Combining cosmological datasets: hyperparameters and Bayesian evidence

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of hyperparameters, which are then marginalised over in order to recover the posterior distribution as a function only of the cosmological parameters of interest. In the case of a Gaussian likelihood function, this marginalisation may be performed analytically. Calculation of the Bayesian evidence for the data, with and without the introduction of hyperparameters, enables a direct determination of whether the data warrant the introduction of weights into the analysis; this generalises the standard likelihood ratio approach to model comparison. The method is illustrated by application to the classic toy problem of fitting a straight line to a set of data. A cosmological illustration of the technique is also presented, in which the latest measurements of the cosmic microwave background power spectrum are used to infer constraints on cosmological parameters.Comment: 12 pages, 6 figures, submitted to MNRA

The Dipole Anisotropy of the 2mass Redshift Survey

We estimate the flux weighted acceleration on the Local Group (LG) from the near-infrared Two Micron All Sky Redshift Survey (2MRS). The near-infrared flux weighted dipoles are very robust because they closely approximate a mass weighted dipole, bypassing the effects of redshift distortions and require no preferred reference frame. We use this method with the redshift information to determine the change in dipole with distance. The LG dipole seemingly converges by 60 Mpc/h. Assuming convergence, the comparison of the 2MRS flux dipole and the CMB dipole provides a value for the combination of the mass density and luminosity bias parameters Omega_m^0.6/b_L= 0.40+/-0.09.Comment: 4 pages, 2 figures, Contribution to Rencontres de Moriond: Contents and Structures of the Universe, March 18-25, 2006, La Thuil

Luminous superclusters: remnants from inflation

We derive the luminosity and multiplicity functions of superclusters compiled for the 2dF Galaxy Redshift Survey, the Sloan Digital Sky Survey (Data Release 4), and for three samples of simulated superclusters. We find for all supercluster samples Density Field (DF) clusters, which represent high-density peaks of the class of Abell clusters, and use median luminosities/masses of richness class 1 DF-clusters to calculate relative luminosity/mass functions. We show that the fraction of very luminous (massive) superclusters in real samples is more than tenfolds greater than in simulated samples. Superclusters are generated by large-scale density perturbations which evolve very slowly. The absence of very luminous superclusters in simulations can be explained either by non-proper treatment of large-scale perturbations, or by some yet unknown processes in the very early Universe.Comment: 6 pages, 3 Figures, submitted for Astronomy and Astrophysic

Superclusters of galaxies from the 2dF redshift survey. I. The catalogue

We use the 2dF Galaxy Redshift Survey data to compile catalogues of superclusters for the Northern and Southern regions of the 2dFGRS, altogether 543 superclusters at redshifts 0.009 < z < 0.2. We analyse methods of compiling supercluster catalogues and use results of the Millennium Simulation to investigate possible selection effects and errors. We find that the most effective method is the density field method using smoothing with an Epanechnikov kernel of radius 8 Mpc/h. We derive positions of the highest luminosity density peaks and find the most luminous cluster in the vicinity of the peak, this cluster is considered as the main cluster and its brightest galaxy the main galaxy of the supercluster. In catalogues we give equatorial coordinates and distances of superclusters as determined by positions of their main clusters. We also calculate the expected total luminosities of the superclusters.Comment: 16 pages, 11 figures, submitted for Astronomy and Astrophysics. High-resolution pdf file and supplementary data can be found at http://www.aai.ee/~maret/2dfscl.htm

The richest superclusters. I. Morphology

We study the morphology of the richest superclusters from the catalogues of superclusters of galaxies in the 2dF Galaxy Redshift Survey and compare the morphology of real superclusters with model superclusters in the Millennium Simulation. We use Minkowski functionals and shapefinders to quantify the morphology of superclusters: their sizes, shapes, and clumpiness. We generate empirical models of simple geometry to understand which morphologies correspond to the supercluster shapefinders. We show that rich superclusters have elongated, filamentary shapes with high-density clumps in their core regions. The clumpiness of superclusters is determined using the fourth Minkowski functional $V_3$. In the $K_1$-$K_2$ shapefinder plane the morphology of superclusters is described by a curve which is characteristic to multi-branching filaments. We also find that the differences between the fourth Minkowski functional $V_3$ for the bright and faint galaxies in observed superclusters are larger than in simulated superclusters.Comment: 14 pages, 8 figures, submitted to Astronomy and Astrophysic

Superclusters of galaxies from the 2dF redshift survey. II. Comparison with simulations

We investigate properties of superclusters of galaxies found on the basis of the 2dF Galaxy Redshift Survey, and compare them with properties of superclusters from the Millennium Simulation. We study the dependence of various characteristics of superclusters on their distance from the observer, on their total luminosity, and on their multiplicity. The multiplicity is defined by the number of Density Field (DF) clusters in superclusters. Using the multiplicity we divide superclusters into four richness classes: poor, medium, rich and extremely rich. We show that superclusters are asymmetrical and have multi-branching filamentary structure, with the degree of asymmetry and filamentarity being higher for the more luminous and richer superclusters. The comparison of real superclusters with Millennium superclusters shows that most properties of simulated superclusters agree very well with real data, the main differences being in the luminosity and multiplicity distributions.Comment: 15 pages, 13 Figures, submitted for Astronomy and Astrophysic

