Modelling galaxy–galaxy weak lensing with Sloan Digital Sky Survey groups

We use galaxy groups selected from the Sloan Digital Sky Survey (SDSS) together with mass models for individual groups to study the galaxy–galaxy lensing signals expected from galaxies of different luminosities and morphological types. We compare our model predictions with the observational results obtained from the SDSS by Mandelbaum et al. for the same samples of galaxies. The observational results are well reproduced in a Λ cold dark matter (ΛCDM) model based on the Wilkinson Microwave Anisotropy Probe ( WMAP ) 3-yr data, but a ΛCDM model with higher σ₈, such as the one based on the WMAP 1-yr data, significantly overpredicts the galaxy–galaxy lensing signal. We model, separately, the contributions to the galaxy–galaxy lensing signals from different galaxies: central versus satellite, early type versus late type and galaxies in haloes of different masses. We also examine how the predicted galaxy–galaxy lensing signal depends on the shape, density profile and the location of the central galaxy with respect to its host halo.     

Scale-dependent galaxy bias in the Sloan Digital Sky Survey as a function of luminosity and colour

It has been known for a long time that the clustering of galaxies changes as a function of galaxy type. This galaxy bias acts as a hindrance to the extraction of cosmological information from the galaxy power spectrum or correlation function. Theoretical arguments show that a change in the amplitude of the clustering between galaxies and mass on large scales is unavoidable, but cosmological information can be easily extracted from the shape of the power spectrum or correlation function if this bias is independent of scale. Scale-dependent bias is generally small on large scales,   k < 0.1  h  Mpc⁻¹  , but on smaller scales can affect the recovery of  Ω_m h   from the measured shape of the clustering signal, and have a small effect on the Baryon Acoustic Oscillations. In this paper, we investigate the transition from scale-independent to scale-dependent galaxy bias as a function of galaxy population. We use the Sloan Digital Sky Survey Data Release 5 sample to fit various models, which attempt to parametrize the turn-off from scale-independent behaviour. For blue galaxies, we find that the strength of the turn-off is strongly dependent on galaxy luminosity, with stronger scale-dependent bias on larger scales for more luminous galaxies. For red galaxies, the scale dependence is a weaker function of luminosity. Such trends need to be modelled in order to optimally extract the information available in future surveys, and can help with the design of such surveys.     

A two-dimensional analysis of percolation and filamentarity in the Sloan Digital Sky Survey Data Release One

We have used the largest cluster statistics and the average filamentarity to quantify respectively the connectivity and the shapes of the patterns seen in the galaxy distribution in two volume-limited subsamples extracted from the equatorial strips of the Sloan Digital Sky Survey (SDSS) Data Release One (DR1). The data was projected on to the equatorial plane and analysed in two dimensions (2D). Comparing the results with Poisson point distributions at various levels of smoothing we find evidence for a network-like topology with filaments being the dominant patterns in the galaxy distribution. With increasing smoothing, a transition from many individual filamentary structures to an interconnected network is found to occur at a filling factor of 0.5–0.6. We have tested the possibility that the connectivity and the morphology of the patterns in the galaxy distribution may be luminosity dependent and find significant evidence for a luminosity–morphology relation, the brighter galaxies exhibiting lower levels of connectivity and filamentarity compared to the fainter ones. Using a statistical technique, Shuffle, we show that the filamentarity in both the SDSS strips is statistically significant up to 80  h ⁻¹ Mpc but not beyond. Larger filaments, though identified, are not statistically significant. Our findings reaffirm earlier work establishing the filaments to be the largest known statistically significant coherent structures in the Universe.     

Exploring star formation using the filaments in the Sloan Digital Sky Survey Data Release Five

We have quantified the average filamentarity of the galaxy distribution in seven nearly two-dimensional strips from the Sloan Digital Sky Survey Data Release Five (SDSS DR5) using a volume-limited sample in the absolute magnitude range  −21 ≤ M _r ≤−20  . The average filamentarity of star-forming (SF) galaxies, which are predominantly blue, is found to be more than that of other galaxies which are predominantly red. This difference is possibly an outcome of the fact that blue galaxies have a more filamentary distribution. Comparing the SF galaxies with only the other blue galaxies, we find that the two show nearly equal filamentarity. Separately analyzing the galaxies with high star formation rates (SFR) and low SFR, we find that the latter has a more filamentary distribution. We interpret this in terms of two effects. (i) A correlation between the SFR and individual galaxy properties like luminosity with the high-SFR galaxies being more luminous. (ii) A relation between the SFR and environmental effects like the density with the high-SFR galaxies preferentially occurring in high-density regions. These two effects are possibly not independent and are operating simultaneously. We do not find any difference in the filamentarity of SF galaxies and active galactic nuclei.     

Non-linear redshift distortions: the two-point correlation function

We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ _s , the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ _s . While the deviations are insignificant for the monopole ξ ₀, the hexadecapole ξ ₄ exhibits large deviations from the linear predictions. For a COBE normalized     ,     cold dark matter (CDM) power spectrum, our results for ξ ₄ deviate from the linear predictions by a factor of two on the scale of ∼10  h ⁻¹ Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only     .
We also show that the commonly used phenomenological model, where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.     

The Durham/UKST Galaxy Redshift Survey – IV. Redshift-space distortions in the two-point correlation function

We have investigated the redshift-space distortions in the optically selected Durham/UKST Galaxy Redshift Survey using the two-point galaxy correlation function perpendicular and parallel to the observer's line of sight, ξ(σ, π). On small, non-linear scales we observe an elongation of the constant ξ(σ, π) contours in the line-of-sight direction. This is a result of the galaxy velocity dispersion and is the common 'Finger of God' effect seen in redshift surveys. Our result for the one-dimensional pairwise rms velocity dispersion is 〈 w ²〉^1/2=416±36 km s⁻¹, which is consistent with those from recent redshift surveys and canonical values, but inconsistent with SCDM or LCDM models. On larger, linear scales we observe a compression of the ξ(σ, π) contours in the line-of-sight direction. This is caused by the infall of galaxies into overdense regions, and the Durham/UKST data favours a value of (Ω^0.6/ b )∼0.5, where Ω is the mean mass density of the Universe and b is the linear bias factor that relates the galaxy and mass distributions. Comparison with other optical estimates yields consistent results, with the conclusion that the data do not favour an unbiased critical-density universe.     

The Durham/UKST Galaxy Redshift Survey – III. Large-scale structure via the two-point correlation function

We have investigated the statistical clustering properties of galaxies by calculating the two-point galaxy correlation function from the optically selected Durham/UKST Galaxy Redshift Survey. This survey is magnitude-limited to b _J∼17, contains ∼2500 galaxies sampled at a rate of one-in-three and surveys a ∼4×10⁶ ( h ⁻¹ Mpc)³ volume of space. We have empirically determined the optimal method of estimating the two-point correlation function from just such a magnitude-limited survey. Applying our methods to this survey, we find that our redshift-space results agree well with those from previous optical surveys. In particular, we confirm the previously claimed detections of large-scale power out to ∼40 h ⁻¹ Mpc scales. We compare with two common models of cosmological structure formation and find that our two-point correlation function has power significantly in excess of the standard cold dark matter model in the 10–30 h ⁻¹ Mpc region. We therefore support the observational results of the APM galaxy survey. Given that only the redshift-space clustering can be measured directly, we use standard modelling methods and indirectly estimate the real-space two-point correlation function from the projected two-point correlation function. We then invert this projected correlation function to obtain an estimate of the spatial two-point correlation function in real space. This correlation function in real space has a lower amplitude than that in redshift space, but a steeper slope.