Testing spherical evolution for modelling void abundances

We compare analytical predictions of void volume functions to those measured from N-body simulations, detecting voids with the zobov void finder. We push to very small, non-linear voids, below few Mpc radius, by considering the unsampled dark matter density field. We also study the case where voids are identified using haloes. We develop analytical formula for the void abundance of both the excursion set approach and the peaks formalism. These formulas are valid for random walks smoothed with a top-hat filter in real space, with a large class of realistic barrier models. We test the extent to which the spherical evolution approximation, which forms the basis of the analytical predictions, models the highly aspherical voids that occur in the cosmic web, and are found by a watershed-based algorithm such as zobov. We show that the volume function returned by zobov is quite sensitive to the choice of treatment of subvoids, a fact that has not been appreciated previously. For reasonable choices of subvoid exclusion, we find that the Lagrangian density delta(v) of the zobov voids - which is predicted to be a constant delta(v) a parts per thousand -2.7 in the spherical evolution model - is different from the predicted value, showing substantial scatter and scale dependence. This result applies to voids identified atz = 0 with effective radius between 1 and 10 h(-1) Mpc. Our analytical approximations are flexible enough to give a good description of the resulting volume function; however, this happens for choices of parameter values that are different from those suggested by the spherical evolution assumption. We conclude that analytical models for voids must move away from the spherical approximation in order to be applied successfully to observations, and we discuss some possible ways forward.