The Correlation Function of Clusters of Galaxies and the Amplitude of Mass Fluctuations in the Universe

We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus if the shape of the initial fluctuation spectrum is known, its amplitude $\sigma_8$ can be estimated directly from the correlation length of a cluster sample in a way which is independent of the value of $\Omega_0$. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity $\sigma_8\Omega_0^{0.6}$. Thus cluster data should allow both $\sigma_8$ and $\Omega_0$ to be determined observationally. We explore these questions using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length $r_0$ in excess of 20\mpch for Abell clusters would require $\sigma_8>1$, while r_0<15\mpch would require $\sigma_8<0.5$. With conventional estimates of the relevant mass threshold these imply \Omega_0\la 0.3 and \Omega_0\ga 1 respectively.Comment: Latex, 25 pages (including 8 PS figures). The PS-file of the paper is also available via anonymous ftp at: ftp://ibm-3.mpa-garching.mpg.de/pub/jing/xicc.ps . Submitted to MNRAS. In the replaced version, a typo in Eq.(1a) is fixe

An analytical model for the non-linear redshift-space power spectrum

We use N-body simulations to test the predictions of the redshift distortion in the power spectrum given by the halo model in which the clustering of dark matter particles is considered as a result both of the clustering of dark halos in space and of the distribution of dark matter particles in individual dark halo. The predicted redshift distortion depends sensitively on several model parameters in a way different from the real-space power spectrum. An accurate model of the redshift distortion can be constructed if the following properties of the halo population are modelled accurately: the mass function of dark halos, the velocity dispersion among dark halos, and the non-linear nature of halo bias on small scales. The model can be readily applied to interpreting the clustering properties and velocity dispersion of different populations of galaxies once a cluster-weighted bias (or equivalently an halo occupation number model) is specified for the galaxies. Some non-trivial bias features observed from redshift surveys of optical galaxies and of IRAS galaxies relative to the standard low-density cold dark matter model can be easily explained in the cluster weighted bias model. The halo model further indicates that a linear bias can be a good approximation only on for k <= 0.1 hMpc^{-1}.Comment: 10 pages, 10 figures, accepted for publication in MNRA

Lyman #alpha# absorption at low redshifts and hot gas in galactic haloes

Motivated by recent observation of Lanzetta et al. that most luminous galaxies at low redshifts produce Ly#alpha# absorption at impact parameter l&lt;or#approx#160 h&quot;-&quot;1 kpc, we propose that these absorbers are clouds confined by the pressure of ambient hot gas in galactic haloes. We determine the properties of this hot gas and of the absorption systems on the basis of observational and theoretical constraints. The absorbing clouds need to be replenished on about one orbital time (#propor to#10&quot;9 yrs) in the galactic halo. The pressure and temperature of the gas at radius r #propor to#100 kpc are P=(10-100) cm&quot;-&quot;3 K, T=10&quot;(&quot;5&quot;.&quot;5&quot;-&quot;6&quot;.&quot;5&quot;) K. The model requires that about 10% of the gas in low-redshift galactic haloes is in the hot phase. Such gas in galactic haloes emits X-ray with bolometric luminosity of the order 10&quot;3&quot;7&quot;-&quot;4&quot;0 erg s&quot;-&quot;1. The plausibility for such gas to exist in current models of galaxy formation is discussed. (orig.)Available from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The growth and structure of dark matter haloes

SIGLEAvailable from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

An analytic model for the gravitational clustering of dark matter haloes

We develop a simple analytic model for the gravitational clustering of dark haloes. The statistical properties of dark haloes are determined from the initial density field (assumed to be Gaussian) through an extension of the Press-Schechter formalism. Gravitational clustering is treated by a spherical model which describes the concentration of dark haloes in collapsing regions. We test this model against results from a variety of N-body simulations. The autocorrelation function of dark haloes in such simulations depends significantly on how haloes are identified. Our predictions agree well with results based on algorithms which break clusters into subgroups more efficiently than the standard friends-of-friends algorithm. The agreement is better than that found by assuming haloes to lie at the present positions of peaks of the linear density field. We use these techniques to study how the distribution of haloes identified at a given redshift and having circular velocities #upsilon#_c = #upsilon#_c&quot;*(z) (i.e. mass equal to the characteristic nonlinear mass M&quot;* at that redshift) are very weakly correlated with the linear density field or among themselves. As a result of dynamical evolution, however, the present-day correlations of these haloes are similar to those of the mass. Haloes with lower #upsilon#_c are biased toward regions with negative overdensity, while those with higher #upsilon#_c are biased toward regions with positive overdensity. Among the haloes identified at any given epoch, those with higher circular velocities are more strongly correlated today. Among the haloes of given circular velocity, those at higher redshifts are also more strongly clustered today. In the 'standard CDM' model, haloes with #upsilon#_c = 200 km s&quot;-&quot;1 and identified at redshift z &gt;or#approx# 2 have present-day autocorrelation comparable to that of normal galaxies in the real universe. (orig.)SIGLEAvailable from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The abundance and clustering of dark haloes in the standard #LAMBDA#CDM cosmogony

