Self-Similar Mass Accretion History in Scale-Free Simulations

TL;DR

This study examines the self-similarity of halo mass accretion histories in scale-free simulations, demonstrating that with sufficient evolution, these histories converge to self-similarity with high accuracy even with few particles, and comparing two halo finders.

Contribution

It provides a detailed comparison of halo finders in scale-free simulations, showing how self-similarity convergence depends on the halo finder and simulation evolution.

Findings

ROCKSTAR shows superior self-similarity convergence compared to COMPASO.

Convergence to self-similarity improves with simulation evolution.

Few particles are needed for high-accuracy convergence after sufficient evolution.

Abstract

Using a scale-free $N$-body simulation generated with the ABACUS $N$-body code, we test the robustness of halo mass accretion histories via their convergence to self-similarity. We compare two halo finders, ROCKSTAR and COMPASO. We find superior self-similarity in halo mass accretion histories determined using ROCKSTAR, with convergence to 5% or better between $\sim10^2$ to $10^5$ particles. For COMPASO we find weaker convergence over a similar region, with at least 10% between $\sim10^2$ to $10^4$ particles. Furthermore, we find the convergence to self-similarity improves as the simulation evolves, with the largest and deepest regions of convergence appearing after the scale factor quadrupled from the time at which non-linear structures begin to form. With sufficient time evolution, halo mass accretion histories are converged to self-similarity within 5% with as few as $\sim70$ particles for COMPASO and within 2% for as few as $\sim30$ particles for ROCKSTAR.