Universal Density Profile for Cosmic Voids

We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in $\mathrm{\Lambda }\mathrm{CDM}$ $N$-body simulations. This function is universal across void size and redshift, accurately describing a large radial range of scales around void centers with only two free parameters. In analogy to halo density profiles, these parameters describe the scale radius and the central density of voids. While we initially start with a more general four-parameter model, we find two of its parameters to be redundant, as they follow linear trends with the scale radius in two distinct regimes of the void sample, separated by its compensation scale. Assuming linear theory, we derive an analytic formula for the velocity profile of voids and find an excellent agreement with the numerical data as well. In our companion paper [Sutter et al., arXiv:1309.5087 [Mon. Not. R. Astron. Soc. (to be published)]], the presented density profile is shown to be universal even across tracer type, properly describing voids defined in halo and galaxy distributions of varying sparsity, allowing us to relate various void populations by simple rescalings. This provides a powerful framework to match theory and simulations with observational data, opening up promising perspectives to constrain competing models of cosmology and gravity.

Figure 1

Stacked density (left) and velocity (right) profiles of voids at redshift zero in eight contiguous bins in void radius with mean values and void counts indicated in the inset. Shaded regions depict the standard deviation $\sigma$ within each of the stacks (scaled down by 20 for visibility), while error bars show standard errors on the mean profile $\sigma /\sqrt{N_v}$. Solid lines represent our best-fit solutions from Eq. (2) for density and from Eqs. (4) and (6) for velocity profiles. Dashed lines show the linear theory predictions obtained from evaluating the velocity profile equation at the best-fit parameters obtained from the density stacks.

Figure 2

Best-fit parameters obtained from the density stacks of Fig. 1. Error bars designate 95% confidence regions and straight lines show linear regressions through the data points, with corresponding best-fit values stated alongside. The vertical line indicates the compensation scale of the void sample.

Figure 3

Same as Fig. 1 for voids of fixed comoving radius at different redshifts as indicated along with the best-fit parameters.