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

Physical constraints on the halo mass function

We analyse the effect of two relevant physical constraints on the mass multiplicity function of dark matter halos in a Press--Schechter type algorithm. Considering the random--walk of linear Gaussian density fluctuations as a function of the smoothing scale, we simultaneously i) account for mass semi--positivity and ii) avoid the cloud--in--cloud problem. It is shown that the former constraint implies a severe cutoff of low--mass objects, balanced by an increase on larger mass scales. The analysis is performed both for scale--free power--spectra and for the standard cold dark matter model. Our approach shows that the well--known ``infrared" divergence of the standard Press--Schechter mass function is caused by unphysical, negative mass events which inevitably occur in a Gaussian distribution of density fluctuations.Comment: Revised version (accepted for publication in MNRAS) including a new comparison with numerical results, a new appendix and new references. uuencoded gzip'ed tar archive containing many LaTex files (the main file is mass.tex). 16 pages with 6 figures (all included

Properties of Dark Matter Haloes in Clusters, Filaments, Sheets and Voids

Using a series of high-resolution N-body simulations of the concordance cosmology we investigate how the formation histories, shapes and angular momenta of dark-matter haloes depend on environment. We first present a classification scheme that allows to distinguish between haloes in clusters, filaments, sheets and voids in the large-scale distribution of matter. This method is based on a local-stability criterion for the orbits of test particles and closely relates to the Zel'dovich approximation. Applying this scheme to our simulations we then find that: i) Mass assembly histories and formation redshifts strongly depend on environment for haloes of mass M<M* (haloes of a given mass tend to be older in clusters and younger in voids) and are independent of it for larger masses; ii) Low-mass haloes in clusters are generally less spherical and more oblate than in other regions; iii) Low-mass haloes in clusters have a higher median spin than in filaments and present a more prominent fraction of rapidly spinning objects; we identify recent major mergers as a likely source of this effect. For all these relations, we provide accurate functional fits as a function of halo mass and environment. We also look for correlations between halo-spin directions and the large-scale structures: the strongest effect is seen in sheets where halo spins tend to lie within the plane of symmetry of the mass distribution. Finally, we measure the spatial auto-correlation of spin directions and the cross-correlation between the directions of intrinsic and orbital angular momenta of neighbouring haloes. While the first quantity is always very small, we find that spin-orbit correlations are rather strong especially for low-mass haloes in clusters and high-mass haloes in filaments.Comment: 13 pages, 13 figures. Version accepted for publication in MNRAS (references added). Version with high-resolution figures available at http://www.exp-astro.phys.ethz.ch/hahn/pub/HPCD06.pd

The Halo Distribution of 2dF Galaxies

We use the clustering results obtained by Madgwick et al. (2003) for a sample of 96,791 2dF galaxies with redshift 0.01 \lt z \lt 0.15 to study the distribution of late-type and early-type galaxies within dark matter haloes of different mass. Within the framework of our models, galaxies of both classes are found to be as spatially concentrated as the dark matter within haloes even though, while the distribution of star-forming galaxies can also allow for some steeper profiles, this is drastically ruled out in the case of early-type galaxies. We also find evidence for morphological segregation, as late-type galaxies appear to be distributed within haloes of mass scales corresponding to groups and clusters up to about two virial radii, while passive objects show a preference to reside closer to the halo centre. If we assume a broken power-law of the form =(m/m_0)^{alpha_1} for m_{cut}\le m<m_0 and =(m/m_0)^{alpha_2} at higher masses to describe the dependence of the average number of galaxies within haloes on the halo mass, fits to the data show that star-forming galaxies start appearing in haloes of masses m_{cut}~10^{11}m_{sun}, much smaller than what is obtained for early-type galaxies (m_{cut}~10^{12.6}m_{sun}). In the high-mass regime m\ge m_0, $ increases with halo mass more slowly (alpha_2~0.7) in the case of late-type galaxies than for passive objects which present alpha_2~1.1. We stress that there is no degeneracy in the determination of the best functional forms for rho(r) and , as they affect the behaviour of the galaxy-galaxy correlation function on different scales.Comment: Revised version to appear in MNRAS, extended analysis, some new result

Cosmological information in the redshift-space bispectrum

We use the Fisher-matrix formalism to investigate whether the galaxy bispectrum in redshift space, B, contains additional cosmological information with respect to the power spectrum, P. We focus on a Euclid-like survey and consider cosmological models dominated by dark energy and cold dark matter with Gaussian primordial perturbations. After discussing the phenomenology of redshift-space distortions for the bispectrum, we derive an expression for the cross-covariance between B and P at leading order in perturbation theory. Our equation generalizes previous results that did not consider binning in the orientation of wavevector triangles with respect to the line of sight. By considering Fourier modes with wavenumbe

