Characterizing the assembly of dark matter haloes with protohalo size histories: I. Redshift evolution, relation to descendant haloes, and halo assembly bias

Abstract

ABSTRACT We propose a novel method to quantify the assembly histories of dark matter haloes with the redshift evolution of the mass-weighted spatial variance of their progenitor haloes, that is, the protohalo size history. We find that the protohalo size history for each individual halo at z ∼ 0 can be described by a double power-law function. The amplitude of the fitting function strongly correlates to the central-to-total stellar mass ratios of descendant haloes. The variation of the amplitude of the protohalo size history can induce a strong halo assembly bias effect for massive haloes. This effect is detectable in observation using the central-to-total stellar mass ratio as a proxy of the protohalo size. The correlation to the descendant central-to-total stellar mass ratio and the halo assembly bias effect seen in the protohalo size are much stronger than that seen in the commonly adopted half-mass formation time derived from the mass accretion history. This indicates that the information loss caused by the compression of halo merger trees to mass accretion histories can be captured by the protohalo size history. Protohalo size thus provides a useful quantity to connect protoclusters across cosmic time and to link protoclusters with their descendant clusters in observations.