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

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.

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The Anglo-Australian Redshift Survey

Symposium - International Astronomical Union ◽

10.1017/s0074180900038894 ◽

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.

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The Local Large-Scale Structure from HIPASS

Symposium - International Astronomical Union ◽

10.1017/s0074180900196639 ◽

2005 ◽

Vol 216 ◽

pp. 196-202

Author(s):

Martin Zwaan ◽

Martin Meyer ◽

Rachel Webster ◽

Lister Staveley-Smith

Keyword(s):

Large Scale ◽

Large Scale Structure ◽

Scale Structure ◽

Sky Survey ◽

The Galaxy ◽

Point Correlation ◽

Point Correlation Function ◽

Fisher Relation ◽

Galaxy Population ◽

Mass Functions

The HI Parkes All Sky Survey (HIPASS) offers a unique perspective on the galaxy population in the local universe. A catalogue of 4315 HI-selected galaxies has been extracted from the southern region of the survey (δ < +2°). This catalogue gives a clear view of the local large-scale structure and is used to study the two-point correlation function, the Tully-Fisher relation, and galaxy luminosity and mass functions. Some initial results are discussed here.

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THE LARGE-SCALE THREE-POINT CORRELATION FUNCTION OF SLOAN DIGITAL SKY SURVEY LUMINOUS RED GALAXIES

The Astrophysical Journal ◽

10.1088/0004-637x/737/2/97 ◽

2011 ◽

Vol 737 (2) ◽

pp. 97 ◽

Cited By ~ 46

Author(s):

Felipe Marín

Keyword(s):

Correlation Function ◽

Large Scale ◽

Sloan Digital Sky Survey ◽

Luminous Red Galaxies ◽

Sky Survey ◽

Point Correlation ◽

Point Correlation Function ◽

Red Galaxies

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General Superclustering

Highlights of Astronomy ◽

10.1017/s1539299600005980 ◽

1983 ◽

Vol 6 ◽

pp. 753-756

Author(s):

G.O. Abell

Keyword(s):

High Speed ◽

Large Scale ◽

Statistical Approach ◽

Clusters Of Galaxies ◽

National Geographic Society ◽

National Geographic ◽

Large Numbers ◽

Sky Survey ◽

Point Correlation ◽

Point Correlation Function

The distribution of rich clusters of galaxies revealed on the photographs taken for the National Geographic Society-Palomar Observatory Sky Survey shows a strong dumpiness on a scale of 100 Mpc (for H = 50 km s–1 Mpc–1), with vast intraclump regions apparently void of rich clusters (Abell 1958; 1961). Studies of the n-point correlation function by Peebles and his associates (e.g., Peebles 1980 and references therein) show that this large-scale dumpiness applies also to individual galaxies. Peebles’ statistical approach does not, of course, indicate individual superclusters or their structures; that kind of information awaited the breakthrough provided by the development of high-speed detectors, with which radial velocities of large numbers of galaxies can be obtained in reasonable observing times.

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Spatial correlations of extended cosmological structures

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa732 ◽

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.

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N-Body Simulation of Large Scale Structure in the Universe with Oscillating Scalar Field

Symposium - International Astronomical Union ◽

10.1017/s0074180900132693 ◽

1999 ◽

Vol 183 ◽

pp. 252-252

Author(s):

K. Kawabata ◽

H. Taguchi ◽

Y. Andoh

Keyword(s):

Scalar Field ◽

Large Scale ◽

Large Scale Structure ◽

Scale Structure ◽

Homogeneous Distribution ◽

Coupling Constant ◽

Mesh Method ◽

Point Correlation ◽

Point Correlation Function ◽

The Universe

Using the particle-mesh method with 1283 grids and 643 particles, we have carried out a number of N-body simulations of the large scale structure for the cosmological model proposed by Fukuyama et al.(1996): this model contains the matter(Ω0) as well as a scalar field(Φ) with a finite mass that couples non-minimally with the scalar curvature R through the form of 1/2ηΦ2R, where η(= −80) is the coupling constant.For simplicity, we have adopted the same values as those employed by Fukuyama et al.(1996) for all the parameters other than Ω0, fo which we have varied from 0.001 to 0.15. In performing our simulation, we further assume that only the density of matter ρ spatially fluctuates. The initial condition is created by perturbing the homogeneous distribution of the particles by means of the random Gaussian Harrison-Zeldovich spectrum.The two-point correlation function ξ(r) is then compputed for each of the resulting structures to compare with the observational data(Davis and Peebles, 1983). It is interesting to note that the structure formation appears to be achieved rather straightforwardly with the scalar field model. However, in order to yield an agreement between the theoretical and the observational two-point correlation functions, we seem to require the Ω0 value much larger than 0.01 adopted by Fukuyama et al.(1996).

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HIERARCHIES IN THE LARGE-SCALE STRUCTURES OF THE UNIVERSE

International Journal of Modern Physics D ◽

10.1142/s0218271806008905 ◽

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.

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

Symposium - International Astronomical Union ◽

10.1017/s0074180900048361 ◽

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.

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Building a digital twin of a luminous red galaxy spectroscopic survey: galaxy properties and clustering covariance

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab434 ◽

2021 ◽

Vol 503 (2) ◽

pp. 2318-2339 ◽

Cited By ~ 1

Author(s):

César Hernández-Aguayo ◽

Francisco Prada ◽

Carlton M Baugh ◽

Anatoly Klypin

Keyword(s):

Galaxy Formation ◽

Large Scale ◽

Linear Growth Rate ◽

Acoustic Oscillations ◽

Luminous Red Galaxies ◽

Point Correlation ◽

Point Correlation Function ◽

Red Galaxies ◽

Halo Occupation Distribution ◽

The Universe

ABSTRACT Upcoming surveys will use a variety of galaxy selections to map the large-scale structure of the Universe. It is important to make accurate predictions for the properties and clustering of such galaxies, including the errors on these statistics. Here, we describe a novel technique which uses the semi-analytical model of galaxy formation galform, embedded in the high-resolution N-body Planck-Millennium simulation, to populate a thousand halo catalogues generated using the Parallel-PM N-body glam code. Our hybrid scheme allows us to make clustering predictions on scales that cannot be modelled in the original N-body simulation. We focus on luminous red galaxies (LRGs) selected in the redshift range z = 0.6 − 1 from the galform output using similar colour-magnitude cuts in the r, z, and W1 bands to those that will be applied in the Dark Energy Spectroscopic Instrument (DESI) survey, and call this illustrative sample ‘DESI-like’ LRGs. We find that the LRG-halo connection is non-trivial, leading to the prediction of a non-standard halo occupation distribution; in particular, the occupation of central galaxies does not reach unity for the most massive haloes, and drops with increasing mass. The glam catalogues reproduce the abundance and clustering of the LRGs predicted by galform. We use the glam mocks to compute the covariance matrices for the two-point correlation function and power spectrum of the LRGs and their background dark matter density field, revealing important differences. We also make predictions for the linear-growth rate and the baryon acoustic oscillations distances at z = 0.6, 0.74, and 0.93. All ‘DESI-like’ LRG catalogues are made publicly available.

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