On the linearity of tracer bias around voids

Abstract

The large-scale structure of the universe can only be observed via luminous tracers of the dark matter. However, the clustering statistics of tracers are biased and depend on various properties, such as their host-halo mass and assembly history. On very large scales this tracer bias results in a constant offset in the clustering amplitude, known as linear bias. Towards smaller non-linear scales, this is no longer the case and tracer bias becomes a complicated function of scale and time. We focus on tracer bias centred on cosmic voids, depressions of the density field that spatially dominate the universe. We consider three types of tracers: galaxies, galaxy clusters and AGN, extracted from the hydrodynamical simulation Magneticum Pathfinder. In contrast to common clustering statistics that focus on auto-correlations of tracers, we find that void-tracer cross-correlations are successfully described by a linear-bias relation. The tracerdensity profile of voids can thus be related to their matter-density profile by a single number. We show that it coincides with the linear tracer bias extracted from the large-scale autocorrelation function and expectations from theory, if sufficiently large voids are considered. For smaller voids we observe a shift towards higher values. This has important consequences on cosmological parameter inference, as the problem of unknown tracer bias is alleviated up to a constant number. The smallest scales in existing datasets become accessible to simpler models, providing numerous modes of the density field that have been disregarded so far, but may help to further reduce statistical errors in constraining cosmology.

Cosmic voids uncovered – first-order statistics of depressions in the biased density field

“…Given the high level of uncertainty in the inner regions of the profiles, due to the sparsity of tracers, we exclude all the values with r ≤ 0.5 r eff . In agreement with the results by Pollina et al (2017), we find that the densities measured with the two different tracers, that is DM particles and haloes, are linearly related:…”

“…Given the hypothesis that voids in tracers are centred in the same position of their DM counterparts, we search for the density contrast that voids identified in the tracer distribution reach in the underlying DM distribution. By taking the ratio between the two profiles, as suggested by Pollina et al (2017), one can infer the relation between the density measured from biased tracers and the underlying unbiased DM density. Figure 4 shows the ratio between all the stacked profiles obtained for each catalogue, markers with error bars representing the uncertainty on the mean in the bin.…”

The void size function in dynamical dark energy cosmologies

“…• The theoretical void size function is referred to the statistical properties of matter, not of the tracers. We follow Pollina et al [20,66] to compute the threshold in the matter δ m v,NL , which corresponds to the one in the halo distribution and then invert the linear bias relation δ H v,NL = b eff × δ m v,NL (with b eff being the tracer bias). • In order to calculate the theoretical void size function, we need to express the matter underdensity threshold in linear theory.…”

Cosmological exploitation of cosmic void statistics

“…To overcome this issue, we implemented a simpler method to embed the bias dependency in the underdensity threshold value. Pollina et al (2017) found that the relation between the non-linear density contrast of tracers, δ NL v, tr , and matter, δ NL v, DM , around voids is linear and determined by a multiplicative constant which corresponds to the value of the bias parameter of the tracer sample, b:…”