# Black hole mergers from quadruples

## TL;DR

This study uses high-precision simulations to analyze black hole mergers in quadruple systems, revealing higher merger fractions and significant eccentricities that could impact gravitational wave observations.

## Contribution

It provides the first systematic statistical analysis of quadruple black hole systems, highlighting their potential importance in gravitational wave event rates.

## Key findings

- Quadruple systems have a higher merger fraction than triples.
- Merging black holes in quadruples often have high eccentricities in the LIGO band.
- Quadruples could contribute significantly to observed gravitational wave events.

## Abstract

With the hundreds of merging binary black hole (BH) signals expected to be detected by LIGO/Virgo, LISA and other instruments in the next few years, the modeling of astrophysical channels that lead to the formation of compact-object binaries has become of fundamental importance. In this paper, we carry out a systematic statistical study of quadruple BHs consisting of two binaries in orbit around their center of mass, by means of high-precision direct $N$-body simulations including Post-Newtonian (PN) terms up to 2.5PN order. We found that most merging systems have high initial inclinations and the distributions peak at $\sim 90^\circ$ as for triples, but with a more prominent broad distribution tail. We show that BHs merging through this channel have a significant eccentricity in the LIGO band, typically much larger than BHs merging in isolated binaries and in binaries ejected from star clusters, but comparable to that of merging binaries formed via the GW capture scenario in clusters, mergers in hierarchical triples, or BH binaries orbiting intermediate-mass black holes in star clusters. We show that the merger fraction can be up to $\sim 3$--$4\times$ higher for quadruples than for triples. Thus even if the number of quadruples is $20\%$--$25\%$ of the number of triples, the quadruple scenario can represent an important contribution to the events observed by LIGO/VIRGO.