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

The bispectrum of redshifted 21-cm fluctuations from the dark ages

Brightness-temperature fluctuations in the redshifted 21-cm background from the cosmic dark ages are generated by irregularities in the gas-density distribution and can then be used to determine the statistical properties of density fluctuations in the early Universe. We first derive the most general expansion of brightness-temperature fluctuations up to second order in terms of all the possible sources of spatial fluctuations. We then focus on the three-point statistics and compute the angular bispectrum of brightness-temperature fluctuations generated prior to the epoch of hydrogen reionization. For simplicity, we neglect redshift-space distortions. We find that low-frequency radio experiments with arcmin angular resolution can easily detect non-Gaussianity produced by non-linear gravity with high signal-to-noise ratio. The bispectrum thus provides a unique test of the gravitational instability scenario for structure formation, and can be used to measure the cosmological parameters. Detecting the signature of primordial non-Gaussianity produced during or right after an inflationary period is more challenging but still possible. An ideal experiment limited by cosmic variance only and with an angular resolution of a few arcsec has the potential to detect primordial non-Gaussianity with a non-linearity parameter of f_NL ~ 1. Additional sources of error as weak lensing and an imperfect foreground subtraction could severely hamper the detection of primordial non-Gaussianity which will benefit from the use of optimal estimators combined with tomographic techniques.Comment: 15 pages, 4 figures, revised version accepted for publication in ApJ (contains an improved discussion of gas temperature fluctuations

Structure formation from non-Gaussian initial conditions: multivariate biasing, statistics, and comparison with N-body simulations

We study structure formation in the presence of primordial non-Gaussianity of the local type with parameters f_NL and g_NL. We show that the distribution of dark-matter halos is naturally described by a multivariate bias scheme where the halo overdensity depends not only on the underlying matter density fluctuation delta, but also on the Gaussian part of the primordial gravitational potential phi. This corresponds to a non-local bias scheme in terms of delta only. We derive the coefficients of the bias expansion as a function of the halo mass by applying the peak-background split to common parametrizations for the halo mass function in the non-Gaussian scenario. We then compute the halo power spectrum and halo-matter cross spectrum in the framework of Eulerian perturbation theory up to third order. Comparing our results against N-body simulations, we find that our model accurately describes the numerical data for wavenumbers k < 0.1-0.3 h/Mpc depending on redshift and halo mass. In our multivariate approach, perturbations in the halo counts trace phi on large scales and this explains why the halo and matter power spectra show different asymptotic trends for k -> 0. This strongly scale-dependent bias originates from terms at leading order in our expansion. This is different from what happens using the standard univariate local bias where the scale-dependent terms come from badly behaved higher-order corrections. On the other hand, our biasing scheme reduces to the usual local bias on smaller scales where |phi| is typically much smaller than the density perturbations. We finally discuss the halo bispectrum in the context of multivariate biasing and show that, due to its strong scale and shape dependence, it is a powerful tool for the detection of primordial non-Gaussianity from future galaxy surveys.Comment: 26 pages, 16 figures. Minor modifications, version accepted by Phys. Rev.

On the spatial distribution of dark matter halos

We study the spatial distribution of dark matter halos in the Universe in terms of their number density contrast, related to the underlying dark matter fluctuation via a non-local and non-linear bias random field. The description of the matter dynamics is simplified by adopting the `truncated' Zel'dovich approximation to obtain both analytical results and simulated maps. The halo number density field in our maps and its probability distribution reproduce with excellent accuracy those of halos in a high-resolution N-body simulation with the same initial conditions. Our non-linear and non-local bias prescription matches the N-body halo distribution better than any Eulerian linear and local bias.Comment: 4 pages, LaTeX (uses emulateapj; included psfig.tex), 3 figures, 1 table. Shortened version, matching the size requirements of ApJ Letters. Accepted for publicatio

