[Paper Review] Large SDSS quasar groups and their statistical significance

Changbom Park, Hyunmi Song+3 more|arXiv (Cornell University)|Feb 12, 2015

Galaxies: Formation, Evolution, Phenomena6 references4 citations

TL;DR

This study analyzes large-scale quasar groups in the SDSS DR7 catalog using the Friends-of-Friends (FoF) algorithm with varying linking lengths (LL), finding that the statistically largest quasar group reported by Clowes et al. (U1.27) is not significantly different from random point distributions. At LL = 70 h⁻¹ Mpc, observed quasar groups match random catalogs in size (92.4% probability) and richness (58.1% probability), suggesting U1.27 is likely a chance alignment rather than a physically coherent structure.

ABSTRACT

We use a volume-limited sample of quasars in the Sloan Digital Sky Survey (SDSS) DR7 quasar catalog to identify quasar groups and address their statistical significance. This quasar sample has a uniform selection function on the sky and nearly a maximum possible contiguous volume that can be drawn from the DR7 catalog. Quasar groups are identified by using the Friend-of-Friend algorithm with a set of fixed comoving linking lengths. We find that the richness distribution of the richest 100 quasar groups or the size distribution of the largest 100 groups are statistically equivalent with those of randomly-distributed points with the same number density and sky coverage when groups are identified with the linking length of 70 h-1Mpc. It is shown that the large-scale structures like the huge Large Quasar Group (U1.27) reported by Clowes et al. (2013) can be found with high probability even if quasars have no physical clustering, and does not challenge the initially homogeneous cosmological models. Our results are statistically more reliable than those of Nadathur (2013), where the test was made only for the largest quasar group. It is shown that the linking length should be smaller than 50 h-1Mpc in order for the quasar groups identified in the DR7 catalog not to be dominated by associations of quasars grouped by chance. We present 20 richest quasar groups identified with the linking length of 70 h-1Mpc for further analyses.

Motivation & Objective

• To rigorously assess the statistical significance of the large quasar group U1.27 reported by Clowes et al. (2013), which claims to be the largest known structure in the universe.
• To investigate whether the observed quasar group properties—size and richness—are consistent with random point distributions or indicate physical clustering.
• To determine the critical linking length (LL) that separates physically clustered quasar systems from chance associations in the SDSS DR7 quasar catalog.
• To challenge the cosmological interpretation of extreme large-scale structures by testing their significance against null models of homogeneous Poisson processes.
• To advocate for statistically robust methods in identifying large-scale structures, especially given the sensitivity of group properties to linking length and low quasar number density.

Proposed method

• Uses a volume-limited, spectroscopically confirmed quasar sample from the SDSS DR7 catalog with M_i ≤ -22.0 and redshift range 0.03 ≤ z ≤ 3.5.
• Applies the Friends-of-Friends (FoF) algorithm to identify quasar groups using a range of linking lengths (LL) from 10 to 100 h⁻¹ Mpc.
• Compares the observed quasar group size and richness distributions with those from 1000 randomized point catalogs with the same number density and sky coverage.
• Calculates the probability of observing groups as large or richer than U1.27 in random catalogs to assess statistical significance.
• Identifies the critical LL (≤50 h⁻¹ Mpc) at which quasar groups are dominated by physically clustered systems rather than chance associations.
• Uses mock catalogs from simulated homogeneous universes to compare observed structures with null models of random clustering.

Experimental results

Research questions

• RQ1 Is the large quasar group U1.27, with a size of ~870 h⁻¹ Mpc and 73 quasars, statistically significant or likely a chance alignment?
• RQ2 What is the critical linking length (LL) that ensures quasar groups are physically clustered rather than artifacts of the FoF algorithm?
• RQ3 How do the size and richness distributions of observed quasar groups compare to those expected from random point processes with the same density?
• RQ4 To what extent do the observed properties of large quasar groups depend on the choice of linking length in the FoF algorithm?
• RQ5 Can the existence of structures as large as U1.27 be explained within the standard ΛCDM model without violating the Cosmological Principle?

Key findings

• At a linking length of 70 h⁻¹ Mpc, the probability of finding a quasar group as large as U1.27 in a random catalog is 92.4%, indicating no statistical significance.
• The probability of finding a quasar group richer than U1.27 (73 members) in a random catalog is 58.1%, further suggesting it is not a rare physical structure.
• The observed quasar group with the largest size and richness in the SDSS DR7 catalog is not significantly different from random distributions at LL = 70 h⁻¹ Mpc.
• Quasar groups identified with LL ≤ 50 h⁻¹ Mpc are statistically dominated by physically clustered systems, indicating this threshold separates physical clustering from chance associations.
• The U1.27 quasar group is best interpreted as a chain of smaller, physically clustered quasar systems connected by a very large linking length, not a single coherent structure.
• The study cautions against drawing cosmological conclusions from large-scale structures without rigorous statistical testing, especially given the sensitivity of group properties to linking length and low quasar density.