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

Understand

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.