Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in the light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes, which provide a good fit to large numerical simulations; (3) more accurate mass–temperature relations from larger catalogues of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multiparameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on σ ₈, the normalization of the matter power spectrum on scales of 8  h ⁻¹ Mpc, as a function of the matter density and cosmological constant in a universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the normalization, approximately independent of power spectrum shape, can be expressed as constraints on σ at an appropriate cluster normalization scale R _Cl. We provide fitting formulas for R _Cl and σ ( R _Cl) for general cosmologies, as well as for σ ₈ as a function of cosmology and shape parameter Γ. For flat models we find approximately σ ₈≃(0.495_−0.037^+0.034)Ω_M^−0.60 for Γ=0.23, where the error bar is dominated by uncertainty in the mass–temperature relation.     

Properties of spherical galaxies and clusters with an NFW density profile

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high-resolution cosmological N -body simulations by Navarro, Frenk & White (NFW). We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial OsipkovMerritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half-mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line-of-sight as well as aperture-velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW surface density profile is found to fit HubbleReynolds laws well. It is also well fitted by Sérsic R ^{1/ m} laws, for     but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass-to-light ratio that increases outwards at all radii.     

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, P ( k ), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P ( k ) can be approximated by a power law, P ( k )∝ kⁿ , with n ≈−1.6 over the wavenumber range 0.04< k <0.1 h Mpc⁻¹. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k ∼0.03 h Mpc⁻¹. We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N -body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers k ≳0.02 h Mpc⁻¹. These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a near-scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.     

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 apparent and intrinsic shape of the APM galaxy clusters

We estimate the distribution of intrinsic shapes of APM galaxy clusters from the distribution of their apparent shapes. We measure the projected cluster ellipticities using two alternative methods. The first method is based on moments of the discrete galaxy distribution while the second is based on moments of the smoothed galaxy distribution. We study the performance of both methods using Monte Carlo cluster simulations covering the range of APM cluster distances and including a random distribution of background galaxies. We find that the first method suffers from severe systematic biases, whereas the second is more reliable. After excluding clusters dominated by substructure and quantifying the systematic biases in our estimated shape parameters, we recover a corrected distribution of projected ellipticities. We use the non-parametric kernel method to estimate the smooth apparent ellipticity distribution, and numerically invert a set of integral equations to recover the corresponding distribution of intrinsic ellipticities under the assumption that the clusters are either oblate or prolate spheroids. The prolate spheroidal model fits the APM cluster data best.     

Star formation in galaxies falling into clusters along supercluster-scale filaments

With the help of a statistical parameter derived from optical spectra, we show that the current star formation rate of a galaxy, falling into a cluster along a supercluster filament, is likely to undergo a sudden enhancement before the galaxy reaches the virial radius of the cluster. From a sample of 52 supercluster-scale filaments of galaxies joining a pair of rich clusters of galaxies within the two-degree Field Redshift Survey region, we find a significant enhancement of star formation, within a narrow range between ∼2 and  3  h ⁻¹₇₀ Mpc  of the centre of the cluster into which the galaxy is falling. This burst of star formation is almost exclusively seen in the fainter dwarf galaxies  ( M _B ≥−20)  . The relative position of the peak does not depend on whether the galaxy is a member of a group or not, but non-group galaxies have on average a higher rate of star formation immediately before falling into a cluster. From the various trends, we conclude that the predominant process responsible for this rapid burst is the close interaction with other galaxies falling into the cluster along the same filament, if the interaction occurs before the gas reservoir of the galaxy gets stripped off due to the interaction with the intracluster medium.     

The alignment of clusters using large-scale simulations

The alignment of clusters of galaxies with their nearest neighbours and between clusters within a supercluster is investigated using simulations of 512³ dark matter particles for ΛCDM and τ CDM cosmological models. Strongly significant alignments are found for separations of up to 15  h ⁻¹ Mpc in both cosmologies, but for the ΛCDM model the alignments extend up to separations of 30  h ⁻¹ Mpc. The effect is strongest for nearest neighbours, but is not significant enough to be useful as an observational discriminant between cosmologies. As a check of whether this difference in alignments is present in other cosmologies, smaller simulations with 256³ particles are investigated for four different cosmological models. Because of poor number statistics, only the standard CDM model shows indications of having different alignments from the other models.     

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.     

