The void spectrum in two-dimensional numerical simulations of gravitational clustering

We test an algorithm for deriving a spectrum of void sizes from two- dimensional high-resolution numerical simulations of gravitational clustering, and verify that it produces the correct results where those results can be anticipated. We use the method to study the growth of voids as clustering proceeds. We find that the most stable indicator of the characteristic void "size" in the simulations is the mean fractional area covered by voids of diameter d, in a density field smoothed at its correlation length. We find very accurate scaling behavior in power-law numerical models as they evolve. Eventually, this scaling breaks down as the nonlinearity reaches larger scales. We show that this breakdown is a manifestation of the undesirable effect of boundary conditions on simulations, even with the very large dynamic range possible here. We suggest a simple criterion for deciding when simulations with modest large-scale power may systematically underestimate the frequency of larger voids.