Constraining stellar-mass black hole mergers in AGN disks detectable with LIGO

Black hole (BH) mergers detectable with the Laser Interferometer Gravitational-wave Observatory (LIGO) can occur in active galactic nucleus (AGN) disks. Here we parameterize the merger rates, the mass spectrum, and the spin spectrum of BHs in AGN disks. The predicted merger rate spans ∼10−3–104 Gpc−1 yr−1, so upper limits from LIGO (<212 Gpc−1 yr−1) already constrain it. The predicted mass spectrum has the form of a broken power law, consisting of a pre-existing BH power-law mass spectrum and a harder power-law mass spectrum resulting from mergers. The predicted spin spectrum is multipeaked with the evolution of retrograde spin BHs in the gas disk playing a key role. We outline the large uncertainties in each of these LIGO observables for this channel and we discuss ways in which they can be constrained in the future.