Cosmic Web Reconstruction through Density Ridges: Method and Algorithm

TL;DR

This paper introduces a method using the SCMS algorithm to detect cosmic web filaments as density ridges, with bootstrap-based uncertainty estimates, applied to galaxy survey data and validated against galaxy clusters.

Contribution

It presents a novel application of the SCMS algorithm for filament detection in cosmology, including uncertainty quantification, improving inference about the cosmic web structure.

Findings

SCMS effectively detects filaments in galaxy data.

Uncertainty bands can be reliably estimated using bootstrap methods.

Filaments are significantly closer to galaxy clusters than random points.

Abstract

The detection and characterization of filamentary structures in the cosmic web allows cosmologists to constrain parameters that dictates the evolution of the Universe. While many filament estimators have been proposed, they generally lack estimates of uncertainty, reducing their inferential power. In this paper, we demonstrate how one may apply the Subspace Constrained Mean Shift (SCMS) algorithm (Ozertem and Erdogmus (2011); Genovese et al. (2012)) to uncover filamentary structure in galaxy data. The SCMS algorithm is a gradient ascent method that models filaments as density ridges, one-dimensional smooth curves that trace high-density regions within the point cloud. We also demonstrate how augmenting the SCMS algorithm with bootstrap-based methods of uncertainty estimation allows one to place uncertainty bands around putative filaments. We apply the SCMS method to datasets sampled from the P3M N-body simulation, with galaxy number densities consistent with SDSS and WFIRST-AFTA and to LOWZ and CMASS data from the Baryon Oscillation Spectroscopic Survey (BOSS). To further assess the efficacy of SCMS, we compare the relative locations of BOSS filaments with galaxy clusters in the redMaPPer catalog, and find that redMaPPer clusters are significantly closer (with p-values $< 10^{-9}$) to SCMS-detected filaments than to randomly selected galaxies.