas on large scales they trace the occupied halos. Our clustering predictions are robust to changes in the parameters of the galaxy formation model, provided only those models that match the bright end of the galaxy luminosity function are considered.

1986

In the Cold Dark Matter (hereafter CDM) scenario even isolated density peaks contain a high fraction of small scale clumps having velocities larger than the average escape velocity from the structure. These clumps populate protoclusters, especially in the peripheral regions, r ≥ R f (where R f is the filtering scale). During the cluster collapse and the subsequent secondary infall, collapsing or infalling clumps (having v < vesc) interact with the quoted unbound clumps (or high speed clumps, as we also call them) having v > vesc. We study the interaction between these two kind of clumps by means of the impulse approximation 1 and we find that the collapse of bound clumps is accelerated with respect to the homogeneous case (Gunn & Gott's model, Ref. 2). The acceleration of the collapse increases with decreasing height of the peak, ν. We finally compare the acceleration produced by this effect to the slowing down effect produced by the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-clusters studied in Del Popolo & Gambera 3 . We find that the magnitude of the slowing down effect is larger than the acceleration produced by the effect studied in this paper, only in the outskirts of the cluster. We want to stress that the one which we study in this paper is also present in an isolated protocluster, being produced by the interaction of the collapsing clumps with the unbound substructure internal to the collapsing clumps itself while that studied in Ref. 3 is produced by substructure external to the density peak.

Monthly Notices of the Royal Astronomical Society, 1997

We outline a simple approach to understanding the physical origin of bias in the distribution of galaxies relative to that of dark matter. The rst step is to specify how collapsed, virialized halos of dark matter trace the overall matter distribution.

Aims. In the present paper, we improve the " extended secondary infall model " (ESIM) of Williams and collaborators to obtain further insights into the cusp/core problem. Methods. A secondary infall model close to the collapse reality is obtained by simultaneously taking into account effects that till now have been studied separately, namely ordered and random angular momentum, dynamical friction, and baryon adiabatic contraction. The model is applied to structures on galactic scales (normal and dwarf spiral galaxies) and on galaxy cluster scales. Results. Our results imply that angular momentum and dynamical friction are able, on galactic scales, of overcoming the competing effect of adiabatic contraction and eliminating the Cusp. The NFW profile is not the standard outcome of the model, and it can be recovered in our model only if the system consists entirely of dark matter and the magnitude of angular momentum and dynamical friction are lower than the values predicted by the model itself. Comparison of the rotation curves of LSB galaxies with the results of our model are in good agreement. On scales smaller than 10 11 h −1 M , the slope is α 0, and on cluster scales we observe a similar evolution in the dark matter density profile but in this case the density profile slope flattens to α 0.7 for a cluster of 10 14 h −1 M. The total mass profile differs from that of dark matter showing a central cusp that is reproduced by a NFW model.

Monthly Notices of the Royal Astronomical Society, 1998

This paper presents a stochastic approach to the clustering evolution of dark matter haloes in the Universe. Haloes, identified by a Press-Schechter-type algorithm in Lagrangian space, are described in terms of 'counting fields', acting as non-linear operators on the underlying Gaussian density fluctuations. By ensemble averaging these counting fields, the standard Press-Schechter mass function as well as analytic expressions for the halo correlation function and corresponding bias factors of linear theory are obtained, extending the recent results by Mo and White. The non-linear evolution of our halo population is then followed by solving the continuity equation, under the sole hypothesis that haloes move by the action of gravity. This leads to an exact and general formula for the bias field of dark matter haloes, defined as the local ratio between their number density contrast and the mass density fluctuation. Besides being a function of position and 'observation' redshift, this random field depends upon the mass and formation epoch of the objects and is both non-linear and non-local. The latter features are expected to leave a detectable imprint on the spatial clustering of galaxies, as described, for instance, by statistics like the bispectrum and the skewness. Our algorithm may have several interesting applications, among which the possibility of generating mock halo catalogues from low-resolution N-body simulations.

International Journal of Modern Physics A, 2002

In the Cold Dark Matter (hereafter CDM) scenario even isolated density peaks contain a high fraction of small scale clumps having velocities larger than the average escape velocity from the structure. These clumps populate protoclusters, especially in the peripheral regions, r≥R f (where R f is the filtering scale). During the cluster collapse and the subsequent secondary infall, collapsing or infalling clumps (having vv esc . We study the interaction between these two kinds of clumps by means of the impulse approximation1 and we find that the collapse of bound clumps is accelerated with respect to the homogeneous case (Gunn and Gott&#39;s model, Ref. 2). The acceleration of the collapse increases with decreasing height of the peak, ν. We finally compare the acceleration produced by this effect to the slowing down effect produced by the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-clusters studied by Del...

