Scaling of the 1-halo terms with bias

TL;DR

This paper demonstrates that the 1-halo terms in galaxy correlation functions scale steeply with bias for highly biased tracers, significantly impacting large-scale structure analyses.

Contribution

It reveals the steep bias dependence of 1-halo terms in power spectrum and trispectrum, highlighting their importance at large scales.

Findings

1-halo term scales steeply with bias for highly biased tracers

1-halo term of the trispectrum also exhibits steep bias scaling

1-halo contributions can dominate large-scale correlation functions

Abstract

In the Halo Model, galaxies are hosted by dark matter halos, while the halos themselves are biased tracers of the underlying matter distribution. Measurements of galaxy correlation functions include contributions both from galaxies in different halos, and from galaxies in the same halo (the so-called 1-halo terms). We show that, for highly biased tracers, the 1-halo term of the power spectrum obeys a steep scaling relation in terms of bias. We also show that the 1-halo term of the trispectrum has a steep scaling with bias. The steepness of these scaling relations is such that the 1-halo terms can become key contributions to the $n$-point correlation functions, even at large scales. We interpret these results through analytical arguments and semi-analytical calculations in terms of the statistical properties of halos.