The Coarse Geometry of Merger Trees in \Lambda CDM

TL;DR

This paper introduces the contour process to analyze the geometry of merger trees in DM cosmology, revealing scale-dependent properties and differences between simulated and Markovian trees.

Contribution

It presents a novel contour process method to characterize merger tree geometry and compares properties across different data sources and models.

Findings

Contour walk length correlates with progenitor count.

A transitional mass scale around 3 0^{12} h^{-1} M_sol is identified.

Markovian trees show larger scatter in properties compared to Millennium Run trees.

Abstract

We introduce the contour process to describe the geometrical properties of merger trees. The contour process produces a one-dimensional object, the contour walk, which is a translation of the merger tree. We portray the contour walk through its length and action. The length is proportional to to the number of progenitors in the tree, and the action can be interpreted as a proxy of the mean length of a branch in a merger tree. We obtain the contour walk for merger trees extracted from the public database of the Millennium Run and also for merger trees constructed with a public Monte-Carlo code which implements a Markovian algorithm. The trees correspond to halos of final masses between 10^{11} h^{-1} M_sol and 10^{14} h^{-1} M_sol. We study how the length and action of the walks evolve with the mass of the final halo. In all the cases, except for the action measured from Markovian trees, we find a transitional scale around 3 \times 10^{12} h^{-1} M_sol. As a general trend the length and action measured from the Markovian trees show a large scatter in comparison with the case of the Millennium Run trees.