SIGLEAvailable from: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Spatial correlation function and pairwise velocity dispersion of galaxies: CDM models versus the Las Campanas Survey

We show, with the help of large N-body simulations, that the real-space two-point correlation function and pairwise velocity dispersion of galaxies can both be measured reliably from the Las Campanas Redshift Survey. The real-space correlation function is well fitted by the power law #xi#(r)=(r_0/r)&quot;#gamma# with r_0=(5.06#+-#0.12) h&quot;-&quot;1 Mpc and #gamma#=1.862#+-#0.034, and the pairwise velocity dispersion at 1 h&quot;-&quot;1 Mpc is (570#+-#80) km s&quot;-&quot;1. A detailed comparison between these observational results and the predictions of current CDM cosmogonies is carried out. We construct 60 mock samples for each theoretical model from a large set of high resolution N-body simulations, which allows us to include various observational selection effects in the analyses and to use exactly the same methods for both real and theoretical samples. We demonstrate that such a procedure is essential in the comparison between models and observations. The observed two-point correlation function is significantly flatter than the mass correlation function in current CDM models on scales &lt;or#approx#1 h&quot;-&quot;1 Mpc. The observed pairwise velocity dispersion is also lower than that of dark matter particles in these models. We propose a simple antibias model to explain these discrepancies. This model assumes that the number of galaxies per unit dark matter mass, N/M, decreases with the mass of dark haloes. The predictions of CDM models with #sigma#_8#OMEGA#_0&quot;0&quot;.&quot;6#propor to#0.4-0.5 and #GAMMA##propor to#0.2 are in agreement with the observational results, if the trend of N/M with M is at the level already observed for rich clusters of galaxies. Thus CDM models with #GAMMA##propor to#0.2 and with cluster-abundance normalization are consistent with the observed correlation function and pairwise velocity dispersion of galaxies. A high level of velocity bias is not required in these models. (orig.)Available from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

High-order correlations of peaks and halos: A step toward understanding galaxy biasing

We develop an analytic model for the hierarchical correlation amplitudesS_j_,_g(R)#ident to# anti #xi#_j_,_g(R) anti #xi#_2_,_g&quot;j&quot;-&quot;1(R) [where j=3, 4, 5, and anti #xi#_j_,_g(R) is the jth order connected moment of counts in spheres of radius R] of density peaks and dark matter halos in the quasi-linear regime. The statistical distributions of density peaks and dark matter halos within the initial density field (assumed Gaussian) are determined by the peak formalism of Bardeen et al. (1986) and by an extension of the Press-Schechter formalism, respectively. Modifications of these distributions caused by gravitationally induced motions are treated using a spherical collapse model. We test our model against results for S_3_,_g(R) and S_4_,_g(R) from a variety of N-body simulations. The model works well for peaks even on scales where the second moment of mass (anti #xi#_2) is significantly greater than unity. The model also works successfully for halos that are identified earlier than the time when the moments are calculated. Because halos are spatially exclusive at the time of their identification, our model is only qualitatively correct for halos identified at the same time as the moments are calculated45 refs.Available from TIB Hannover: RR 4697(938) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes

SIGLEAvailable from: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The evolution of correlation functions and power spectra in gravitational clustering

Hamilton et al. (1991) proposed a simple formula relating the nonlinear autocorrelation function of the mass distribution to the primordial spectrum of density fluctuations for gravitational clustering in an #OMEGA# = 1 universe. High resolution N-body simulations show this formulal to work well for scale-free spectra P(k) #propor to# k&quot;n when the spectral index n #approx# 0, but not when n &lt;or#approx# - 1. We show that a modified version of the formula can work well provided its form depends on n. This dependence can be derived from a simple physical model for collapse from Gaussian initial conditions. Our modified formula is easy to apply and is an excellent fit to N-body simulations with 0 #&lt;=# n #&lt;=# -2. It can also be applied to non-power law initial spectra such as that of the standard Cold Dark Matter model by using the local spectral index at the current nonlinear scale as the effective value of n at any given redshift. We give analytic expressions both for the nonlinear correlation function and for the nonlinear power spectrum. (orig.)Available from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman