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Asymmetric emission of gravitational waves during mergers of black holes(BHs) produces a recoil kick, which can set a newly formed BH on a bound orbitaround the center of its host galaxy, or even completely eject it. To studythis population of recoiling BHs we extract properties of galaxies with mergingBHs from Illustris TNG300 simulation and then employ both analytical andnumerical techniques to model unresolved process of BH recoil.  This comparative analysis between analytical and numerical models shows that,on cosmological scales, numerically modeled recoiling BHs have a higher escapeprobability and predict a greater number of offset active galactic nuclei(AGN). BH escaped probability $>40~ \%$ is expected in 25 $\%$ of mergerremnants in numerical models, compared to 8$\%$ in analytical models. At thesame time, the predicted number of offset AGN at separations $>5$ kpc changesfrom 58 $\%$ for numerical models to 3 $\%$ for analytical models. Since BHejections in major merger remnants occur in non-virialized systems, staticanalytical models cannot provide an accurate description. Thus we argue thatnumerical models should be used to estimate the expected number density ofescaped BHs and offset AGN.

Statistical analysis of kicked black holes from TNG300 simulation