Tracing cosmic voids with fast simulations

Abstract

Context. Cosmic voids are vast underdense regions in the cosmic web that encode crucial information about structure formation, the composition of the Universe, and its expansion history. Due to their lower density, these regions are less affected by non-linear gravitational dynamics, making them suitable candidates for analysis using semi-analytic methods. Aims. We assess the accuracy of the PINOCCHIO code, a fast tool for generating dark matter halo catalogs based on Lagrangian Perturbation Theory, in modeling the statistical properties of cosmic voids. We validate this approach by comparing the resulting void statistics measured from PINOCCHIO to those obtained from N-body simulations. Methods. We generate a set of simulations using PINOCCHIO and OpenGADGET3, assuming a fiducial cosmology and varying the resolution. For a given resolution, the simulations share the same initial conditions between the different simulation codes. Snapshots are saved at multiple redshifts for each simulation and post-processed using the watershed void finder VIDE to identify cosmic voids. For each simulation code, we measure the following statistics: void size function, void ellipticity function, core density function, and the void radial density profile. We use these statistics to quantify the accuracy of PINOCCHIO relative to OpenGADGET3 in the context of cosmic voids. Results. We find agreement for all void statistics at better than 2σ between PINOCCHIO and OpenGADGET3, with no systematic difference in redshift trends. This demonstrates that the PINOCCHIO code can reliably produce void statistics with high computational efficiency compared to full N-body simulations.

Figures (22)

• Figure 1: Comparison of the HMFs (left panel) at $z=0.0$ for low- and high-resolution simulations. Jackknife errors are shown as filled regions. In the middle panel, the shaded band indicates a $\pm 10\%$ range around the OpenGADGET3 result, offering a reference for the level of agreement with PINOCCHIO. The filled regions indicates the Jackknife errors around the residual curves. The right panel displays the relative difference between the two HMFs, normalized by the maximum and minimum statistical uncertainties, as described in Eqs. \ref{['eq:errors_min']} and \ref{['eq:errors_max']}, and expressed in units of $\sigma$. The shaded region indicates the $\pm2\sigma$ range, highlighting the level of statistical consistency between the two HMFs. The filled region further illustrates the variation range between these two error estimates.
• Figure 2: Left panels: relative difference between the two HMFs at different redshifts $z = (0.0 , 0.5 , 1.0 , 1.5, 2.0)$, with low-resolution results shown on the top and high-resolution results on the bottom. Each line represents the difference between PINOCCHIO and OpenGADGET3 normalized by the Jackknife errors from the OpenGADGET3 estimates as defined in Eq. \ref{['eq:errors_max']}. The shaded area indicates the $\pm 2\sigma$ range, highlighting the region of statistical agreement between the two methods. The horizontal dashed line at $\sigma = 0$ serves as a reference for perfect agreement. Right panels: overall distribution of the measurements in the left panels, aggregated over all redshifts and size bins, with overlaid Gaussian fits.
• Figure 3: Same as Figure \ref{['HMF_comparison']}, but for the VSFs.
• Figure 4: Same as Figure \ref{['HMF_evolution']}, but for the VSFs as a function of $R_{\mathrm{Eff}}$.
• Figure 5: Same as Figure \ref{['HMF_comparison']}, but for the VEFs.