Percolation Statistics in the MillenniumTNG Simulations

The statistical analysis of cosmic large-scale structure is most often based on simple two-point summary statistics, like the power spectrum or the two-point correlation function of a sample of galaxies or other types of tracers. In contrast, topological measures of clustering are also sensitive to higher-order correlations, and thus offer the prospect to access additional information that may harbor important constraining power. We here revisit one such geometric measure of the cosmic web in the form of the so-called percolation analysis, using the recent MillenniumTNG simulation suite of the LCDM paradigm. We analyze continuum percolation statistics both for high resolution dark matter particle distributions, as well as for galaxy mock catalogues from a semi-analytic galaxy formation model within a periodic simulation volume of 3000 Mpc on a side. For comparison, we also investigate the percolation statistics of random particle sets and neutrino distributions with two different summed particle masses. We find that the percolation statistics of the dark matter distribution evolves strongly with redshift and thus clustering strength, yielding progressively lower percolation threshold towards later times. However, there is a sizable residual dependence on numerical resolution which we interpret as a residual influence of different levels of shot noise. This is corroborated by our analysis of galaxy mock catalogues whose results depend on sampling density more strongly than on galaxy selection criteria. While this limits the discriminative power of percolation statistics, our results suggest that it still remains useful as a complementary cosmological test when controlled for sampling density.