Large-scale galaxy distribution in the Las Campanas Redshift Survey

We make use of three-dimensional clustering analysis, inertia tensor methods, and the minimal spanning tree technique to estimate some physical and statistical characteristics of the large-scale galaxy distribution and, in particular, of the sample of overdense regions seen in the Las Campanas Redshift Survey (LCRS). Our investigation provides additional evidence for a network of structures found in our core sampling analysis of the LCRS : a system of rich sheet-like structures, which in turn surround large underdense regions criss-crossed by a variety of filamentary structures.
We find that the overdense regions contain ∼40–50 per cent of LCRS galaxies and have proper sizes similar to those of nearby superclusters. The formation of such structures can be roughly described as a non-linear compression of protowalls of typical cross-sectional size ∼ 20–25  h ⁻¹ Mpc; this scale is ∼5 times the conventional value for the onset of non-linear clustering – to wit, r ₀, the autocorrelation length for galaxies.
The comparison with available simulations and theoretical estimates shows that the formation of structure elements with parameters similar to those observed is presently possible only in low-density cosmological models, Ω_m h ∼0.2–0.3, with a suitable large-scale bias between galaxies and dark matter.     

Mass selection bias in galaxy cluster peculiar velocities from the kinetic Sunyaev–Zel'dovich effect

Upcoming surveys for galaxy clusters using the Sunyaev–Zel'dovich effect are potentially sensitive enough to create a peculiar velocity catalogue. The statistics of these peculiar velocities are sensitive to cosmological parameters. We develop a method to explore parameter space using N -body simulations in order to quantify dark matter halo velocity statistics which will be useful for cluster peculiar velocity observations. We show that mass selection bias from a kinetic Sunyaev–Zel'dovich velocity catalogue forecasts rms peculiar velocities with a much more complicated  Ω_m  dependency than suggested by linear perturbation theory. In addition, we show that both two-point functions for velocities disagree with linear theory predictions out to  ∼40  h ⁻¹ Mpc  separations. A pedagogical appendix is included developing linear theory notation with respect to the two-point peculiar velocities functions.     

The matter power spectrum from the Lyα forest: an optical depth estimate

We measure the matter power spectrum from 31 Lyα spectra spanning the redshift range of 1.6–3.6. The optical depth, τ, for Lyα absorption of the intergalactic medium is obtained from the flux using the inversion method of Nusser & Haehnelt. The optical depth is converted to density by using a simple power-law relation,  τ∝ (1 +δ)^α  . The non-linear 1D power spectrum of the gas density is then inferred with a method that makes simultaneous use of the one- and two-point statistics of the flux and compared against theoretical models with a likelihood analysis. A cold dark matter model with standard cosmological parameters fits the data well. The power-spectrum amplitude is measured to be (assuming a flat Universe),  σ₈= (0.92 ± 0.09) × (Ω_m/0.3)^−0.3  , with α varying in the range of 1.56–1.8 with redshift. Enforcing the same cosmological parameters in all four redshift bins, the likelihood analysis suggests some evolution in the temperature–density relation and the thermal smoothing length of the gas. The inferred evolution is consistent with that expected if reionization of He  ii occurred at   z ∼ 3.2  . A joint analysis with the Wilkinson Microwave Anisotropy Probe results together with a prior on the Hubble constant as suggested by the Hubble Space Telescope key project data, yields values of Ω_m and σ₈ that are consistent with the cosmological concordance model. We also perform a further inversion to obtain the linear 3D power spectrum of the matter density fluctuations.     

Reconstruction of the early Universe as a convex optimization problem

We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales – a few Mpc – where multistreaming becomes significant. Above 6 h ⁻¹ Mpc we propose and implement an effective Monge–Ampère–Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O ( N ³) time complexity and reasonable CPU time requirements. Testing against N -body cosmological simulations gives over 60 per cent of exactly reconstructed points.
We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge–Ampère equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.     

Wide triplets of galaxies: collapse on spatial scales of ∼1 Mpc

We study triple systems of galaxies with mean projected harmonic separation ≃0.6  h ⁻¹ Mpc     We call the systems 'wide triplets', in contrast to compact triplets with mean projected harmonic separation ≃0.04  h ⁻¹ Mpc, studied by Karachentsev et al. Data are taken for 108 wide triplets from a list compiled by Trofimov & Chernin; at least one-third of them are considered to be probably isolated physical systems. With typical crossing times of about the Hubble time, the wide triplets seem to be in a state of ongoing collapse. This is confirmed by a set of computer models which simulate well the observational characteristics of the ensemble of wide triplets. The simulations also give a statistical estimate of the total mass of a typical wide triplet: it proves to be ≃10¹³ M_⊙. This figure indicates that the dark matter mass is 15–30 times the mass of baryonic matter in the systems. The dynamics of wide triplets, as well as their dark matter content, provide new direct cosmological constraints by establishing that hierarchical evolution is occurring on a mass scale of ∼10¹³ M_⊙ and a spatial scale of ∼1 Mpc.     