Structures in the Great Attractor region

To further our understanding of the Great Attractor (GA), we have undertaken a redshift survey using the 2-degree Field (2dF) instrument on the Anglo-Australian Telescope (AAT). Clusters and filaments in the GA region were targeted with 25 separate pointings resulting in approximately 2600 new redshifts. Targets included poorly studied X-ray clusters from the Clusters in the Zone of Avoidance (CIZA) Catalogue as well as the Cen–Crux and PKS 1343−601 clusters, both of which lie close to the classic GA centre. For nine clusters in the region, we report velocity distributions as well as virial and projected mass estimates. The virial mass of CIZA J1324.7−5736, now identified as a separate structure from the Cen–Crux cluster, is found to be  ∼3 × 10¹⁴ M_⊙  , in good agreement with the X-ray inferred mass. In the PKS 1343−601 field, five redshifts are measured of which four are new. An analysis of redshifts from this survey, in combination with those from the literature, reveals the dominant structure in the GA region to be a large filament, which appears to extend from Abell S0639  ( l = 281°, b =+11°)  to  ( l ∼ 5°, b ∼−50°)  , encompassing the Cen–Crux, CIZA J1324.7−5736, Norma and Pavo II clusters. Behind the Norma cluster at   cz ∼ 15 000 km s⁻¹  , the masses of four rich clusters are calculated. These clusters (Triangulum Australis, Ara, CIZA J1514.6−4558 and CIZA J1410.4−4246) may contribute to a continued large-scale flow beyond the GA. The results of these observations will be incorporated into a subsequent analysis of the GA flow.     

The 2dF Galaxy Redshift Survey: the nature of the relative bias between galaxies of different spectral type

We present an analysis of the relative bias between early- and late-type galaxies in the Two-degree Field Galaxy Redshift Survey (2dFGRS) – as defined by the η parameter of Madgwick et al., which quantifies the spectral type of galaxies in the survey. We calculate counts in cells for flux-limited samples of early- and late-type galaxies, using approximately cubical cells with sides ranging from 7 to  42 h ⁻¹ Mpc  . We measure the variance of the counts in cells using the method of Efstathiou et al., which we find requires a correction for a finite volume effect equivalent to the integral constraint bias of the autocorrelation function. Using a maximum-likelihood technique we fit lognormal models to the one-point density distribution, and develop methods of dealing with biases in the recovered variances resulting from this technique. We then examine the joint density distribution function,   f (δ_E, δ_L)  , and directly fit deterministic bias models to the joint counts in cells. We measure a linear relative bias of ≈1.3, which does not vary significantly with ℓ. A deterministic linear bias model is, however, a poor approximation to the data, especially on small scales  (ℓ≤ 28  h ⁻¹ Mpc)  where deterministic linear bias is excluded at high significance. A power-law bias model with index   b ₁≈ 0.75  is a significantly better fit to the data on all scales, although linear bias becomes consistent with the data for  ℓ≳ 40  h ⁻¹ Mpc  .     

Interaction-induced star formation in a complete sample of 105 nearby star-forming galaxies

We investigate the clustering properties of a complete sample of 10⁵ star-forming galaxies drawn from the data release 4 (DR4) of the Sloan Digital Sky Survey. On scales less than 100 kpc, the amplitude of the correlation function exhibits a strong dependence on the specific star formation rate (SSFR) of the galaxy. We interpret this as the signature of enhanced star formation induced by tidal interactions. We then explore how the average star formation rate (SFR) in a galaxy is enhanced as the projected separation r _p between the galaxy and its companions decreases. We find that the enhancement strongly depends on r _p, but very weakly on the relative luminosity of the companions. The enhancement is also stronger in low-mass galaxies than in high-mass galaxies. In order to explore whether a tidal interaction is not only sufficient, but also necessary to trigger enhanced star formation in a galaxy, we compute background subtracted neighbour counts for the galaxies in our sample. The average number of close neighbours around galaxies with low to average values of SFR/ M _* is close to zero. At the highest SSFRs, however, more than 40 per cent of the galaxies in our sample have a companion within a projected radius of 100 kpc. Visual inspection of the highest SFR/ M _* galaxies without companions reveals that more than 50 per cent of these are clear interacting or merging systems. We conclude that tidal interactions are the dominant trigger of enhanced star formation in the most strongly star-forming systems. Finally, we find clear evidence that tidal interactions not only lead to enhanced star formation in galaxies, but also cause structural changes such as an increase in concentration.