HIERARCHIES IN THE LARGE-SCALE STRUCTURES OF THE UNIVERSE

2006 ◽  
Vol 15 (08) ◽  
pp. 1199-1215
Author(s):  
T. GOLDMAN ◽  
JUAN PÉREZ-MERCADER
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Matter Density ◽  
Density Fluctuations ◽  
Mass Hierarchy ◽  
Maximal Correlation ◽  
Order Of Magnitude ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Universe

We study the common relationships that exist between the various structures in the Universe, and show that a unifying description appears when these are considered as emerging from dynamical critical phenomena characterized by complex exponents in the two-point correlation function of matter density fluctuations. Since gravity drives their formation, structures are more likely to form where there is maximal correlation in the matter density. Applying this simple principle of maximal correlation to the two-point correlation function in a scaling regime with complex exponents leads to a hierarchy of structures where: (1) the structures can be classified according to an integer and (2) there is a common real exponent for the two-point correlation function across the range of structures. This in turn implies the existence of both universal size and mass hierarchy-order relationships. We show that these relationships are in good agreement with observations, and that sizes and masses for the known structures, from Globules in the Interstellar Medium to Clusters of Galaxies, can be classified (essentially to within one order of magnitude out of more than 10 orders of magnitude) in terms of just three constants.

scholarly journals The Anglo-Australian Redshift Survey

1983 ◽  
Vol 104 ◽  
pp. 175-175
Author(s):  
J. Bean ◽  
G. Efstathiou ◽  
R. S. Ellis ◽  
B. A. Peterson ◽  
T. Shanks ◽  
...  
Keyword(s):  
Correlation Function ◽  
Luminosity Function ◽  
Large Scale ◽  
Peculiar Velocities ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Density Inhomogeneities ◽  
The Universe

The aim of the survey is to sample a relatively large, randomly chosen volume of the Universe in order to study the large-scale distribution of galaxies using the two-point correlation function, the peculiar velocities between galaxy pairs and to provide an estimate of the galaxian luminosity function that is unaffected by density inhomogeneities and Virgo infall.

scholarly journals UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

2019 ◽  
Vol 487 (4) ◽  
pp. 5346-5362 ◽  
Author(s):  
Suk Sien Tie ◽  
David H Weinberg ◽  
Paul Martini ◽  
Wei Zhu ◽  
Sébastien Peirani ◽  
...  
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Mass Density ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Density Fluctuations ◽  
Data Sets ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h−1 Mpc)3 Horizon hydrodynamic simulation to a (1 h−1 Gpc)3N-body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving nq ≈ 10−5h3 Mpc−3 placed either in massive haloes or randomly. On scales of 10–30 h−1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ123/(ξ12ξ13 + ξ12ξ23 + ξ13ξ23) ≈ −4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h−1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q. For λ = 100 or 50 h−1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ −3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1–2.6. At r = 10 and 20 h−1 Mpc, we predict a signal-to-noise ratio (SNR) of ∼9 and ∼7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ∼37 and ∼25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h−1 Mpc the predicted SNR is lower by a factor of ∼3–5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.

scholarly journals Spatial correlations of extended cosmological structures

2020 ◽  
Vol 494 (3) ◽  
pp. 3227-3234
Author(s):  
V Santucho ◽  
H E Luparello ◽  
M Lares ◽  
D G Lambas ◽  
A N Ruiz ◽  
...  
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Relative Distribution ◽  
Spatial Correlations ◽  
Large Scale Structures ◽  
Large Structures ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Cosmic Voids ◽  
The Universe

ABSTRACT Studies of large-scale structures in the Universe, such as superstructures or cosmic voids, have been widely used to characterize the properties of the cosmic web through statistical analyses. On the other hand, the two-point correlation function of large-scale tracers such as galaxies or haloes provides a reliable statistical measure. However, this function applies to the spatial distribution of point-like objects, and therefore it is not appropriate for extended large structures that strongly depart from spherical symmetry. Here we present an analysis based on the standard correlation function formalism that can be applied to extended objects exhibiting arbitrary shapes. Following this approach, we compute the probability excess Ξ of having spheres sharing parts of cosmic structures with respect to a realization corresponding to a distribution of the same structures in random positions. For this aim, we identify superstructures defined as future virialized structures (FVSs) in semi-analytic galaxies in the MPDL2 MultiDark simulation. We have also identified cosmic voids to provide a joint study of their relative distribution with respect to the superstructures. Our analysis suggests that Ξ provides useful characterizations of the large-scale distribution, as suggested from an analysis of subsets of the simulation. Even when superstructure properties may exhibit negligible variations across the subsets, Ξ has the sensitivity to statistically distinguish sub-boxes that depart from the mean at larger scales. Thus, our methods can be applied in analysis of future surveys to provide characterizations of large-scale structure suitable to distinguish different theoretical scenarios.

scholarly journals Large-Scale Structure in the Durham/Ukst Galaxy Redshift Survey

1994 ◽  
Vol 161 ◽  
pp. 693-697
Author(s):  
A. Broadbent ◽  
T. Shanks ◽  
F.G. Watson ◽  
Q.A. Parker ◽  
R. Fong ◽  
...  
Keyword(s):  
Correlation Function ◽  
Statistical Analysis ◽  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Galaxy Redshift ◽  
The Universe

