The role of energy in ballistic agglomeration

TL;DR

This paper investigates a ballistic agglomeration process influenced by energy dynamics, deriving simplified equations and asymptotic behaviors, with applications to dark matter clustering.

Contribution

It introduces a novel formalism linking particle energy to cluster densities, simplifying the analysis of ballistic agglomeration processes.

Findings

Derived asymptotic behaviors of cluster densities.

Reduced complex equations to standard Smoluchowski form.

Validated results through numerical simulations.

Abstract

We study a ballistic agglomeration process in the reaction-controlled limit. Cluster densities obey an infinite set of Smoluchowski rate equations, with rates dependent on the average particle energy. The latter is the same for all cluster species in the reaction-controlled limit and obeys an equation depending on densities. We express the average energy through the total cluster density that allows us to reduce the governing equations to the standard Smoluchowski equations. We derive basic asymptotic behaviors and verify them numerically. We also apply our formalism to the agglomeration of dark matter.