The size and shape of local voids

We study the size and shape of low-density regions in the local Universe, which we identify in the smoothed density field of the PSCz flux-limited IRAS galaxy catalogue. After quantifying the systematic biases that enter the detection of voids using our data set and method, we identify, using a smoothing length of 5  h ⁻¹ Mpc, 14 voids within 80  h ⁻¹ Mpc (having volumes 10³  h ⁻³ Mpc³) and, using a smoothing length of 10  h ⁻¹ Mpc, eight voids within 130  h ⁻¹ Mpc (having volumes  8×10³ h⁻³ Mpc³)  . We study the void size distribution and morphologies and find that there is roughly an equal number of prolate and oblate-like spheroidal voids. We compare the measured PSCz void shape and size distributions with those expected in six different cold dark matter (CDM) models and find that only the size distribution can discriminate between models. The models preferred by the PSCz data are those with intermediate values of   σ ₈(≃0.83)  , independent of cosmology.     

The supergalactic plane revisited with the Optical Redshift Survey

We re-examine the existence and extent of the planar structure in the local galaxy density field, the so-called supergalactic plane (SGP). This structure is studied here in three dimensions using both the new Optical Redshift Survey (ORS) and the IRAS 1.2-Jy redshift survey. The density contrast in a slab of thickness 20  h ⁻¹ Mpc and diameter 80 Mpc aligned with the standard de Vaucouleurs supergalactic coordinates is δ _sgp∼0.5 for both ORS and IRAS . The structure of the SGP is not well described by a homogeneous ellipsoid, although it does appear to be a flattened structure, which we quantify by calculating the moment of inertia tensor of the density field. The directions of the principal axes vary with radius, but the minor axis remains within θ _z ∼30° of the standard SGP Z -axis, out to a radius of 80  h ⁻¹ Mpc, for both ORS and IRAS . However, the structure changes shape with radius, varying between a flattened pancake and a dumbbell, the latter at a radius of ∼50  h ⁻¹ Mpc, where the Great Attractor and Perseus–Pisces superclusters dominate the distribution. This calls to question the connectivity of the 'plane' beyond ∼40  h ⁻¹ Mpc. The configuration found here can be viewed as part of a web of filaments and sheets, rather than as an isolated pancake-like structure. An optimal minimum variance reconstruction of the density field using Wiener filtering, which corrects for both redshift distortion and shot noise, yields a similar misalignment angle and behaviour of axes. The background-independent statistic of axes proposed here can be best used for testing cosmological models by comparison with N -body simulations.     

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.     

Resolving cosmic structure formation with the Millennium-II Simulation

We present the Millennium-II Simulation (MS-II), a very large N -body simulation of dark matter evolution in the concordance Λ cold dark matter (ΛCDM) cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size  (100  h ⁻¹ Mpc)  with five times better spatial resolution (a Plummer equivalent softening of  1.0  h ⁻¹ kpc  ) and with 125 times better mass resolution (a particle mass of  6.9 × 10⁶  h ⁻¹ M_⊙  ). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and non-linear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from haloes similar to those hosting Local Group dwarf spheroidal galaxies to haloes corresponding to the richest galaxy clusters. The 'Milky Way' haloes of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass haloes. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogues and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.     

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.     

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.     

Galaxy–dark matter correlations applied to galaxy–galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N -body simulations to make predictions for galaxy–dark matter correlations and apply them to galaxy–galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1  h ⁻¹ Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy–dark matter correlation coefficient and show that it is close to unity on scales above 1  h ⁻¹ Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy–dark matter correlations.     

Gravitational wave background from Population III black hole formation

We study the generation of a stochastic gravitational wave (GW) background produced from a population of core-collapse supernovae, which form black holes in scenarios of structure formation. We obtain, for example, that the formation of a population (Population III) of black holes, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of   h _BG≃10⁻²⁴  and corresponding closure energy density of  Ω_GW∼10⁻⁷  , in the frequency band   ν _obs≃30–470 Hz  (assuming a maximum efficiency of generation of GWs, namely,   ɛ _GWmax=7×10⁻⁴)  for stars forming at redshifts   z ≃30–10  . We show that it will be possible in the future to detect this isotropic GW background by correlating the signals of a pair of 'advanced' LIGO observatories (LIGO III) at a signal-to-noise ratio of ≃40. We discuss what astrophysical information could be obtained from a positive (or even a negative) detection of such a GW background generated in scenarios such as those studied here. One of them is the possibility of obtaining the initial and final redshifts of the emission period from the observed spectrum of GWs.     

