Voids Merging Trees
Observational studies show that voids are prominent features of the large scale structure of the present day Universe. Even though their emerging from the primordial density perturbations and evolutionary patterns differ from dark matter halos, N-body simulations and theoretical models have shown that voids also merge together to form large void structures. In this study, progressing from previous works, we formulate a toy model to construct a merger tree algorithm of isolated spherical voids by adopting the halo merging algorithm given by Lacey and Cole (1993) in the Einstein de Sitter (EdS) universe. To do this, we take into account the general mass distribution of voids which consists of two main void sociologies: merging and collapsing. We show that the mass distribution function can be reduced to a simple form by neglecting the collapse void contribution. As a result of this, the void mass fraction has a contribution only from isolated gradually merging voids. This algorithm becomes the analogue of the halo merging algorithm. Based on this isolated spherical void distribution, we obtain the void merging algorithm, void merging rate and void survival times in terms of the self similar and standard cold dark matter models in the EdS universe.