On the streaming model for redshift-space distortions

The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory approach, we derive the fundamental equations of the streaming model for ordered and unordered pairs. In the first case, we recover the classic equation while we demonstrate that modifications are necessary for unordered pairs. We then discuss several statistical properties of the pairwise velocities for DM particles and haloes by using a suite of high-resolution $N$-body simulations. We test the often used Gaussian ansatz for the PDF of pairwise velocities and discuss its limitations. Finally, we introduce a mixture of Gaussians which is known in statistics as the generalised hyperbolic distribution and show that it provides an accurate fit to the PDF. Once inserted in the streaming equation, the fit yields an excellent description of redshift-space correlations at all scales that vastly outperforms the Gaussian and exponential approximations. Using a principal-component analysis, we reduce the complexity of our model for large redshift-space separations. Our results increase the robustness of studies of anisotropic galaxy clustering and are useful for extending them towards smaller scales in order to test theories of gravity and interacting dark-energy models.Comment: 22 pages, 20 figures, accepted for publication in MNRA

Evolution of the two-point correlation function in the Zel'dovich approximation

We study the evolution of the mass autocorrelation function by describing the growth of density fluctuations through the Zel'dovich approximation. The results are directly compared with the predictions of the scaling hypothesis for clustering evolution extracted from numerical simulations (Hamilton et al. 1991), as implemented by Jain, Mo & White (1995). We find very good agreement between the correlations on mildly non-linear scales and on completely linear scales. In between these regimes, we note that the density fields evolved through the Zel'dovich approximation show more non-linear features than predicted by the scaling ansatz which is, however, forced to match the linear evolution on scales larger than the simulation box. In any case, the scaling ansatz by Baugh & Gaztanaga (1996), calibrated against large box simulations agrees better with ZA predictions on large scales, keeping good accuracy also on intermediate scales. We show that mode-coupling is able to move the first zero crossing of xi(r) as time goes on. A detailed fit of the time dependence of this shifting is given for a CDM model. The evolution of the cross correlation of the density fluctuation field evaluated at two different times is also studied. The possible implications of the results for the analysis of the observed correlation function of high redshift galaxies are discussed.Comment: revised version accepted for publication in MNRAS. The comparison with the scaling ansatz of Baugh & Gaztanaga (1996), one figure and some comments have been added. LaTex, 14 pages, 8 figure

The formation of CDM haloes II: collapse time and tides

We use two cosmological simulations of structure formation in the LambdaCDM scenario to study the evolutionary histories of dark-matter haloes and to characterize the Lagrangian regions from which they form. We focus on haloes identified at redshift z_id=0 and show that the classic ellipsoidal collapse model systematically overestimates their collapse times. If one imposes that halo collapse takes place at z_id, this model requires starting from a significantly lower linear density contrast than what is measured in the simulations at the locations of halo formation. We attempt to explain this discrepancy by testing two key assumptions of the model. First, we show that the tides felt by collapsing haloes due to the surrounding large-scale structure evolve non-linearly. Although this effect becomes increasingly important for low-mass haloes, accounting for it in the ellipsoidal collapse model only marginally improves the agreement with N-body simulations. Second, we track the time evolution of the physical volume occupied by forming haloes and show that, after turnaround, it generally stabilizes at a well-defined redshift, z_c>z_id, contrary to the basic assumption of extended Press-Schechter theory based on excursion sets. We discuss the implications of this result for understanding the origin of the mass-dependence and scatter in the linear threshold for halo formation. Finally, we show that, when tuned for collapse at z_c, a modified version of the ellipsoidal collapse model that also accounts for the triaxial nature of protohaloes predicts their linear density contrast in an unbiased way.Comment: 15 pages, 11 figures, MNRAS in pres

The halo distribution of 2dF galaxies

We use the clustering results obtained by Madgwick et al. (2003) for a sample of 96 791 galaxies from the 2dF Galaxy Redshift Survey with redshift 0.01 < z < 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 ruled out drastically 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, whereas passive objects show a preference to reside closer to the halo centre. If we assume a broken power law of the form 〈Ngal〉(m) = (m/m0) for mcut≤m < m0 and 〈Ngal〉(m) = (m/m0) 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 mcut≃ 1011 M⊙, much smaller than what is obtained for early-type galaxies (mcut≃ 1012.6 M⊙). In the high-mass regime m≥m0, 〈Ngal〉 increases with halo mass more slowly (α2≃ 0.7) in the case of late-type galaxies than for passive objects which present α2≃ 1.1. The above results imply that late-type galaxies dominate the 2dF counts at all mass-scales. We stress that — at variance with previous statements — there is no degeneracy in the determination of the best functional forms for ρ(r) and 〈Ngal〉, as they affect the behaviour of the galaxy-galaxy correlation function on different scale

Luminosity- and redshift-dependent quasar clustering

We present detailed clustering measurements for a flux-limited sample of ∼14 000 quasars extracted from the 2dF QSO Redshift Survey in the redshift range 0.8 1.3. On the other hand, a number of tests based on information theory and Bayesian statistics show only marginal evidence for luminosity-dependent clustering. Anyway, the quality of the data is not good enough to accurately quantify how quasar biasing depends on luminosity. We critically discuss the limitations of our data set and show that a much larger sample is needed to rule out current models for luminosity segregation. Studying the evolution of the clustering amplitude with redshift, we detect an increase of the quasar correlation length with lookback time at the 99.3 per cent confidence level. Adopting the concordance cosmological model, we discuss the evolution of quasar biasing with cosmic epoch and show that quasars are typically hosted by dark matter haloes with mass ∼1013 M