We report on the progress of the compilation and analysis of the Durham/UKST galaxy redshift survey. This survey will probe a large contiguous volume of space within a 1500 sq. deg. area of sky around the SGP. It will contain redshifts of ∼ 4000 galaxies of bJ < 17m providing detailed information about the structure of the Universe on large scales. Large features on scales of ∼ 100h−1 Mpc are clearly visible on examination of the completed section of the survey, although a statistical analysis of the survey by means of the two-point correlation function is close to zero on scales of r > 10h−1 Mpc.

scholarly journals One- and two-point source statistics from the LOFAR Two-metre Sky Survey first data release

2020 ◽  
Vol 643 ◽  
pp. A100
Author(s):  
T. M. Siewert ◽  
C. Hale ◽  
N. Bhardwaj ◽  
M. Biermann ◽  
D. J. Bacon ◽  
...  
Keyword(s):  
Point Source ◽  
Flux Density ◽  
Large Scale ◽  
Value Added ◽  
Radio Sources ◽  
Sky Survey ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Universe ◽  
Density Threshold

Context. The LOFAR Two-metre Sky Survey (LoTSS) will eventually map the complete Northern sky and provide an excellent opportunity to study the distribution and evolution of the large-scale structure of the Universe. Aims. We test the quality of LoTSS observations through a statistical comparison of the LoTSS first data release (DR1) catalogues to expectations from the established cosmological model of a statistically isotropic and homogeneous Universe. Methods. We study the point-source completeness and define several quality cuts, in order to determine the count-in-cell statistics and differential source count statistics, and measure the angular two-point correlation function. We use the photometric redshift estimates, which are available for about half of the LoTSS-DR1 radio sources, to compare the clustering throughout the history of the Universe. Results. For the masked LoTSS-DR1 value-added source catalogue, we find a point-source completeness of 99% above flux densities of 0.8 mJy. The counts-in-cell statistic reveals that the distribution of radio sources cannot be described by a spatial Poisson process. Instead, a good fit is provided by a compound Poisson distribution. The differential source counts are in good agreement with previous findings in deep fields at low radio frequencies and with simulated catalogues from the SKA Design Study and the Tiered Radio Extragalactic Continuum Simulation. Restricting the value added source catalogue to low-noise regions and applying a flux density threshold of 2 mJy provides our most reliable estimate of the angular two-point correlation. Based on the distribution of photometric redshifts and the Planck 2018 best-fit cosmological model, the theoretically predicted angular two-point correlation between 0.1 deg and 6 deg agrees reasonably well with the measured clustering for the sub-sample of radio sources with redshift information. Conclusions. The deviation from a Poissonian distribution might be a consequence of the multi-component nature of a large number of resolved radio sources and/or of uncertainties on the flux density calibration. The angular two-point correlation function is < 10−2 at angular scales > 1 deg and up to the largest scales probed. At a 2 mJy flux density threshold and at a pivot angle of 1 deg, we find a clustering amplitude of A = (5.1 ± 0.6) × 10−3 with a slope parameter of γ = 0.74 ± 0.16. For smaller flux density thresholds, systematic issues are identified, which are most likely related to the flux density calibration of the individual pointings. We conclude that we find agreement with the expectation of large-scale statistical isotropy of the radio sky at the per cent level. The angular two-point correlation agrees well with the expectation of the cosmological standard model.

scholarly journals The large-scale three-point correlation function of the SDSS BOSS DR12 CMASS galaxies

2017 ◽  
Vol 468 (1) ◽  
pp. 1070-1083 ◽  
Author(s):  
Zachary Slepian ◽  
Daniel J. Eisenstein ◽  
Florian Beutler ◽  
Chia-Hsun Chuang ◽  
Antonio J. Cuesta ◽  
...  
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Point Correlation ◽  
Point Correlation Function

TYPICAL SCALES IN THE CLUSTERING OF THE UNIVERSE

1995 ◽  
Vol 04 (04) ◽  
pp. 417-428
Author(s):  
LI-ZHI FANG ◽  
ZU-GAN DENG ◽  
XIAO-YANG XIA
Keyword(s):  
Correlation Function ◽  
Clusters Of Galaxies ◽  
High Confidence ◽  
Scale Free ◽  
Density Perturbations ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Periodic Components ◽  
The Universe ◽  
Characteristic Scales

The cosmic density perturbations are not completely scale-free, i.e. preferential scales should exist in the clustering of the universe. Observations do show the existence of the typical scales, namely, the distribution of various objects cannot be described by a simple fractal law. However, the standard two-point correlation function statistic is ineffective in detecting the typical scales. A better method based on identifying the periodic components in two-point correlation functions was developed. Using this method, the typical scales have been systematically searched for in samples of galaxies, clusters of galaxies, quasars and absorption lines of quasars. It showed the existence of typical scales in the range of 20–130 h−1 Mpc with high confidence. In particular, two typical scales, 60−1 Mpc and 130−1 Mpc, have been detected in all the samples being analysed. Such “universal” scales are probably the characteristic scales in the primordial fluctuations of the universe. Other theoretical implications of the detected typical scales have also been reviewed.

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