Plausible fluorescent Ly-alpha emitters around the z=3.1 QSO0420-388

We report the results of a survey for fluorescent Ly-alpha emission carried out in the field surrounding the z=3.1 quasar QSO0420-388 using the FORS2 instrument on the VLT. We first review the properties expected for fluorescent Ly-alpha emitters, compared with those of other non-fluorescent Ly-alpha emitters. Our observational search detected 13 Ly-alpha sources sparsely sampling a volume of ~14000 comoving Mpc^3 around the quasar. The properties of these in terms of i) the line equivalent width, ii) the line profile and iii) the value of the surface brightness related to the distance from the quasar, all suggest that several of these may be plausibly fluorescent. Moreover, their number is in good agreement with the expectation from theoretical models. One of the best candidates for fluorescence is sufficiently far behind QSO0420-388 that it would imply that the quasar has been active for (at least) ~60 Myrs. Further studies on such objects will give information about proto-galactic clouds and on the radiative history (and beaming) of the high-redshift quasars.Comment: 10 pages, 4 figures.Update to match the version published on ApJ 657, 135, 2007 March

Properties of dark matter haloes in clusters, filaments, sheets and voids

Using a series of high-resolution N-body simulations of the concordance cosmology we investigate how the formation histories, shapes and angular momenta of dark matter haloes depend on environment. We first present a classification scheme that allows us to distinguish between haloes in clusters, filaments, sheets and voids in the large-scale distribution of matter. This method (which goes beyond a simple measure of the local density) is based on a local-stability criterion for the orbits of test particles and closely relates to the Zel'dovich approximation. Applying this scheme to our simulations we then find that: (i) mass assembly histories and formation redshifts strongly depend on environment for haloes of mass M < M* (haloes of a given mass tend to be older in clusters and younger in voids) and are independent of it for larger masses (M* here indicates the typical mass scale which is entering the non-linear regime of perturbation growth); (ii) low-mass haloes in clusters are generally less spherical and more prolate than in other regions; (iii) low-mass haloes in clusters have a higher median spin than in filaments and present a more prominent fraction of rapidly spinning objects. We identify recent major mergers as a likely source of this effect. For all these relations, we provide accurate functional fits as a function of halo mass and environment. We also look for correlations between halo-spin directions and the large-scale structures: the strongest effect is seen in sheets where halo spins tend to lie within the plane of symmetry of the mass distribution. Finally, we measure the spatial autocorrelation of spin directions and the cross-correlation between the directions of intrinsic and orbital angular momenta of neighbouring haloes. While the first quantity is always very small, we find that spin-orbit correlations are rather strong especially for low-mass haloes in clusters and high-mass haloes in filament

Tidal effects and the environment dependence of halo assembly

We explore a possible origin for the puzzling anti-correlation between the formation epoch of galactic dark-matter haloes and their environment density. This correlation has been revealed from cosmological N-body simulations and is in conflict with the extended Press-Schechter model of halo clustering. Using similar simulations, we first quantify the straightforward association of an early formation epoch with a reduced mass-growth rate at late times. We then find that a primary driver of suppressed growth, by accretion and mergers, is tidal effects dominated by a neighbouring massive halo. The tidal effects range from a slowdown of the assembly of haloes due to the shear along the large-scale filaments that feed the massive halo to actual mass loss in haloes that pass through the massive halo. Using the restricted three-body problem, we show that haloes are prone to tidal mass loss within 1.5 virial radii of a larger halo. Our results suggest that the dependence of the formation epoch on environment density is a secondary effect induced by the enhanced density of haloes in filaments near massive haloes where the tides are strong. Our measures of assembly rate are particularly correlated with the tidal field at high redshifts z∼

The evolution of dark matter halo properties in clusters, filaments, sheets and voids

We use a series of high-resolution N-body simulations of the concordance cosmology to investigate the redshift evolution since z= 1 of the properties and alignment with the large-scale structure (LSS) of haloes in clusters, filaments, sheets and voids. We find that (i) once a rescaling of the halo mass with M*(z), the typical mass scale collapsing at redshift z, is performed, there is no further significant redshift dependence in the halo properties; (ii) the environment influences the halo shape and formation time at all investigated redshifts for haloes with masses M≲M* and (iii) there is a significant alignment of both spin and shape of haloes with filaments and sheets. In detail, at all redshifts up to z= 1: (a) haloes with masses below ∼M* tend to be more oblate when located in clusters than in the other environments; this trend is reversed at higher masses: above about M*, haloes in clusters are typically more prolate than similar massive haloes in sheets, filaments and voids. (b) The haloes with M≳M* in filaments spin more rapidly than similar mass haloes in clusters; haloes in voids have the lowest median spin parameters. (c) Haloes with M≲M* tend to be younger in voids and older in clusters. (d) In sheets, halo spin vectors tend to lie preferentially within the sheet plane independent of halo mass; in filaments, instead, haloes with M≲M* tend to spin parallel to the filament and higher mass haloes perpendicular to it. For halo masses M≳M*, the major axis of haloes in filaments and sheets is strongly aligned with the host filament or the sheet plane, respectively. Such halo-LSS alignments may be of importance in weak lensing analyses of cosmic shear. A question that is opened by our study is why, in the 0 < z < 1 redshift regime that we have investigated, the mass scale for gravitational collapse, M*, sets roughly the threshold below which the LSS environment either begins to affect, or reverses, fundamental properties of dark matter haloe