# The Breakdown Scale of HI Bias Linearity

## TL;DR

This paper investigates the scale at which HI bias remains linear in 21 cm intensity mapping, finding it holds at BAO scales but breaks down at smaller scales, with a redshift-dependent bias behavior.

## Contribution

It introduces three methods to generate mock HI density and identifies the scale and redshift conditions for HI bias linearity and nonlinearity.

## Key findings

- HI bias is linear at BAO scales but not below 0.1 h/Mpc.
- A redshift near 1 exists where HI bias remains scale-independent at small scales.
- Linear HI bias approximately scales with redshift for z ≤ 3.

## Abstract

The 21 cm intensity mapping experiments promise to obtain the large-scale distribution of HI gas at the post-reionization epoch. In order to reveal the underlying matter density fluctuations from the HI mapping, it is important to understand how HI gas traces the matter density distribution. Both nonlinear halo clustering and nonlinear effects modulating HI gas in halos may determine the scale below which the HI bias deviates from linearity. We employ three approaches to generate the mock HI density from a large-scale N-body simulation at low redshifts, and demonstrate that the assumption of HI linearity is valid at the scale corresponding to the first peak of baryon acoustic oscillations, but breaks down at $k \gtrsim 0.1\,h\, {\rm Mpc}^{-1}$. The nonlinear effects of halo clustering and HI content modulation counteract each other at small scales, and their competition results in a model-dependent "sweet-spot" redshift near $z$=1 where the HI bias is scale-independent down to small scales. We also find that the linear HI bias scales approximately linearly with redshift for $z\le 3$.