Estimating the galaxy two-point correlation function using a split random catalog

Keihänen, E.; Kurki-Suonio, H.; Lindholm, V.; Viitanen, A.; Suur-Uski, A.-S.; Allevato, V.; Branchini, E.; Marulli, F.; Norberg, Peder; Torre, S. de la; Väliviita, J.; Viel, Matteo; Bel, J.; Frailis, M.; Sánchez, Ariel G.

doi:10.1051/0004-6361/201935828

Cited by 29 publications

(25 citation statements)

References 47 publications

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“…The variance on the random sample counts depends on the number of points in the sample and, thus, we may ask what is the number of random points needed to achieve the same accuracy as in the analytical method. Keihänen et al (2019) showed that the relative variance on RR in a given bin is: (22) with N r the number of random points, and G p , G t terms are (Landy & Szalay 1993):…”

Section: Rr Countsmentioning

confidence: 99%

“…makes use of additional data-random pairs DR. To estimate the correlation function, we therefore need to compute the number of pairs as a function of the separation. To avoid introducing bias in the estimator and to minimise variance, the random catalogue must be much larger than the data catalogue (Landy & Szalay 1993;Keihänen et al 2019). We usually consider that taking at least about 20−50 times more random points than objects in the data is enough to avoid introducing additional variance (e.g., Samushia et al 2012;de la Torre et al 2013;Sánchez et al 2017;Bautista et al 2021).…”

Section: Introductionmentioning

confidence: 99%

“…Nonetheless, the complexity can be reduced, at best, to O(N) using appropriate algorithms and various efficient codes that implement them have been developed (e.g., Moore et al 2001;Jarvis et al 2004;Alonso 2012;Hearin et al 2017;Marulli et al 2016;Slepian & Eisenstein 2016;Sinha & Garrison 2020). For the random-random pairs calculation specifically, additional strategies can be used to speed up the computation beyond parallelisation, such as splitting the random sample and averaging the counts over subsamples (Keihänen et al 2019). Still, for large surveys, the computational time for estimating the correlation function, especially random-random pairs, can become an issue.…”

Section: Introductionmentioning

confidence: 99%

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Fast analytical calculation of the random pair counts for realistic survey geometry

Breton

Torre

2021

A&A

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Galaxy clustering is a standard cosmological probe that is commonly analysed through two-point statistics. In observations, the estimation of the two-point correlation function crucially relies on counting pairs in a random catalogue. The latter contains a large number of randomly distributed points, which accounts for the survey window function. Random pair counts can also be advantageously used for modelling the window function in the observed power spectrum. Since pair counting scales as 𝒪(N2), where N is the number of points, the computational time to measure random pair counts can be very expensive for large surveys. In this work, we present an alternative approach for estimating those counts that does not rely on the use of a random catalogue. We derived an analytical expression for the anisotropic random-random pair counts that accounts for the galaxy radial distance distribution, survey geometry, and possible galaxy weights. We show that a prerequisite is the estimation of the two-point correlation function of the angular selection function, which can be obtained efficiently using pixelated angular maps. Considering the cases of the VIPERS and SDSS-BOSS redshift surveys, we find that the analytical calculation is in excellent agreement with the pair counts obtained from random catalogues. The main advantage of this approach is that the primary calculation only takes a few minutes on a single CPU and it does not depend on the number of random points. Furthermore, it allows for an accuracy on the monopole equivalent to what we would otherwise obtain when using a random catalogue with about 1500 times more points than in the data at hand. We also describe and test an approximate expression for data-random pair counts that is less accurate than for random-random counts, but still provides subpercent accuracy on the monopole. The presented formalism should be very useful in accounting for the window function in next-generation surveys, which will necessitate accurate two-point window function estimates over huge observed cosmological volumes.

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Section: Rr Countsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast analytical calculation of the random pair counts for realistic survey geometry

Breton

Torre

2021

A&A

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“…While several estimators have been proposed to compute the 2PCF (e.g. Peebles & Hauser 1974;Hewett 1982;Davis & Peebles 1983;Landy & Szalay 1993;Hamilton 1993;Keihänen et al 2019), fewer studies have been performed so far for the 3PCF (e.g., Jing & Börner 1998;Szapudi & Szalay 1998;Sosa Nuñez & Niz 2020). Here we will exploit the widely used formulation proposed by Szapudi & Szalay (1998), that provides an unbiased and with minimal variance estimator based on the counting of triplets between the input catalog (that we will label as data catalog, D), and a corresponding random catalog (that we will label as R), constructed to reproduce the geometric distribution of the input catalog, but with zero clustering.…”

