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The Active Galatic Nuclei(AGN) disk has been proposed as a potential channelfor the merger of binary black holes. The population of massive stars and blackholes in AGN disks captured from the nuclei cluster plays a crucial role indetermining the efficiency of binary formation and final merger rate within theAGN disks. In this paper, we investigate the capture process using analyticaland numerical approaches. We discover a new constant integral of motion for oneobject's capture process. Applying this result to the whole population of thenuclei cluster captured by the AGN disk, we find that the population ofcaptured objects depends on the angular density and eccentricity distributionof the nuclei clusters and is effectively independent of the radial densityprofile of the nuclei cluster and disk models. An isotropic nuclei cluster withthermal eccentricity distribution predicts a captured profile $d N/d r \proptor^{-1/4}$. The captured objects are found to be dynamically crowded within thedisk. Direct binary formation right after the capture would be promising,especially for stars. The conventional migration traps that help pile up singleobjects in AGN disks for black hole mergers might not be required.

Stellar/BH Population in AGN Disks: Direct Binary Formation from Capture Objects in Nuclei Clusters