# Halo concentrations from extended Press-Schechter merger histories

## TL;DR

This paper investigates the relationship between dark matter halo concentrations and their formation histories using merger trees from excursion set theory, identifying missing environmental effects and proposing modifications to improve scatter predictions.

## Contribution

It demonstrates that incorporating environmental dependence into excursion set merger trees enhances the accuracy of halo concentration scatter predictions.

## Key findings

- Model predicts median concentration-mass relation accurately.
- Environmental dependence increases scatter in concentration predictions.
- Modified merger trees show correct correlation between environment and formation epoch.

## Abstract

We apply the model relating halo concentration to formation history proposed by Ludlow et al. to merger trees generated using an algorithm based on excursion set theory. We find that while the model correctly predicts the median relation between halo concentration and mass, it underpredicts the scatter in concentration at fixed mass. Since the same model applied to N-body merger trees predicts the correct scatter, we postulate that the missing scatter is due to the lack of any environmental dependence in merger trees derived from excursion set theory. We show that a simple modification to the merger tree construction algorithm, which makes merger rates dependent on environment, can increase the scatter by the required amount, and simultaneously provide a qualitatively correct correlation between environment and formation epoch in the excursion set merger trees.