VOBOZ: an almost-parameter-free halo-finding algorithm

We have developed an algorithm, called VOBOZ (VOronoi BOund Zones), to find haloes in an N-body dark matter simulation; it has as little dependence on free parameters as we can manage. By using the Voronoi diagram, we achieve non-parametric, `natural' measurements of each particle's density and set of neighbours. We then eliminate much of the ambiguity in merging sets of particles together by identifying every possible density peak, and measuring the probability that each does not arise from Poisson noise. The main halo in a cluster tends to have a high probability, while its subhaloes tend to have lower probabilities. The first parameter in VOBOZ controls the subtlety of particle unbinding, and may be eliminated if one is cavalier with processor time; even if one is not, the results saturate to the parameter-free answer when the parameter is sufficiently small. The only parameter that remains, an outer density cut-off, does not influence whether or not haloes are identified, nor does it have any effect on subhaloes; it only affects the masses returned for supercluster haloes.