Reconstructed Density and Velocity Fields from the 2MASS Redshift Survey

We present the reconstructed real-space density and the predicted velocity fields from the Two Mass Redshift Survey (2MRS). The 2MRS is the densest all-sky redshift survey to date and includes about 23,200 galaxies with extinction corrected magnitudes brighter than K = 11.25. Our method is based on the expansion of these fields in Fourier-Bessel functions. Within this framework, the linear redshift distortions only affect the density field in the radial direction and can easily be deconvolved using a distortion matrix. Moreover, in this coordinate system, the velocity field is related to the density field by a simple linear transformation. The shot noise errors in the reconstructions are suppressed by means of a Wiener filter which yields a minimum variance estimate of the density and velocity fields. Using the reconstructed real-space density fields, we identify all major superclusters and voids. At 50 Mpc/h, our reconstructed velocity field indicates a back-side infall to the Great Attractor region of vi = (491 +/- 200)(beta/0.5) km/sec in the Local Group frame and v = (64 +/- 205)(beta/0.5) km/sec in the cosmic microwave background (CMB) frame and beta is the redshift distortion parameter. The direction of the reconstructed dipole agrees well with the dipole derived by Erdogdu et al. (2006). The misalignment between the reconstructed 2MRS and the CMB dipoles drops to 13 degrees at around 5000 km/sec but then increases at larger distances. A version of this paper with high resolution figures can be obtained from http://www.nottingham.ac.uk/~ppzzpeComment: 21 pages. 22 figures, accepted for publication in MNRAS. The figures are coarsely resolved, a version of this paper with high resolution figures can be obtained from http://www.nottingham.ac.uk/~ppzzp

Upper limits on neutrino masses from the 2dFGRS and WMAP: the role of priors

Solar, atmospheric, and reactor neutrino experiments have confirmed neutrino oscillations, implying that neutrinos have non-zero mass, but without pinning down their absolute masses. While it is established that the effect of neutrinos on the evolution of cosmic structure is small, the upper limits derived from large-scale structure data could help significantly to constrain the absolute scale of the neutrino masses. In a recent paper the 2dF Galaxy Redshift Survey (2dFGRS) team provided an upper limit m_nu,tot < 2.2 eV, i.e. approximately 0.7 eV for each of the three neutrino flavours, or phrased in terms of their contributioin to the matter density, Omega_nu/Omega_m < 0.16. Here we discuss this analysis in greater detail, considering issues of assumed 'priors' like the matter density Omega_m and the bias of the galaxy distribution with respect the dark matter distribution. As the suppression of the power spectrum depends on the ratio Omega_nu/Omega_m, we find that the out-of- fashion Mixed Dark Matter Model, with Omega_nu=0.2, Omega_m=1 and no cosmological constant, fits the 2dFGRS power spectrum and the CMB data reasonably well, but only for a Hubble constant H_0<50 km/s/Mpc. As a consequence, excluding low values of the Hubble constant, e.g. with the HST Key Project is important in order to get a strong constraint on the neutrino masses. We also comment on the improved limit by the WMAP team, and point out that the main neutrino signature comes from the 2dFGRS and the Lyman alpha forest.Comment: 24 pages, 12 figures Minor changes to matched version published in JCA

Superclusters of galaxies in the 2dF redshift survey. III. The properties of galaxies in superclusters

We use catalogues of superclusters of galaxies from the 2dF Galaxy Redshift Survey to study the properties of galaxies in superclusters. We compare the properties of galaxies in high and low density regions of rich superclusters, in poor superclusters and in the field, as well as in groups, and of isolated galaxies in superclusters of various richness. We show that in rich superclusters the values of the luminosity density smoothed on a scale of 8 \Mpc are higher than in poor superclusters: the median density in rich superclusters is $\delta \approx 7.5$, in poor superclusters $\delta \approx 6.0$. Rich superclusters contain high density cores with densities $\delta > 10$ while in poor superclusters such high density cores are absent. The properties of galaxies in rich and poor superclusters and in the field are different: the fraction of early type, passive galaxies in rich superclusters is slightly larger than in poor superclusters, and is the smallest among the field galaxies. Most importantly, in high density cores of rich superclusters ($\delta > 10$) there is an excess of early type, passive galaxies in groups and clusters, as well as among those which do not belong to groups or clusters. The main galaxies of superclusters have a rather limited range of absolute magnitudes. The main galaxies of rich superclusters have larger luminosities than those of poor superclusters and of groups in the field. Our results show that both the local (group/cluster) environments and global (supercluster) environments influence galaxy morphologies and their star formation activity.Comment: 13 pages, 10 figures, submitted to Astronomy and Astrophysic

The Signature of Large Scale Structures on the Very High Energy Gamma-Ray Sky

If the diffuse extragalactic gamma ray emission traces the large scale structures of the universe, peculiar anisotropy patterns are expected in the gamma ray sky. In particular, because of the cutoff distance introduced by the absorption of 0.1-10 TeV photons on the infrared/optical background, prominent correlations with the local structures within a range of few hundreds Mpc should be present. We provide detailed predictions of the signal based on the PSCz map of the local universe. We also use mock N-body catalogues complemented with the halo model of structures to study some statistical features of the expected signatures. The results are largely independent from cosmological details, and depend mostly on the index of correlation (or bias) of the sources with respect to the large scale distribution of galaxies. For instance, the predicted signal in the case of a quadratic correlation (as it may happen for a dark matter annihilation contribution to the diffuse gamma flux) differs substantially from a linear correlation case, providing a complementary tool to unveil the nature of the sources of the diffuse gamma ray emission. The chances of the present and future space and ground based observatories to measure these features are discussed.Comment: 26 pages, 9 figures; matches published versio