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As the universe evolves, gravity pulls small structures together to assemble larger structures (i.e. hierarchical growth). Within the numerical simulation, such “halos” are typically identified using a Friends-of-Friends (FoF) algorithm which detects gravitationally bound systems of particles and determines their properties (e.g. Davis et al. 1985; Springel et al. 2001; More et al. 2011). Structures within structures (i.e. sub-structures) can be found using a variety of methods . TAO uses the Rockstar algorithm to find sub-halos (e.g. Springel et al. 20052001;Behroozi, Wechsler & Wu 20112013). Such sub-halos are typically expected to host smaller satellite galaxies; the evolution of these satellite galaxies is greatly influenced by the central galaxy and its host dark matter halos. More massive halos accrete less massive halos, along with their galaxies. These galaxies will eventually merge with the more massive central galaxy.

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This information, calculated across all time-steps in a simulation for a particular object, defines its merger tree. The collection of such trees is then used as input to construct a galaxy formation model. An example halo merger tree from the Millennium Simulation (Springel et al. 2005) is shown here. Here, the top panel shows the tree itself for a 1.9 × 1013 Msun halo at z = 0 (assuming h = 0.73), while the corresponding mass growth history with time is shown in the lower panel.

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