Gravitational-wave background from compact objects embedded in active galactic nuclei accretion disks

Abstract

We consider a model in which massive stars form in a self-gravitating accretion disk around an active galactic nucleus (AGN). These stars may evolve and collapse to form compact objects on a time scale shorter than the accretion time, thus producing an important family of sources for LISA. Assuming the compact object formation/inspiral rate is proportional to the steady-state gas accretion rate, we use the intrinsic hard x ray AGN luminosity function to estimate expected event rates and signal strengths. We find that these sources will produce a continuous low-frequency $(\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{mHz})$ background detectable by LISA if more than $\ensuremath{\sim}1%$ of the accreted matter is in the form of compact objects. For compact objects with masses $\ensuremath{\gtrsim}10{M}_{\ensuremath{\bigodot}}$, the last stages of the inspiral events should be resolvable above a few mHz, with rates as high as a few hundred per year.