Chandra measurements of the distribution of mass in the luminous lensing cluster Abell 2390

We present spatially resolved X-ray spectroscopy of the luminous lensing cluster Abell 2390, using observations made with the Chandra observatory. The temperature of the X-ray gas rises with increasing radius within the central ∼ 200 kpc of the cluster, and then remains approximately isothermal, with kT =11.5_−1.6^+1.5 keV , out to the limits of the observations at r ∼1.0 Mpc . The total mass profile determined from the Chandra data has a form in good agreement with the predictions from numerical simulations. Using the parametrization of Navarro, Frenk and White, we measure a scale radius r _s∼0.8 Mpc and a concentration parameter c ∼3 . The best-fitting X-ray mass model is in good agreement with independent gravitational lensing results and optical measurements of the galaxy velocity dispersion in the cluster. The X-ray gas to total mass ratio rises with increasing radius with f _gas∼21 per cent at r =0.9 Mpc . The azimuthally averaged 0.3–7.0 keV surface brightness profile exhibits a small core radius and a clear 'break' at r ∼500 kpc , where the slope changes from S _X ∼^∝  r ^−1.5 to S _X ∼^∝  r ^−3.6 . The data for the central region of the cluster indicate the presence of a cooling flow with a mass deposition rate of 200–300 M_⊙ yr⁻¹ and an effective age of 2–3 Gyr .     

Peculiar velocity reconstruction with the fast action method: tests on mock redshift surveys

We present extensive tests of the fast action method (FAM) for recovering the past orbits of mass tracers in an expanding universe from their redshift-space coordinates at the present epoch. The tests focus on the reconstruction of present-day peculiar velocities using mock catalogues extracted from high-resolution N -body simulations. The method allows for a self-consistent treatment of redshift-space distortions by direct minimization of a modified action for a cosmological gravitating system. When applied to ideal, volume-limited catalogues, FAM recovers unbiased peculiar velocities with a one-dimensional, 1σ error of ∼220 km  s⁻¹  , if velocities are smoothed on a scale of  5 h ⁻¹  Mpc. Alternatively, when no smoothing is applied, FAM predicts nearly unbiased velocities for objects residing outside the highest density regions. In this second case the 1σ error decreases to a level of ∼150 km  s⁻¹  . The correlation properties of the peculiar velocity fields are also correctly recovered on scales larger than  5 h ⁻¹  Mpc. Similar results are obtained when FAM is applied to flux-limited catalogues mimicking the IRAS PSC z survey. In this case FAM reconstructs peculiar velocities with similar intrinsic random errors, while velocity–velocity correlation properties are well reproduced beyond scales of  ∼8 h ⁻¹  Mpc. We also show that FAM provides better velocity predictions than other, competing methods based on linear theory or the Zel'dovich approximation. These results indicate that FAM can be successfully applied to presently available galaxy redshift surveys such as IRAS PSC z .     

Principal-component analysis of the cosmic microwave background anisotropies: revealing the tensor degeneracy

A principal-component analysis of cosmic microwave background (CMB) anisotropy measurements is used to investigate degeneracies among cosmological parameters. The results show that a degeneracy with tensor modes – the 'tensor degeneracy'– dominates uncertainties in estimates of the baryon and cold dark matter densities,   ω _b=Ω_b  h ²  ,   ω _c=Ω_c  h ²  , ¹ from an analysis of CMB anisotropies alone. The principal-component analysis agrees well with a maximum-likelihood analysis of the observations, identifying the main degeneracy directions and providing an impression of the effective dimensionality of the parameter space.     

Observational biases in Lagrangian reconstructions of cosmic velocity fields

Lagrangian reconstruction of large-scale peculiar velocity fields can be strongly affected by observational biases. We develop a thorough analysis of these systematic effects by relying on specially selected mock catalogues. For the purpose of this paper, we use the Monge–Ampère–Kantorovitch (MAK) reconstruction method, although any other Lagrangian reconstruction method should be sensitive to the same problems. We extensively study the uncertainty in the mass-to-light assignment due to incompleteness (missing luminous mass tracers), and the poorly determined relation between mass and luminosity. The impact of redshift distortion corrections is analysed in the context of MAK and we check the importance of edge and finite-volume effects on the reconstructed velocities. Using three mock catalogues with different average densities, we also study the effect of cosmic variance. In particular, one of them presents the same global features as found in observational catalogues that extend to 80 h ⁻¹ Mpc scales. We give recipes, checked using the aforementioned mock catalogues, to handle these particular observational effects, after having introduced them into the mock catalogues so as to quantitatively mimic the most densely sampled currently available galaxy catalogue of the nearby Universe. Once biases have been taken care of, the typical resulting error in reconstructed velocities is typically about a quarter of the overall velocity dispersion, and without significant bias. We finally model our reconstruction errors to propose an improved Bayesian approach to measure Ω_m in an unbiased way by comparing the reconstructed velocities to the measured ones in distance space, even though they may be plagued by large errors. We show that, in the context of observational data, it is possible to build a nearly unbiased estimator of Ω_m using MAK reconstruction.     

The dark matter distribution in disc galaxies

We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ ₀∼1–4×10⁻²⁴ g cm⁻³) and core radii ( r ₀∼5–15 kpc) scaling as ρ ₀∝ r ₀^−2/3.