Sunyaev - Zel'dovich fluctuations from spatial correlations between clusters of galaxies

We present angular power spectra of the cosmic microwave background radiation anisotropy due to fluctuations of the Sunyaev-Zel'dovich (SZ) effect through clusters of galaxies. A contribution from the correlation among clusters is especially focused on, which has been neglected in the previous analyses. Employing the evolving linear bias factor based on the Press-Schechter formalism, we find that the clustering contribution amounts to 20-30% of the Poissonian one at degree angular scales. If we exclude clusters in the local universe, it even exceeds the Poissonian noise, and makes dominant contribution to the angular power spectrum. As a concrete example, we demonstrate the subtraction of the ROSAT X-ray flux-limited cluster samples. It indicates that we should include the clustering effect in the analysis of the SZ fluctuations. We further find that the degree scale spectra essentially depend upon the normalization of the density fluctuations, i.e., \sigma_8, and the gas mass fraction of the cluster, rather than the density parameter of the universe and details of cluster evolution models. Our results show that the SZ fluctuations at the degree scale will provide a possible measure of \sigma_8, while the arc-minute spectra a probe of the cluster evolution. In addition, the clustering spectrum will give us valuable information on the bias at high redshift, if we can detect it by removing X-ray luminous clusters.Comment: 11 pages, 4 figures, submitted to Astrophysical Journa

The Galaxy Cluster Luminosity-Temperature Relationship and Iron Abundances - A Measure of Formation History ?

Both the X-ray luminosity-temperature (L-T) relationship and the iron abundance distribution of galaxy clusters show intrinsic dispersion. Using a large set of galaxy clusters with measured iron abundances we find a correlation between abundance and the relative deviation of a cluster from the mean L-T relationship. We argue that these observations can be explained by taking into account the range of cluster formation epochs expected within a hierarchical universe. The known relationship of cooling flow mass deposition rate to luminosity and temperature is also consistent with this explanation. From the observed cluster population we estimate that the oldest clusters formed at z>~2. We propose that the iron abundance of a galaxy cluster can provide a parameterization of its age and dynamical history.Comment: 13 pages Latex, 2 figures, postscript. Accepted for publication in ApJ Letter

An Analytical Approach to Inhomogeneous Structure Formation

We develop an analytical formalism that is suitable for studying inhomogeneous structure formation, by studying the joint statistics of dark matter halos forming at two points. Extending the Bond et al. (1991) derivation of the mass function of virialized halos, based on excursion sets, we derive an approximate analytical expression for the ``bivariate'' mass function of halos forming at two redshifts and separated by a fixed comoving Lagrangian distance. Our approach also leads to a self-consistent expression for the nonlinear biasing and correlation function of halos, generalizing a number of previous results including those by Kaiser (1984) and Mo & White (1996). We compare our approximate solutions to exact numerical results within the excursion-set framework and find them to be consistent to within 2% over a wide range of parameters. Our formalism can be used to study various feedback effects during galaxy formation analytically, as well as to simply construct observable quantities dependent on the spatial distribution of objects. A code that implements our method is publicly available at http://www.arcetri.astro.it/~evan/GeminiComment: 41 Pages, 11 figures, published in ApJ, 571, 585. Reference added, Figure 2 axis relabele

Accurate determination of the Lagrangian bias for the dark matter halos

We use a new method, the cross power spectrum between the linear density field and the halo number density field, to measure the Lagrangian bias for dark matter halos. The method has several important advantages over the conventional correlation function analysis. By applying this method to a set of high-resolution simulations of 256^3 particles, we have accurately determined the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our result for massive halos with $M \ge M_*$ ($M_*$ is a characteristic non-linear mass) is in very good agreement with the analytical formula of Mo & White for the Lagrangian bias, but the analytical formula significantly underestimates the Lagrangian clustering for the less massive halos $M < M_*. Our simulation result however can be satisfactorily described, with an accuracy better than 15%, by the fitting formula of Jing for Eulerian bias under the assumption that the Lagrangian clustering and the Eulerian clustering are related with a linear mapping. It implies that it is the failure of the Press-Schechter theories for describing the formation of small halos that leads to the inaccuracy of the Mo & White formula for the Eulerian bias. The non-linear mapping between the Lagrangian clustering and the Eulerian clustering, which was speculated as another possible cause for the inaccuracy of the Mo & White formula, must at most have a second-order effect. Our result indicates that the halo formation model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages with 2 figures include

Clustering of dark matter halos on the light-cone: scale-, time- and mass-dependence of the halo biasing in the Hubble volume simulations

We develop a phenomenological model to predict the clustering of dark matter halos on the light-cone by combining several existing theoretical models. Assuming that the velocity field of halos on large scales is approximated by linear theory, we propose an empirical prescription of a scale-, mass-, and time-dependence of halo biasing. We test our model against the Hubble Volume $N$-body simulation and examine its validity and limitations. We find a good agreement in two-point correlation functions of dark matter halos between the phenomenological model predictions and measurements from the simulation for $R>5h^{-1}$Mpc both in the real and redshift spaces. Although calibrated on the mass scale of groups and clusters and for redshifts up to $z\sim2$, the model is quite general and can be applied to a wider range of astrophysical objects, such as galaxies and quasars, if the relation between dark halos and visible objects is specified.Comment: 5 pages, 2 figures, ApJL accepted. New references adde

The abundance of high-redshift objects as a probe of non-Gaussian initial conditions

