Properties of Dark Matter Haloes and their Correlations: the Lesson from Principal Component Analysis

TL;DR

This study uses Principal Component Analysis to explore the relationships among dark matter halo properties, revealing that mass is less dominant than previously thought and that halo environment has limited influence at fixed mass.

Contribution

The paper applies PCA to identify key factors influencing dark matter halo properties, challenging assumptions about mass dominance and environmental effects in halo models.

Findings

Mass and concentration explain much of the variance.

Halo relaxedness is a significant factor.

Halo environment has limited impact at fixed mass.

Abstract

We study the correlations between the structural parameters of dark matter haloes using Principal Component Analysis (PCA). We consider a set of eight parameters, six of which are commonly used to characterize dark matter halo properties: mass, concentration, spin, shape, overdensity, and the angle ($\Phi_L$) between the major axis and the angular momentum vector. Two additional parameters ($\x_{off}$ and $\rho_{rms}$) are used to describe the degree of `relaxedness' of the halo. We find that we can account for much of the variance of these properties with halo mass and concentration, on the one hand, and halo relaxedness on the other. Nonetheless, three principle components are usually required to account for most of the variance. We argue that halo mass is not as dominant as expected, which is a challenge for halo occupation models and semi-analytic models that assume that mass determines other halo (and galaxy) properties. In addition, we find that the angle $\Phi_L$ is not significantly correlated with other halo parameters, which may present a difficulty for models in which galaxy disks are oriented in haloes in a particular way. Finally, at fixed mass, we find that a halo's environment (quantified by the large-scale overdensity) is relatively unimportant.