Estimating β from redshift-space distortions in the 2dF galaxy survey

Given the failure of existing models for redshift-space distortions to provide a highly accurate measure of the β -parameter, and the ability of forthcoming surveys to obtain data with very low random errors, it becomes necessary to develop better models for these distortions. Here we review the failures of the commonly used velocity dispersion models and present an empirical method for extracting β from the quadrupole statistic that has little systematic offset over a wide range of β and cosmologies. This empirical model is then applied to an ensemble of mock 2dF southern strip surveys, to illustrate the technique and see how accurately we can recover the true value of β . We compare this treatment with the error we expect to find caused only by the finite volume of the survey. We find that non-linear effects reduce the range of scales over which β can be fitted, and introduce covariances between nearby modes in addition to those introduced by the convolution with the survey window function. The result is that we are only able to constrain β to a 1 σ accuracy of 25 per cent ( β =0.55±0.14 for the cosmological model considered). We explore one possible means of reducing this error, that of cluster collapse, and show that accurate application of this method can greatly reduce the effect of non-linearities, improving the determination of β . We conclude by demonstrating that, when the contaminating effects of clusters are dealt with, this simple analysis of the full 2dF survey yields β =0.55±0.04. For this model, this represents a determination of β to an accuracy of 8 per cent and hence an important constraint on the cosmological density parameter Ω₀.     

The clustering of hot and cold IRAS galaxies: the redshift-space correlation function

We measure the autocorrelation function, ξ , of galaxies in the IRAS Point Source Catalogue galaxy redshift (PSC z ) survey and investigate its dependence on the far-infrared colour and absolute luminosity of the galaxies. We find that the PSC z survey correlation function can be modelled out to a scale of 10  h ⁻¹ Mpc as a power law of slope 1.30±0.04 and correlation length 4.77±0.20 . At a scale of 75  h ⁻¹ Mpc we find the value of J ₃ to be 1500±400 .
We also find that galaxies with higher 100 μm/60 μm flux ratio, corresponding to cooler dust temperatures, are more strongly clustered than warmer galaxies. Splitting the survey into three colour subsamples, we find that, between 1 and 10  h ⁻¹ Mpc, the ratio of ξ is a factor of 1.5 higher for the cooler galaxies compared with the hotter galaxies. This is consistent with the suggestion that hotter galaxies have higher star formation rates, and correspond to later-type galaxies which are less clustered than earlier types.
Using volume-limited subsamples, we find a weak variation of ξ as a function of absolute luminosity, in the sense that more luminous galaxies are less clustered than fainter galaxies. The trend is consistent with the colour dependence of ξ and the observed colour–luminosity correlation, but the large uncertainties mean that it has a low statistical significance.     

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.     

The Gaussian cell two-point 'energy-like' equation: application to large-scale galaxy redshift and peculiar motion surveys

We introduce a simple linear equation relating the line-of-sight peculiar-velocity and density contrast correlation functions. The relation, which we call the Gaussian cell two-point 'energy-like' equation , is valid at the distant-observer limit and requires Gaussian smoothed fields. In the variance case, i.e. at zero lag, the equation is similar in its mathematical form to the Irvine–Layzer cosmic energy equation. β estimation with this equation from the Point Source Catalogue Redshift (PSC) survey and the SEcat catalogue of peculiar velocities is carried out, returning a value of  β= 0.44 ± 0.08  . The applicability of the method for the 6dF galaxy redshift and peculiar motions survey is demonstrated with mock data where it is shown that β could be determined with ≈10 per cent accuracy. The prospects for constraining the dark energy equation of state with this method from the kinematic and thermal Sunyaev–Zel'dovich cluster surveys are discussed. The equation is also used to construct a non-parametric mass-density power-spectrum estimator from peculiar-velocity data.     

Reconstruction of cosmological initial conditions from galaxy redshift catalogues

We present and test a new method for the reconstruction of cosmological initial conditions from a full-sky galaxy catalogue. This method, called ZTRACE, is based on a self-consistent solution of the growing mode of gravitational instabilities according to the Zel'dovich approximation and higher order in Lagrangian perturbation theory. Given the evolved redshift-space density field, smoothed on some scale, ZTRACE finds, via an iterative procedure, an approximation to the initial density field for any given set of cosmological parameters; real-space densities and peculiar velocities are also reconstructed. The method is tested by applying it to N -body simulations of an Einstein–de Sitter and an open cold dark matter universe. It is shown that errors in the estimate of the density contrast dominate the noise of the reconstruction. As a consequence, the reconstruction of real-space density and peculiar velocity fields using non-linear algorithms is little improved over those based on linear theory. The use of a mass-preserving adaptive smoothing, equivalent to a smoothing in Lagrangian space, allows an unbiased (although noisy) reconstruction of initial conditions, as long as the (linearly extrapolated) density contrast does not exceed unity. The probability distribution function of the initial conditions is recovered to high precision, even for Gaussian smoothing scales of ∼5  h ⁻¹ Mpc, except for the tail at δ ≥1. This result is insensitive to the assumptions of the background cosmology.     

The clustering of barred galaxies in the local Universe

We study the clustering properties of barred galaxies using data from the Sloan Digital Sky Survey. We compute projected redshift-space two-point cross-correlation functions   w _p( r _p)  for a sample of nearly 1000 galaxies for which we have performed detailed structural decompositions using the methods described in Gadotti. The sample includes 286 barred galaxies. The clustering of barred and unbarred galaxies of similar stellar mass is indistinguishable over all the scales probed (∼20 kpc–30 Mpc). This result also holds even if the sample is restricted to bars with bluer   g − i   colours (and hence younger ages). Our result also does not change if we split our sample of barred galaxies according to bar-to-total luminosity ratio, bar boxyness, effective surface brightness, length or the shape of the surface density profile within the bar. There is a hint that red, elliptical bars are more strongly clustered than red and less elliptical bars, on scales  ≳1 Mpc  , although the statistical significance is not high. We conclude that there is no significant evidence that bars are a product of mergers or interactions. We tentatively interpret the stronger clustering of the more elliptical bars as evidence that they are located in older galaxies, which reside in more massive haloes.     

The origin of spatial intermittency in the galaxy distribution

The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrödinger equation coupled to a Poisson equation determining the gravitational potential. This approach has a number of interesting features, many of which were pointed out in a seminal paper by Widrow & Kaiser. In particular we show that this approach yields an elegant reformulation of an idea of Jones concerning the origin of lognormal intermittency in the galaxy distribution.