Were recently reported MHz events planet mass primordial black hole mergers?

TL;DR

This paper examines whether recent MHz gravitational wave events could be from planet-mass primordial black hole mergers, concluding it's highly unlikely, but such signals might be detectable in the future.

Contribution

It provides an analysis of the likelihood that MHz gravitational wave events originate from planet-mass primordial black hole mergers, offering insights into their detectability and implications for dark matter.

Findings

The probability of such an event occurring within the local volume per year is extremely low (~1 in 10^24).

The detected signals are unlikely due to planet-mass primordial black hole mergers.

Future detectors like DECIGO and BBO could observe the stochastic background of such black hole binaries.

Abstract

A bulk acoustic wave cavity as high frequency gravitational wave antenna has recently detected two rare events at $5.5$MHz. Assuming that the detected events are due to gravitational waves, their characteristic strain amplitude lies at about $h_c\approx 2.5 \times 10^{-16}$. While a cosmological signal is out of the picture due to the large energy carried by the high frequency waves, the signal could be due to the merging of two planet mass primordial black holes ($\approx 4\times 10^{-4} M_\odot$) inside the Oort cloud at roughly $0.025$ pc ($5300$ AU) away. In this short note, we show that the probability of one such event to occur within this volume per year is around $1:10^{24}$, if such Saturn-like mass primordial black holes are $1\%$ of the dark matter. Thus, the detected signal is very unlikely to be due the merger of planet mass primordial black holes. Nevertheless, the stochastic background of saturn mass primordial black holes binaries might be seen by next generation gravitational wave detectors, such as DECIGO and BBO.