# Effects of the merger history on the merger rate density of primordial black hole binaries

## TL;DR

This paper introduces a formalism to compute the merger rate density of primordial black hole binaries considering their merger history, highlighting how different mass functions influence the dominance of single or multiple merger events.

## Contribution

It presents a novel formalism for calculating merger rate density of primordial black holes with various mass functions, incorporating merger history effects.

## Key findings

- Monochromatic mass function dominated by single-merger events.
- Power-law and log-normal mass functions show significant multiple-merger contributions.
- Merger history effects vary depending on the black hole mass function.

## Abstract

We develop a formalism to calculate the merger rate density of primordial black hole binaries with a general mass function, by taking into account the merger history of primordial black holes. We apply the formalism to three specific mass functions, monochromatic, power-law and log-normal cases. In the former case, the merger rate density is dominated by the single-merger events, while in the latter two cases, the contribution of the multiple-merger events on the merger rate density can not be ignored. The effects of the merger history on the merger rate density depend on the mass function.