Self-Consistent Theory of Halo Mergers - II: CDM Power Spectra

TL;DR

This paper refines the parameters of a dark matter halo merger rate model using Smoluchowski's coagulation equation, ensuring mass conservation and improving the match to observed halo mass functions.

Contribution

It constrains the merger rate parameters through coagulation equations, demonstrating the limitations and applicability of the model for dark matter halo evolution.

Findings

Constraints form a degenerate plane in parameter space.

The model better matches the evolution of massive halo mass functions.

Current solutions are sufficiently accurate for most applications.

Abstract

We place additional constraints on the three parameters of the dark matter halo merger rate function recently proposed by Parkinson, Cole & Helly by utilizing Smoluchowski's coagulation equation, which must be obeyed by any binary merging process which conserves mass. We find that the constraints from Smoluchowski's equation are degenerate, limiting to a thin plane in the three dimensional parameter space. This constraint is consistent with those obtained from fitting to N-body measures of progenitor mass functions, and provides a better match to the evolution of the overall dark matter halo mass function, particularly for the most massive halos. We demonstrate that the proposed merger rate function does not permit an exact solution of Smoluchowski's equation and, therefore, the choice of parameters must reflect a compromise between fitting various parts of the mass function. The techniques described herein are applicable to more general merger rate functions, which may permit a more accurate solution of Smoluchowski's equation. The current merger rate solutions are most probably sufficiently accurate for the vast majority of applications.