Identifying intermediate mass binary black hole mergers in AGN disks using LISA

We show that Laser Interferometer Space Antenna can uniquely identify the sites of intermediate-mass binary black hole (IMBBH) mergers if they occur in active galactic nuclei (AGN) disks with a gas density $\ensuremath{\rho}\ensuremath{\ge}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{g}/\mathrm{cc}$ via measurement of dynamical friction effect in the gravitational waveform. We find that even a single observation of a gravitational wave source with a total mass of ${10}^{3}{M}_{\ensuremath{\bigodot}}$ and a mass ratio of 2 at a luminosity distance of 3 Gpc is sufficient to confidently associate the merger to be in an AGN disk with a density $\ensuremath{\sim}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{g}/\mathrm{cc}$, as it allows estimation of the density with an error bar $\mathcal{O}(100%)$. This provides a new way of inferring AGN disk densities that complement traditional x-ray observations. Further, we find that neglecting the presence of environmental effects in the waveform models used for parameter estimation can bias the chirp mass, mass ratio, and arrival time of a merger. If not corrected, this can significantly impact our ability to carry out multiband data analysis of IMBBHs that combines information from LISA and ground-based gravitational wave detectors.