Orbital Parameters of Merging Dark Matter Halos

In order to specify cosmologically motivated initial conditions for major galaxy mergers (mass ratios $\leq$ 4:1) that are supposed to explain the formation of elliptical galaxies we study the orbital parameters of major mergers of cold dark matter halos using a high-resolution cosmological simulation. Almost half of all encounters are nearly parabolic with eccentricities $e \approx 1$ and no correlations between the halo spin planes or the orbital planes. The pericentric argument $\omega$ shows no correlation with the other orbital parameters and is distributed randomly. In addition we find that 50 % of typical pericenter distances are larger than half the halo's virial radii which is much larger than typically assumed in numerical simulations of galaxy mergers. In contrast to the usual assumption made in semi-analytic models of galaxy formation the circularities of major mergers are found to be not randomly distributed but to peak around a value of $\epsilon \approx 0.5$. Additionally all results are independent of the minimum progenitor mass and major merger definitions (i.e. mass ratios $\leq$ 4:1; 3:1; 2:1).Comment: 11 pages, 20 figures, replaced by version accepted to A&A, figure 1 low re

A gravitational lensing explanation for the excess of strong Mg-II absorbers in GRB afterglow spectra

GRB afterglows offer a probe of the intergalactic medium out to high redshift which complements observations along more abundant quasar lines-of-sight. Although both quasars and GRB afterglows should provide a-priori random sight-lines through the intervening IGM, it has been observed that strong Mg-II absorbers are twice as likely to be found along sight-lines toward GRBs. Several proposals to reconcile this discrepancy have been put forward, but none has been found sufficient to explain the magnitude of the effect. In this paper we estimate the effect of gravitational lensing by galaxies and their surrounding mass distributions on the statistics of Mg-II absorption. We find that the multi-band magnification bias could be very strong in the spectroscopic GRB afterglow population and that gravitational lensing can explain the discrepancy in density of absorbers, for plausibly steep luminosity functions. The model makes the prediction that approximately 20%-60% of the spectroscopic afterglow sample (i.e. ~ 5-15 of 26 sources) would have been multiply imaged, and hence result in repeating bursts. We show that despite this large lensing fraction it is likely that none would yet have been identified by chance owing to the finite sky coverage of GRB searches. We predict that continued optical monitoring of the bright GRB afterglow locations in the months and years following the initial decay would lead to identification of lensed GRB afterglows. A confirmation of the lensing hypothesis would allow us to constrain the GRB luminosity function down to otherwise inaccessibly faint levels, with potential consequences for GRB models.Comment: 8 pages, 3 figures. Submitted to MNRAS

On the Clustering of Sub-millimeter Galaxies

We measure the angular two-point correlation function of sub-millimeter galaxies (SMGs) from 1.1-millimeter imaging of the COSMOS field with the AzTEC camera and ASTE 10-meter telescope. These data yields one of the largest contiguous samples of SMGs to date, covering an area of 0.72 degrees^2 down to a 1.26 mJy/beam (1-sigma) limit, including 189 (328) sources with S/N greater than 3.5 (3). We can only set upper limits to the correlation length r_0, modeling the correlation function as a power-law with pre-assigned slope. Assuming existing redshift distributions, we derive 68.3% confidence level upper limits of r_0 < 6-8 h^-1 Mpc at 3.7 mJy, and r_0 < 11-12 h^-1 Mpc at 4.2 mJy. Although consistent with most previous estimates, these upper limits imply that the real r_0 is likely smaller. This casts doubts on the robustness of claims that SMGs are characterized by significantly stronger spatial clustering, (and thus larger mass), than differently selected galaxies at high-redshift. Using Monte Carlo simulations we show that even strongly clustered distributions of galaxies can appear unclustered when sampled with limited sensitivity and coarse angular resolution common to current sub-millimeter surveys. The simulations, however, also show that unclustered distributions can appear strongly clustered under these circumstances. From the simulations, we predict that at our survey depth, a mapped area of two degrees^2 is needed to reconstruct the correlation function, assuming smaller beam sizes of future surveys (e.g. the Large Millimeter Telescope's 6" beam size). At present, robust measures of the clustering strength of bright SMGs appear to be below the reach of most observations.Comment: 23 pages, 8 figures, accepted for publication in The Astrophysical Journa