A Second-order bias model for the Logarithmic Halo Mass Density

TL;DR

This paper introduces an analytic second-order bias model for dark matter halos in a LCDM universe, effectively fitting the relation between halo and matter densities across various conditions using logarithmic densities.

Contribution

The model uses log halo mass density and second-order polynomial expansion, providing an accurate fit across different halo masses, scales, and redshifts, with a partially predictable stochastic term.

Findings

Second-order polynomial fits the data well.

Model remains accurate across multiple halo masses and scales.

Some stochasticity correlates with the shear tensor.

Abstract

We present an analytic model for the local bias of dark matter halos in a LCDM universe. The model uses the halo mass density instead of the halo number density and is searched for various halo mass cuts, smoothing lengths, and redshift epoches. We find that, when the logarithmic density is used, the second-order polynomial can fit the numerical relation between the halo mass distribution and the underlying matter distribution extremely well. In this model the logarithm of the dark matter density is expanded in terms of log halo mass density to the second order. The model remains excellent for all halo mass cuts (from M_{cut}=3\times10^{11}$ to $3\times10^{12}h^{-1}M_{\odot}$), smoothing scales (from $R=5h^{-1}$Mpc to $50h^{-1}$Mpc), and redshift ranges (from z=0 to 1.0) considered in this study. The stochastic term in the relation is found not entirely random, but a part of the term can be determined by the magnitude of the shear tensor.