On the linearity of tracer bias around voids

The large-scale structure of the universe can only be observed directly via luminous tracers of the underlying distribution of dark matter. However, the clustering statistics of tracers are biased and depend on various properties of the tracers themselves, such as their host-halo mass and formation and assembly history. On very large scales, where density fluctuations are within the linear regime, this tracer bias results in a constant offset in the clustering amplitude, which is 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 centered on cosmic voids, depressions of the density field that spatially dominate the universe. We consider three different types of tracers: galaxies, galaxy clusters and AGNs, extracted from the hydrodynamical simulation suite Magneticum Pathfinder. In contrast to common clustering statistics that focus on the auto-correlation of tracers, we find that void-tracer cross-correlations are successfully described by a linear bias-relation within voids. The tracer-density profile of voids can thus be related to their matter-density profile by a single number. We show that this number coincides with the linear tracer bias extracted from the large-scale auto-correlation 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 from large-scale structure, 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 modes of the density field that have been disregarded so far, but may help to further reduce statistical errors and to constrain cosmology on smaller scales.