The observed abundance of high-redshift galaxies and clusters contains precious information about the properties of the initial perturbations. We present a method to compute analytically the number density of objects as a function of mass and redshift for a range of physically motivated non-Gaussian models. In these models the non-Gaussianity can be dialed from zero and is assumed to be small. We compute the probability density function for the smoothed dark matter density field and we extend the Press and Schechter approach to mildly non-Gaussian density fields. The abundance of high-redshift objects can be directly related to the non-Gaussianity parameter and thus to the physical processes that generated deviations from the Gaussian behaviour. Even a skewness parameter of order 0.1 implies a dramatic change in the predicted abundance of z\gap 1 objects. Observations from NGST and X-ray satellites (XMM) can be used to accurately measure the amount of non-Gaussianity in the primordial density field.Comment: Minor changes to match the accepted ApJ version (ApJ, 539

The non-Gaussian tail of cosmic-shear statistics

Due to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of high-redshift galaxy images due to the tidal gravitational field of the large-scale matter distribution, called cosmic shear, can be used to investigate the statistical properties of the LSS. In particular, non-Gaussian properties of the LSS will lead to a non-Gaussian distribution of cosmic-shear statistics. The aperture mass ($M_{\rm ap}$) statistics, recently introduced as a measure for cosmic shear, is particularly well suited for measuring these non-Gaussian properties. In this paper we calculate the highly non-Gaussian tail of the aperture mass probability distribution, assuming Press-Schechter theory for the halo abundance and the `universal' density profile of haloes as obtained from numerical simulations. We find that for values of $M_{\rm ap}$ much larger than its dispersion, this probability distribution is closely approximated by an exponential, rather than a Gaussian. We determine the amplitude and shape of this exponential for various cosmological models and aperture sizes, and show that wide-field imaging surveys can be used to distinguish between some of the currently most popular cosmogonies. Our study here is complementary to earlier cosmic-shear investigations which focussed more on two-point statistical properties.Comment: 9 pages, 5 figures, submitted to MNRA

The Role of Heating and Enrichment in Galaxy Formation

We show that the winds identified with high-redshift low-mass galaxies may strongly affect the formation of stars in more massive galaxies that form later. With 3D realizations of a simple linear growth model we track gas shocking, metal enrichment, and cooling, together with dark halo formation. We show that outflows typically strip baryonic material out of collapsing intermediate mass halos, suppressing star formation. More massive halos can trap the heated gas but collapse late, leading to a broad bimodal redshift distribution, with a larger characteristic mass associated with the lower redshift peak. This scenario accounts for the observed bell-shaped luminosity function of early type galaxies, explains the small number of Milky Way satellite galaxies relative to Cold Dark Matter models predictions, and provides a possible explanation for the lack of metal poor G-dwarfs in the solar neighborhood and the more general lack of low-metallicity stars in massive galaxies relative to ``closed-box'' models of chemical enrichment. Intergalactic medium heating from outflows should produce spectral distortions in the cosmic microwave background that will be measurable with the next generation of experiments.Comment: 19 pages, 12 figures, accepted to ApJ, models refined and minor revisions mad

Environmental Effects on Real-Space and Redshift-Space Galaxy Clustering

Galaxy formation inside dark matter halos, as well as the halo formation itself, can be affected by large-scale environments. Evaluating the imprints of environmental effects on galaxy clustering is crucial for precise cosmological constraints with data from galaxy redshift surveys. We investigate such an environmental impact on both real-space and redshift-space galaxy clustering statistics using a semi-analytic model derived from the Millennium Simulation. We compare clustering statistics from original SAM galaxy samples and shuffled ones with environmental influence on galaxy properties eliminated. Among the luminosity-threshold samples examined, the one with the lowest threshold luminosity (~0.2L_*) is affected by environmental effects the most, which has a ~10% decrease in the real-space two-point correlation function (2PCF) after shuffling. By decomposing the 2PCF into five different components based on the source of pairs, we show that the change in the 2PCF can be explained by the age and richness dependence of halo clustering. The 2PCFs in redshift space are found to change in a similar manner after shuffling. If the environmental effects are neglected, halo occupation distribution modeling of the real-space and redshift-space clustering may have a less than 6.5% systematic uncertainty in constraining beta from the most affected SAM sample and have substantially smaller uncertainties from the other, more luminous samples. We argue that the effect could be even smaller in reality. In the Appendix, we present a method to decompose the 2PCF, which can be applied to measure the two-point auto-correlation functions of galaxy sub-samples in a volume-limited galaxy sample and their two-point cross-correlation functions in a single run utilizing only one random catalog.Comment: 13 pages, 6 figures, Accepted by AP

Efficient Simulations of Early Structure Formation and Reionization

We present a method to construct semi-numerical ``simulations'', which can efficiently generate realizations of halo distributions and ionization maps at high redshifts. Our procedure combines an excursion-set approach with first-order Lagrangian perturbation theory and operates directly on the linear density and velocity fields. As such, the achievable dynamic range with our algorithm surpasses the current practical limit of N-body codes by orders of magnitude. This is particularly significant in studies of reionization, where the dynamic range is the principal limiting factor. We test our halo-finding and HII bubble-finding algorithms independently against N-body simulations with radiative transfer and obtain excellent agreement. We compute the size distributions of ionized and neutral regions in our maps. We find even larger ionized bubbles than do purely analytic models at the same volume-weighted mean hydrogen neutral fraction. We also generate maps and power spectra of 21-cm brightness temperature fluctuations, which for the first time include corrections due to gas bulk velocities. We find that velocities widen the tails of the temperature distributions and increase small-scale power, though these effects quickly diminish as reionization progresses. We also include some preliminary results from a simulation run with the largest dynamic range to date: a 250 Mpc box that resolves halos with masses M >~ 2.2 x10^8 M_sun. We show that accurately modeling the late stages of reionization requires such large scales. The speed and dynamic range provided by our semi-numerical approach will be extremely useful in the modeling of early structure formation and reionization.Comment: 13 pages, 10 figures; ApJ submitte