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

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.

9 pages, 7 figures; V2, references added, discussion added, title changed. v3, a new subsection added

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