PREPRINT
FE1A0072-F527-4612-92A4-4F5C05809041

# Assembly bias in the local PNG halo bias and its implication for ${f}_{\mathrm{N}\mathrm{L}}$ constraints

Titouan Lazeyras, Alexandre Barreira, Fabian Schmidt, Vincent Desjacques

Submitted on 15 September 2022

## Abstract

We use $N$-body simulations to study halo assembly bias (i.e., the dependence of halo clustering on properties beyond total mass) in the density and primordial non-Gaussianity (PNG) linear bias parameters ${b}_{1}$ and ${b}_{\varphi }$, respectively. We consider concentration, spin and sphericity as secondary halo properties, for which we find a clear detection of assembly bias for ${b}_{1}$ and ${b}_{\varphi }$. At fixed total mass, halo spin and sphericity impact ${b}_{1}$ and ${b}_{\varphi }$ in a similar manner, roughly preserving the shape of the linear ${b}_{\varphi }\left({b}_{1}\right)$ relation satisfied by the global halo population. Halo concentration, however, drives ${b}_{1}$ and ${b}_{\varphi }$ in opposite directions. This induces significant changes to the ${b}_{\varphi }\left({b}_{1}\right)$ relation, with higher concentration halos having higher amplitude of ${b}_{\varphi }\left({b}_{1}\right)$. For $z=0.5$ and ${b}_{1}\approx 2$ in particular, the population comprising either all halos, those with the $33\mathrm{%}$ lowest or those with the $33\mathrm{%}$ highest concentrations have a PNG bias of ${b}_{\varphi }\approx 3$, ${b}_{\varphi }\approx -1$ and ${b}_{\varphi }\approx 9$, respectively. Varying the halo concentration can make ${b}_{\varphi }$ very small and even change its sign. These results have important ramifications for galaxy clustering constraints of the local PNG parameter ${f}_{\mathrm{N}\mathrm{L}}$ that assume fixed forms for the ${b}_{\varphi }\left({b}_{1}\right)$ relation. We illustrate the significant impact of halo assembly bias in actual data using the BOSS DR12 galaxy power spectrum: assuming that BOSS galaxies are representative of all halos, the $33\mathrm{%}$ lowest or the $33\mathrm{%}$ highest concentration halos yields ${\sigma }_{{f}_{\mathrm{N}\mathrm{L}}}=44,165,19$, respectively. Our results suggest taking host halo concentration into account in galaxy selection strategies to maximize the signal-to-noise on ${f}_{\mathrm{N}\mathrm{L}}$. They also motivate more simulation-based efforts to study the ${b}_{\varphi }\left({b}_{1}\right)$ relation of halos and galaxies.

## Preprint

Comment: 21 pages, 4 figures, comments welcome

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics