[Paper Review] Testing statistical significance of large quasar groups with sheets model of large scale structure

Sergey Pilipenko, Alexander Malinovsky|arXiv (Cornell University)|Jun 17, 2013

Geochemistry and Geologic Mapping3 citations

TL;DR

This paper tests the statistical significance of the large quasar group U1.27, claiming it is not significantly different from random fluctuations in a Poisson-distributed quasar field. Using minimal spanning tree (MST) and convex hull methods on SDSS DR7 and DR8 data, the authors find a 1.4% probability (2.45σ) of such a group arising by chance, with model-based simulations showing that percolation through sheet-like large-scale structure can mimic extreme clustering without implying cosmological significance.

ABSTRACT

We argue that the largest group of quasars (LQG) U1.27 discovered by Clowes et al. (2013) in the SDSS DR7 catalogue does not contradict the hypothesis of Poisson distribution of quasars. We found that random catalogues with the same shape and number of QSOs as the real sample may contain groups which resemble U1.27. By simulating quasar catalogues with embedded model of the large scale structure we also found that the size of LQGs selected by MST and similar methods does not correspond to the scale of homogeneity of the Universe and can be explained by the percolation process.

Motivation & Objective

• To test whether the large quasar group U1.27, reported as a 1240 Mpc structure, is statistically significant or a random fluctuation.
• To assess whether the observed clustering in U1.27 contradicts the scale of homogeneity in the ΛCDM model.
• To evaluate the robustness of MST-based clustering methods in detecting large-scale structures in sparse quasar surveys.
• To investigate whether the percolation effect in structured large-scale environments can mimic extreme clustering in random catalogues.
• To compare results between SDSS DR7 and DR8 quasar catalogues, accounting for redshift measurement differences.

Proposed method

• Applied the Minimal Spanning Tree (MST) method to identify quasar groups in SDSS DR7 and DR8 quasar catalogues using magnitude and redshift cuts (i ≤ 19.1, 0.8 < z < 1.9).
• Generated 10,000 random catalogues by preserving angular coordinates and assigning random redshifts to maintain constant number density, using a pseudorandom number generator.
• Used the Convex Hull of Member Spheres (CHMS) method to estimate group volumes and normalized them by mass (V_CHMS = 73V/M) for statistical comparison.
• Developed a sheet-based large-scale structure model inspired by Zel’dovich pancakes, with randomly oriented, distributed sheets of radius R, mean separation D, and Gaussian displacement q perpendicular to sheets.
• Simulated quasar catalogues with embedded sheet structures and compared the resulting LQG statistics to Poisson-distributed and real data.
• Computed percolation thresholds and compared the number of LQGs as a function of linking length between random and structured catalogues to detect systematic shifts indicating real structure.

Experimental results

Research questions

• RQ1 What is the statistical significance of the U1.27 quasar group when tested against random realizations of the SDSS DR7 quasar catalogue?
• RQ2 Does the observed size and mass of U1.27 exceed the scale of homogeneity predicted by the ΛCDM model?
• RQ3 To what extent do MST-based clustering algorithms detect artificial large-scale structures due to percolation through multiconnected large-scale structure?
• RQ4 How do redshift measurement differences between SDSS DR7 and DR8 affect the identification and significance of the U1.27 group?
• RQ5 Can a sheet-like large-scale structure model explain the emergence of extreme LQGs without requiring cosmologically significant over-densities?

Key findings

• The probability of finding a group as large and massive as U1.27 in a random catalogue is 1.4% (2.45σ), significantly lower than the 3.81σ claimed by Clowes et al. (2013).
• When accounting for a sheet-based large-scale structure model, the probability increases to 2.8% (2.2σ), still substantially below the original significance estimate.
• The U1.27 group's geometric and topological properties—such as 2L = 553 Mpc, L_trunk = 2390 Mpc, and V_CHMS = 1.02×10⁸ Mpc³—fall within 1–2σ of random cluster distributions.
• In the DR8 catalogue, no significant group matching U1.27 is found at the same linking length; the first comparable group appears only at ℓ = 101 Mpc, and it does not coincide with U1.27.
• Redshift differences between DR7 and DR8 lead to average distance shifts of ⟨Δr⟩ = -2.8 Mpc (σ = 6.6 Mpc), with individual shifts up to -20.8 Mpc, indicating high sensitivity to redshift measurement precision.
• For higher quasar number densities (n = 4×10⁻⁶ Mpc⁻³), the sheet model predicts LQGs with M > 700 and sizes >15D (>1275 Mpc) with significance >7σ, but these are artifacts of percolation, not cosmological homogeneity scales.