The bias field of dark matter haloes

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, thereby 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 bispectrum and skewness. Our algorithm may have several interesting applications, among which the possibility of generating mock halo catalogues from low-resolution N-body simulations.Comment: 23 pages, LaTeX (included psfig.tex), 4 figures. Few comments and references have been added, and minor typos and errors corrected. This version matches the refereed one, in press in MNRA

Time-Series BVI Photometry for the Globular Cluster NGC 6981 (M72)

We present new BVI photometry of the globular cluster NGC 6981 (M72), based mostly on ground-based CCD archive images. We present a new color-magnitude diagram (CMD) that reaches almost four magnitudes below the turn-off level. We performed new derivations of metallicity and morphological parameters of the evolved sequences, in good agreement with previous authors, obtaining a value of [Fe/H] ~ -1.50 in the new UVES scale. We also identify the cluster's blue straggler population. Comparing the radial distribution of these stars with the red giant branch population, we find that the blue stragglers are more centrally concentrated, as found in previous studies of blue stragglers in globular clusters. Taking advantage of the large field of view covered by our study, we analyzed the surface density profile of the cluster, finding extratidal main sequence stars out to r ~ 14.1 arcmin or about twice the tidal radius. We speculate that this may be due to tidal disruption in the course of M72's orbit, in which case tidal tails associated with the cluster may exist. We also take a fresh look at the variable stars in the cluster, recovering all previous known variables, including three SX Phoenicis stars, and adding three previously unknown RR Lyrae (1 c-type and 2 ab-type) to the total census. Finally, comparing our CMD with unpublished data for M3 (NGC 5272), a cluster with similar metallicity and horizontal branch morphology, we found that both objects are essentially coeval.Comment: Accepted for publication in A

The Nonlinear Evolution of Galaxy Intrinsic Alignments

The non-Gaussian contribution to the intrinsic halo spin alignments is analytically modeled and numerically detected. Assuming that the growth of non-Gaussianity in the density fluctuations caused the tidal field to have nonlinear-order effect on the orientations of the halo angular momentum, we model the intrinsic halo spin alignments as a linear scaling of the density correlations on large scales, which is different from the previous quadratic-scaling model based on the linear tidal torque theory. Then, we analyze the halo catalogs from the recent high-resolution Millennium Run simulation at four different redshifts (z=0,0.5,1 and 2) and measure quantitatively the degree of the nonlinear effect on the halo spin alignments and its changes with redshifts. A clear signal of spin correlations is found on scales as large as 10 Mpc/h at z=0, which marks a detection of the nonlinear tidal effect on the intrinsic halo alignments. We also investigate how the nonlinear effect depends on the intrinsic properties of the halos. It is found that the degree of the nonlinear tidal effect increases as the halo mass scale decreases, the halo specific angular momentum increases, and the halo peculiar velocity decreases. We discuss implication of our result on the weak gravitational lensing.Comment: ApJ in press, revised version, mistakes and typos corrected, discussion improved, 29 pages, 11 figure

Cosmic Shear from Galaxy Spins

We discuss the origin of galactic angular momentum, and the statistics of the present day spin distribution. It is expected that the galaxy spin axes are correlated with the intermediate principal axis of the gravitational shear tensor. This allows one to reconstruct the shear field and thereby the full gravitational potential from the observed galaxy spin fields. We use the direction of the angular momentum vector without any information of its magnitude, which requires a measurement of the position angle and inclination on the sky of each disk galaxy. We present the maximum likelihood shear inversion procedure, which involves a constrained linear minimization. The theory is tested against numerical simulations. We find the correlation strength of nonlinear structures with the initial shear field, and show that accurate large scale density reconstructions are possible at the expected noise level.Comment: Accepted by the ApJL, revised discussion, minor changes, LaTex file, 8 pages, 1 ps figur