Section: Definitionsmentioning

confidence: 99%

C$^3$-Cluster Clustering Cosmology II. First detection of the BAO peak in the three-point correlation function of galaxy clusters

Moresco,

Veropalumbo,

Marulli

et al. 2020

Preprint

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Third-order statistics of the cosmic density field provides a powerful cosmological probe containing synergistic information to the more commonly explored second-order statistics. Here, we exploit a spectroscopic catalog of 72,563 clusters of galaxies extracted from the Sloan Digital Sky Survey, providing the first detection of the baryon acoustic oscillations (BAO) peak in the three-point correlation function (3PCF) of galaxy clusters. We measure and analyze both the connected and the reduced 3PCF of SDSS clusters from intermediate (r ∼ 10 Mpc/h) up to large (r ∼ 140 Mpc/h) scales, exploring a variety of different configurations. From the analysis of reduced 3PCF at intermediate scales, in combination with the analysis of the two-point correlation function, we constrain both the cluster linear and non-linear bias parameters, b 1 = 2.75 ± 0.03 and b 2 = 1.2 ± 0.5. We analyze the measurements of the 3PCF at larger scales, comparing them with theoretical models. The data show clear evidence of the BAO peak in different configurations, which appears more visible in the reduced 3PCF rather than in the connected one. From the comparison between theoretical models considering or not the BAO peak, we obtain a quantitative estimate of this evidence, with a ∆χ 2 between 2 and 75, depending on the considered configuration. Finally, we set up a generic framework to estimate the expected signal-to-noise ratio of the BAO peak in the 3PCF exploring different possible definitions, that can be used to forecast the most favorable configurations to be explored also in different future surveys, and applied it to the case of the Euclid mission.

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“…The random-random pair count RR(r) was found applying the random number generator ran2 by Press et al (1992), using one or two million particles. To speed up the calculation of random-random pairs we split random samples into 10 independent subsamples, as done also by Keihänen et al (2019).…”

Section: Calculation Of Correlation Functionsmentioning

confidence: 99%

Correlation function: biasing and fractal properties of the cosmic web

Einasto,

Hütsi,

Kuutma

et al. 2020

Preprint

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Aims. Our goal is to find how the spatial correlation function of galaxies describes the multifractal nature of the cosmic web. Methods. We calculate spatial correlation functions of galaxies, ξ(r), structure functions, g(r) = 1 + ξ(r), and fractal dimension functions, D(x) = 3 + γ(r) = 3 + d log g(r)/d log r, using dark matter particles of biased Λ cold dark matter (CDM) simulation, observed galaxies of the Sloan Digital Sky Survey (SDSS), and simulated galaxies of the Millennium and EAGLE simulations. We analyse how these functions describe fractal and other geometrical properties of the cosmic web. Results. Correlation functions of biased ΛCDM model samples describe at small distances (particle/galaxy separations), r ≤ 2.25 h −1 Mpc, the distribution of matter inside DM halos. In real and simulated galaxy samples only brightest galaxies in clusters are visible, and the transition from clusters to filaments occurs at distance r ≈ 0.8 − 1.5 h −1 Mpc. On larger separations correlation functions describe the distribution of matter and galaxies in the whole cosmic web. The effective fractal dimension of the cosmic web is a continuous function of the distance (separation). On small separations, r ≤ 2 h −1 Mpc, the fractal dimension decreases from D ≈ 1.5 to D ≈ 0, reflecting the distribution inside halos/clusters. The minimum of the fractal dimension function D(r) near r ≈ 2 is deeper for more luminous galaxies. On medium separations, 2 ≤ r ≤ 10 h −1 Mpc, the fractal dimension grows from ≈ 0 to ≈ 2, and approaches at large separations 3 (random distribution). Real and simulated galaxies of low luminosity, M r ≥ −19, have almost identical correlation lengths and amplitudes, indicating that dwarf galaxies are satellites of brighter galaxies, and do not form a smooth population in voids. Conclusions. Spatial correlation functions of galaxies contain valuable information on fractal dimension and other geometrical properties of the cosmic web.

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Estimating the galaxy two-point correlation function using a split random catalog

Cited by 29 publications

References 47 publications

Fast analytical calculation of the random pair counts for realistic survey geometry

Fast analytical calculation of the random pair counts for realistic survey geometry

C$^3$-Cluster Clustering Cosmology II. First detection of the BAO peak in the three-point correlation function of galaxy clusters

Correlation function: biasing and fractal properties of the cosmic web

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