Void statistics and void galaxies in the 2dF Galaxy Redshift Survey

In the 2dF Galaxy Redshift Survey, we study the properties of voids and of fainter galaxies within voids that are defined by brighter galaxies. Our results are compared with simulated galaxy catalogues from the Millennium simulation coupled with a semi-analytical galaxy formation recipe. We derive the void size distribution and discuss its dependence on the faint magnitude limit of the galaxies defining the voids. While voids among faint galaxies are typically smaller than those among bright galaxies, the ratio of the void sizes to the mean galaxy separation reaches larger values. This is well reproduced in the mock galaxy samples studied. We provide analytic fitting functions for the void size distribution. Furthermore, we study the galaxy population inside voids defined by galaxies with   B _J− 5 log  h < −20  and diameter larger than  10  h ⁻¹ Mpc  . We find a clear bimodality of galaxies inside voids and in the average field but with different characteristics. The abundance of blue cloud galaxies inside voids is enhanced. There is an indication of a slight blueshift of the blue cloud. Furthermore, galaxies in void centres have slightly higher specific star formation rates as measured by the η parameter. We determine the radial distribution of the ratio of early- and late-type galaxies through the voids. We find and discuss some differences between observations and the Millennium catalogues.     

The pairwise velocity dispersion of galaxies: effects of non-radial motions

I discuss the effect of non-radial motions on the small-scale peculiar pairwise velocity dispersions (PVD) of galaxies in a cold dark matter (CDM) model and calculate the PVD for the SCDM model by means of the refined cosmic virial theorem (CVT), taking account of non-radial motions by means of the Del Popolo & Gambera model. I compare the results of the present model with the data from Davis & Peebles, the IRAS value at 1  h ⁻¹ Mpc of Fisher et al. and Marzke et al. I show that while the SCDM model disagrees with the observed values, as pointed out by several authors, taking account of non-radial motions produces smaller values for the PVD. At r ≤1  h ⁻¹ Mpc the result is in agreement with Bartlett & Blanchard. In the light of this last paper, the result may be also read as a strong dependence of the CVT prediction on the model chosen to describe the mass distribution around galaxies, suggesting that the CVT cannot be taken as a direct evidence for a low-density Universe. Similarly to what is shown by Del Popolo & Gambera and Del Popolo et al., the agreement of our model to the observational data is because of a scale-dependent bias induced by the presence of non-radial motions. As the assumptions on which CVT is based have been questioned by several authors, I also calculated the PVD using the redshift distortion in the redshift-space correlation function, ξ _z( r _p, π), and compared it with the PVD measured from the Las Campanas Redshift Survey by Jing et al. The result confirms that non-radial motions influence the PVD making them agree better with the observed data.     

Clustering of galaxies at high redshifts

Recent observations show a large concentration of galaxies at high redshift. At first sight, strong clustering of galaxies at high redshifts seems to be in contradiction with the models of structure formation. In this paper we show that such structures are a manifestation of the strong clustering of rare peaks in the density field. We compute the frequency of occurrence of such large concentrations of galaxies in some models of structure formation.     

The clustering of Lyman-break galaxies

We calculate the statistical clustering of Lyman-break galaxies predicted in a selection of currently fashionable structure formation scenarios. These models are all based on the cold dark matter model, but vary in the amount of dark matter, the initial perturbation spectrum, the background cosmology and the presence or absence of a cosmological constant term. If Lyman-break galaxies form as a result of hierarchical merging, the amplitude of clustering depends quite sensitively on the minimum halo mass that can host such a galaxy. Interpretation of the recent observations by Giavalisco et al. would therefore be considerably clarified by a direct determination of the relevant halo properties. For a typical halo mass around 10¹¹  h ⁻¹ M⊙ the observations do not discriminate strongly between cosmological models, but if the appropriate mass is larger, say 10¹²  h ⁻¹ M⊙ (which seems likely on theoretical grounds), then the data strongly favour models with a low matter density.     

Decorrelating the power spectrum of galaxies

We show how to decorrelate the (pre-whitened) power spectrum measured from a galaxy survey into a set of high-resolution uncorrelated band-powers. The treatment includes non-linearity, but not redshift distortions. Amongst the infinitely many possible decorrelation matrices, the square root of the Fisher matrix, or a scaled version thereof, offers a particularly good choice, in the sense that the band-power windows are narrow, approximately symmetric, and well-behaved in the presence of noise. We use this method to compute band-power windows for, and the information content of, the Sloan Digital Sky Survey, the Las Campanas Redshift Survey, and the IRAS 1.2-Jy Survey.     

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

Statistical analysis of galaxy surveys – III. The non-linear clustering of red and blue galaxies in the 2dFGRS

We present measurements of the higher order clustering of red and blue galaxies as a function of scale and luminosity made from the two-degree field galaxy redshift survey (2dFGRS). We use a counts-in-cells analysis to estimate the volume-averaged correlation functions,     , as a function of scale up to the order of   p = 5  , and also the reduced void probability function. Hierarchical amplitudes are constructed using the estimates of the correlation functions:     . We find that (i) red galaxies display stronger clustering than blue galaxies at all orders measured; (ii) red galaxies show values of   S _p   that are strongly dependent on luminosity whereas blue galaxies show no segregation in   S _p   within the errors; this is remarkable given the segregation in the variance; (iii) the linear relative bias shows the opposite trend to the hierarchical amplitudes, with little segregation for the red sequence and some segregation for the blue; (iv) faint red galaxies deviate significantly from the 'universal' negative binomial reduced void probabilities followed by all other galaxy populations. Our results show that the characteristic colour of a galaxy population reveals a unique signature in its spatial distribution. Such signatures will hopefully further elucidate the physics responsible for shaping the cosmological evolution of galaxies.     