Weak lensing surveys and the intrinsic correlation of galaxy ellipticities

We explore the possibility that an intrinsic correlation between galaxy ellipticities arising during the galaxy formation process may account for part of the shear signal recently reported by several groups engaged in weak lensing surveys. Using high resolution N-body simulations we measure the projected ellipticities of dark matter halos and their correlations as a function of pair separation. With this simplifying, but not necessarily realistic assumption (halo shapes as a proxy for galaxy shapes), we find a positive detection of correlations up to scales of at least 20 h^-1mpc (limited by the box size). The signal is not strongly affected by variations in the halo finding technique, or by the resolution of the simulations. We translate our 3d results into angular measurements of ellipticity correlation functions and shear variance which can be directly compared to observations. We also measure similar results from simulated angular surveys made by projecting our simulation boxes onto the plane of the sky and applying a radial selection function. Interestingly, the shear variance we measure is a small, but not entirely negligible fraction (from ~10-20 %) of that seen by the observational groups, and the ellipticity correlation functions approximately mimic the functional form expected to be caused by weak lensing. The amplitude depends on the width in redshift of the galaxy distribution. If photometric redshifts are used to pick out a screen of background galaxies with a small width, then the intrinsic correlation may become comparable to the weak lensing signal. Although we are dealing with simulated dark matter halos, whether there is a signal from real galaxies could be checked with a nearby sample with known redshifts.Comment: 12 pages, 11 ps figures, emulateapj.sty, submitted to Ap

On the Average Comoving Number Density of Halos

I compare the numerical multiplicity function given in Yahagi, Nagashima & Yoshii (2004) with the theoretical multiplicity function obtained by means of the excursion set model and an improved version of the barrier shape obtained in Del Popolo & Gambera (1998), which implicitly takes account of total angular momentum acquired by the proto-structure during evolution and of a non-zero cosmological constant. I show that the multiplicity function obtained in the present paper, is in better agreement with Yahagi, Nagashima & Yoshii (2004) simulations than other previous models (Sheth & Tormen 1999; Sheth, Mo & Tormen 2001; Sheth & Tormen 2002; Jenkins et al. 2001) and that differently from some previous multiplicity function models (Jenkins et al. 2001; Yahagi, Nagashima & Yoshii 2004) it was obtained from a sound theoretical background

On the Environmental Dependence of Galaxy Properties Established by the Initial Cosmological Conditions

We study theoretically how the initial cosmological conditions establish the dependence of galaxy properties on the environment. First, we adopt the linear tidal torque theory according to which the angular momentum of a proto-galaxy is generated at first order by the misalignment between the proto-galaxy inertia tensor and the local tidal tensor. Then, we quantify analytically the degree of the misalignment between the two tensors, and show quantitatively that it increases as the density of the environment decreases. It implies that the proto-galaxies forming in the lower density regions should end up with having higher angular momentum than those in the higher density regions, which is consistent with recent numerical finding that the void and field galaxies have higher spin parameters than the cluster galaxies. Since the galaxy angular momentum plays a role of developing a disk-like structure and hindering the star-formation, our theoretical insight provides an answer to such fundamental observational question as why the large void galaxies have young stellar populations and high specific star formation rate, which was not explained by the previous morphology-density relation.Comment: accepted version, ApJL in press, all typos correcte

NGC 5694: another foster son of the Galactic Halo

We present the results of the analysis of high-resolution spectra obtained with UVES-FLAMES@VLT for six red giant branch stars in the outer-halo metal-poor ([Fe/H]I=-1.98 and [Fe/H]II=-1.83) Galactic globular cluster NGC 5694, which has been suggested as a possible incomer by Lee et al. (2006) based on the anomalous chemical composition of a single cluster giant. We obtain accurate abundances for a large number of elements and we find that: (a) the six target stars have the same chemical composition within the uncertainties, except for Na and Al; (b) the average cluster abundance of \alpha\ elements (with the only exception of Si) is nearly solar, at odds with typical halo stars and globular clusters of similar metallicity; (c) Y, Ba, La and Eu abundances are also significantly lower than in Galactic field stars and star clusters of similar metallicity. Hence we confirm the Lee et al. classification of NGC 5694 as a cluster of extra-galactic origin. We provide the first insight on the Na-O and Mg-Al anti-correlations in this cluster: all the considered stars have very similar abundance ratios for these elements, except one that has significantly lower [Na/Fe] and [Al/Fe] ratios, suggesting that some degree of early self-enrichment has occurred also in this cluster.Comment: Accepted for publication by MNRAS. 15 pages, 8 figures, 4 table