Merging Black Holes in the Low-mass and High-mass Gaps from 2 + 2 Quadruple Systems

The origin of the black hole (BH) binary mergers observed by LIGO-Virgo is still uncertain, as are the boundaries of the stellar BH mass function. Stellar evolution models predict a dearth of BHs both at masses ≳50 $M_{\odot }$ and ≲5 $M_{\odot }$, thus leaving low- and high-mass gaps in the BH mass function. A natural way to form BHs of these masses is through mergers of neutron stars (NSs; for the low-mass gap) or lower-mass BHs (for the high-mass gap); the low- or high-mass-gap BH produced as a merger product can then be detected by LIGO-Virgo if it merges again with a new companion. We show that the evolution of a 2 + 2 quadruple system can naturally lead to BH mergers with component masses in the low- or high-mass gaps. In our scenario, the BH in the mass gap originates from the merger of two NSs, or two BHs, in one of the two binaries and the merger product is imparted a recoil kick (from anisotropic gravitational wave emission), which triggers its interaction with the other binary component of the quadruple system. The outcome of this three-body interaction is usually a new eccentric compact binary containing the BH in the mass gap, which can then merge again. The merger rate is ∼10⁻⁷–10⁻² Gpc⁻³ yr⁻¹ and ∼10⁻³–10⁻² Gpc⁻³ yr⁻¹ for BHs in the low-mass and high-mass gap, respectively. As the sensitivity of gravitational wave detectors improves, tighter constraints will soon be placed on the stellar BH mass function.