Enhanced Black-Hole Mergers in Binary-Binary Interactions

Understand

We study the orbital evolution of black hole (BH) binaries in quadruple systems, where the tertiary binary excites large eccentricity in the BH binary through Lidov-Kozai (LK) oscillations, causing the binary BHs to merge via gravitational radiation.

• For typical BH binaries with masses $m_{1,2}\simeq 20M_\odot-30M_\odot$ and initial semimajor axis $a_0\sim100$ AU (such that the binaries have no chance of merging by themselves within $\sim10^{10}$ yrs), we show that binary-binary interactions can significantly increase the LK window for mergers (the range of companion inclinations that allows the BH binary to merge within 10~Gyrs).
• This increase arises from a secular resonance between the LK oscillation of the BH binary and the nodal precession of the outer (binary-binary) orbit driven by the tertiary binary.
• Therefore, in the presence of tertiary binary, the BH merger fraction is increased to $10-30\%$, an order of magnitude larger than the merger fraction found in similar triple systems.