Estimating major merger rates and spin parameters ab initio via the clustering of critical events

TL;DR

This paper develops a first-principles model to predict major merger properties and spin parameters of cosmic structures by analyzing the clustering of critical points in the initial density field, validated with extensive simulations.

Contribution

It introduces a novel theoretical framework linking initial density peaks and saddle points to merger outcomes, incorporating topological connectivity across multiple scales.

Findings

Major mergers peak at three times the smoothing scale in Lagrangian space.

Halos typically experience two major mergers per decade of mass growth.

Mergers contribute a spin of a few tens of percent to the halos.

Abstract

We build a model to predict from first principles the properties of major mergers. We predict these from the coalescence of peaks and saddle points in the vicinity of a given larger peak, as one increases the smoothing scale in the initial linear density field as a proxy for cosmic time. To refine our results, we also ensure, using a suite of $\sim 400$ power-law Gaussian random fields smoothed at $\sim 30$ different scales, that the relevant peaks and saddles are topologically connected: they should belong to a persistent pair before coalescence. Our model allows us to (a) compute the probability distribution function of the satellite-merger separation in Lagrangian space: they peak at three times the smoothing scale; (b) predict the distribution of the number of mergers as a function of peak rarity: haloes typically undergo two major mergers ($>$1:10) per decade of mass growth; (c) recover that the typical spin brought by mergers: it is of the order of a few tens of percent.