Old high-redshift galaxies and primordial density fluctuation spectra

We have discovered a population of extremely red galaxies at z  ≃ 1.5 which have apparent stellar ages of ≳ 3 Gyr, based on detailed spectroscopy in the rest-frame ultraviolet. In order for galaxies to have existed at the high collapse redshifts indicated by these ages, there must be a minimum level of power in the density fluctuation spectrum on galaxy scales. This paper compares the required power with that inferred from other high-redshift populations: damped Lyα absorbers and Lyman-limit galaxies at z  ≃ 3.2. If the collapse redshifts for the old red galaxies are in the range z _c ≃ 6–8, there is general agreement between the various tracers on the required inhomogeneity on 1-Mpc scales. This level of small-scale power requires the Lyman-limit galaxies to be approximately ν ≃ 3.0 fluctuations, implying a very large bias parameter b  ≃ 6. If the collapse redshifts of the red galaxies are indeed in the range z _c = 6–8 required for power spectrum consistency, their implied ages at z  ≃ 1.5 are between 3 and 3.8 Gyr for essentially any model universe of current age 14 Gyr. The age of these objects as deduced from gravitational collapse thus provides independent support for the ages estimated from their stellar populations. Such early-forming galaxies are rare, and their contribution to the cosmological stellar density is consistent with an extrapolation to higher redshifts of the star formation rate measured at z  < 5; there is no evidence for a general era of spheroid formation at extreme redshifts.     

Validity of the 'conservation law' in the evolution of cosmological perturbations

It is shown that the 'conservation law' for metric fluctuations with long wavelengths is indeed applicable for growing modes of perturbations, which are of interest in cosmology, in spite of recent criticism. This is demonstrated both by general arguments and by presenting an explicitly solvable toy model for the evolution of metric perturbations during inflation.     

Joint cosmological formation of QSOs and bulge-dominated galaxies

Older and more recent pieces of observational evidence suggest a strong connection between QSOs and galaxies; in particular, the recently discovered correlation between black hole and galactic bulge masses suggests that QSO activity is directly connected to the formation of galactic bulges. The cosmological problem of QSO formation is analysed in the framework of an analytical model for galaxy formation; for the first time a joint comparison with galaxy and QSO observables is performed. In this model it is assumed that the same physical variable that determines galaxy morphology is able to modulate the mass of the black hole responsible for QSO activity. Both halo spin and the occurrence of a major merger are considered as candidates for this role. The predictions of the model are compared with available data for the type-dependent galaxy mass functions, the star formation history of elliptical galaxies, the QSO luminosity function and its evolution (including the obscured objects contributing to the hard-X-ray background), the mass function of dormant black holes and the distribution of black hole-to-bulge mass ratios. A good agreement with observations is obtained if the halo spin modulates the efficiency of black hole formation, and if the galactic haloes at z =0 have shone in an inverted order with respect to the hierarchical one (i.e., stars and black holes in bigger galactic haloes have formed before those in smaller ones). This inversion of hierarchical order for galaxy formation, which reconciles galaxy formation with QSO evolution, is consistent with many pieces of observational evidence.     

The clustering of colour-selected galaxies

We present measurements of the angular correlation function of galaxies selected from a B _J ∼23.5 multicolour survey of two 5°×5° fields located at high galactic latitudes. The galaxy catalogue of ∼4×10⁵ galaxies is comparable in size to catalogues used to determine the galaxy correlation function at low redshift. Measurements of the z ∼0.4 correlation function at large angular scales show no evidence for a break from a power law, although our results are not inconsistent with a break at ≳15 h⁻¹ Mpc. Despite the large fields-of-view, there are large discrepancies between the measurements of the correlation function in each field, possibly caused by dwarf galaxies within z ∼0.11 clusters near the South Galactic Pole.
Colour selection is used to study the clustering of galaxies from z ∼0 to z ∼0.4. The galaxy correlation function is found to depend strongly on colour, with red galaxies more strongly clustered than blue galaxies by a factor of ≳5 at small scales. The slope of the correlation function is also found to vary with colour, with γ∼1.8 for red galaxies and γ∼1.5 for blue galaxies. The clustering of red galaxies is consistently strong over the entire magnitude range studied, although there are large variations between the two fields. The clustering of blue galaxies is extremely weak over the observed magnitude range, with clustering consistent with r ₀∼2 h⁻¹ Mpc. This is weaker than the clustering of late-type galaxies in the local Universe, and suggests that galaxy clustering is more strongly correlated with colour than morphology. This may also be the first detection of a substantial low-redshift galaxy population with clustering properties similar to faint blue galaxies.     

The growth of linear perturbations in generic defect models for structure formation

We study the growth of linear perturbations induced by a generic causal scaling source as a function of the cosmological parameters h ,     and     . We show that for wavenumbers k ≳0.01  h  Mpc⁻¹ the spectrum of density and velocity perturbations scales in a similar way to that found in inflationary models with primordial perturbations. We show that this result is independent of the more-or-less incoherent nature of the source, the small-scale power spectrum of the source and of deviations from scaling that naturally occur at late times if     .     

Virialization of cosmological structures in models with time-varying equation of state

We study the virialization of the cosmic structures in the framework of flat cosmological models where the dark energy component plays an important role in the global dynamics of the Universe. In particular, our analysis focuses on the study of the spherical matter perturbations, as the latter decouple from the background expansion, start to 'turn around' and finally collapse. We generalize this procedure, taking into account models with an equation of state which vary with time, and provide a complete formulation of the cluster virialization attempting to address the non-linear regime of structure formation. In particular, assuming that clusters have collapsed prior to the epoch of z _f≃ 1.4, in which the most distant cluster has been found, we show that the behaviour of the spherical collapse model depends on the functional form of the equation of state.