Cosmic voids occupy most of the volume of the Universe, and their statistical properties can be exploited for constraining dark energy, as well as for testing theories of gravity. Nevertheless, in spite of their growing popularity as cosmological probes, a gap of knowledge between cosmic void observations and theory still persists. In particular, the void size function models proposed in literature have been proven unsuccessful in reproducing the results obtained from cosmological simulations in which cosmic voids are detected from biased tracers of the density field. The goal of this work is to cover this gap. In particular, we make use of the findings of a previous work in which we have improved the void selection procedure, presenting an algorithm that redefines the void ridges and, consequently, their radii. By applying this algorithm, we validate the volume conserving model of the void size function on a set of unbiased simulated density field tracers. We highlight the difference in the internal structure between voids selected in this way and those identified by the popular vide void finder. We also extend the validation of the model to the case of biased tracers. We find that a relation exists between the tracer used to sample the underlying dark matter density field and its unbiased counterpart. Moreover, we demonstrate that, as long as this relation is accounted for, the size function is a viable approach for studying cosmology with cosmic voids.
