Figure 1

A schematic showing our how tree augmenting algorithm works. Panel a: A simplified diagram of a merger tree extracted from an N-body simulation. Circles represent halos (with radius indicating mass). Time increases in the direction shown by the arrow, and halos are located at quantized redshifts, labeled \(z_{0},\ldots, z_{2}\), and shown by horizontal, dot-dot-dashed lines. Dashed lines connect halos to their direct progenitors. One halo at \(z_{0}\) (highlighted by the yellow color and red outline) is selected for augmentation. This halo’s progenitors at \(z_{1}\) are also highlighted in yellow. Panel b: A trial tree (shown in blue) is generated using the PCH algorithm and compared to the halos of interest in the original tree. In this case, the match between trial tree and original tree halo masses is sufficiently close to be deemed acceptable. Panel c: The accepted trial tree is grafted into the original tree. Note that the augmented node and its progenitors from the original tree are retained (so their masses are unchanged), but now with the structure of the trial tree grafted between them. Panel d: Where the trial tree has halos at \(z_{1}\) which did not match any halo in the existing tree (and are below the resolution of the original tree by construction), a new tree is grown from each such halo and attached. This process is repeated for each of the green halos in the original tree.