We investigate the large-scale distribution of galaxy clusters taken from several X-ray catalogs. Different statistics of clustering like the conditional correlation function (CCF) and the minimal spanning tree (MST) as well as void statistics were used. Clusters show two distinct regimes of clustering: 1) on scales of superclusters (∼ 40h −1 Mpc) the CCF is represented by a power law; 2) on larger scales a gradual transition to homogeneity (∼ 100h −1 Mpc) is observed. We also present the correlation analysis of the galaxy distribution taken from DR6 SDSS main galaxy database. In case of galaxies the limiting scales of the different clustering regimes are 1)10-15 h −1 Mpc; 2) 40 − 50h −1 Mpc. The differences in the characteristic scales and scaling exponents of the cluster and galaxy distribution can be naturally explained within the theory of biased structure formation. We compared the density contrasts of inhomogeneities in the cluster

Physical Review D, 2001

In the cold dark matter model of structure formation, galaxies are assembled hierarchically from mergers and the accretion of subclumps. This process is expected to leave residual substructure in the Galactic dark halo, including partially disrupted clumps and their associated tidal debris. We develop a model for such halo substructure and study its implications for dark matter (WIMP and axion) detection experiments. We combine the Press-Schechter model for the distribution of halo subclump masses with N-body simulations of the evolution and disruption of individual clumps as they orbit through the evolving Galaxy to derive the probability that the Earth is passing through a subclump or stream of a given density. Our results suggest that it is likely that the local complement of dark matter particles includes a 1 − 5% contribution from a single clump. The implications for dark matter detection experiments are significant, since the disrupted clump is composed of a 'cold' flow of high-velocity particles. We describe the distinctive features due to halo clumps that would be seen in the energy and angular spectra of detection experiments. The annual modulation of these features would have a different signature and phase from that for a smooth halo and, in principle, would allow one to discern the direction of motion of the clump relative to the Galactic center.

Monthly Notices of the Royal Astronomical Society, 1999

Measurements of galaxy clustering are now becoming possible over a range of redshifts out to z ∼ 3. We use a semi-analytic model of galaxy formation to compute the expected evolution of the galaxy correlation function with redshift. We illustrate how the degree of clustering evolution is sensitive to the details of sample selection. For a fixed apparent magnitude limit, galaxies selected at higher redshifts are located in progressively rarer dark matter haloes, compared with the general population of galaxies in place at each redshift. As a result these galaxies are highly biased tracers of the underlying dark matter distribution and exhibit stronger clustering than the dark matter. In general, the correlation length measured in comoving units, decreases at first with increasing redshift, before increasing again at higher redshift. We show that the ǫ-model often used to interpret the angular correlation function of faint galaxies gives an inadequate description of the evolution of clustering, and offers no physical insight into the clustering process. We compare our predictions with those of a simple, popular model in which a one-to-one correspondence between galaxies and dark halos is assumed. Qualitatively, this model reproduces the correct evolutionary behaviour at high redshift, but the quantitative results can be significantly in error. Our theoretical expectations are in good agreement with the high redshift clustering data of Carlberg et al. and Postman et al. but are higher than the measurements of Le Fèvre et al.

Monthly Notices of the Royal Astronomical Society, 2010

This is the first of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 cluster detections from the ROSAT All-Sky Survey, and incorporates follow-up observations of 94 of those clusters using the Chandra X-ray Observatory or ROSAT. Here we describe and implement a new statistical framework required to self-consistently produce simultaneous constraints on cosmology and scaling relations from such data, and present results on models of dark energy. In spatially flat models with a constant dark energy equation of state, w, the cluster data yield Ω m = 0.23 ± 0.04, σ 8 = 0.82 ± 0.05, and w = −1.01 ± 0.20, incorporating standard priors on the Hubble parameter and mean baryon density of the Universe, and marginalizing over conservative allowances for systematic uncertainties. These constraints agree well and are competitive with independent data in the form of cosmic microwave background anisotropies, type Ia supernovae, cluster gas mass fractions, baryon acoustic oscillations, galaxy redshift surveys, and cosmic shear. The combination of our data with current microwave background, supernova, gas mass fraction, and baryon acoustic oscillation data yields Ω m = 0.27 ± 0.02, σ 8 = 0.79 ± 0.03, and w = −0.96 ± 0.06 for flat, constant w models. The combined data also allow us to investigate evolving w models. Marginalizing over transition redshifts in the range 0.05-1, we constrain the equation of state at late and early times to be respectively w 0 = −0.88±0.21 and w et = −1.05 +0.20 −0.36 , again including conservative systematic allowances. The combined data provide constraints equivalent to a Dark Energy Task Force figure of merit of 15.5. Our results highlight the power of X-ray studies, which enable the straightforward production of large, complete, and pure cluster samples and admit tight scaling relations, to constrain cosmology. However, the new statistical framework we apply to this task is equally applicable to cluster studies at other wavelengths. 2 We prefer to use Mgas as a proxy for total mass rather than the thermal energy, Y X = MgaskT , because Mgas can be measured more precisely than temperature for a given exposure time, and because Mgas measurements at r 500 are minimally affected by background and emission weighting uncertainties. In addition, Mgas displays exceptionally small scatter with mass (see A08 and Paper II) in the mass range considered here, M > 3 × 10 14 M ⊙ .