The Physical Origin of Scale‐dependent Bias in Cosmological Simulations

Abstract

Using a large-scale hydrodynamic simulation with heuristic criteria for galaxy formation, we investigate how the galaxy field is related to physical parameters such as the mass density and the gas temperature. In our flat cold dark matter model with Ω₀ = 0.37, we find that the relation between the galaxy and mass density fields is a function of scale. The bias b(R) ≡ σ_g(R)/σ(R), where σ_g(R) is the variance of galaxy counts in spheres of radius R and σ(R) is the same for mass, varies from 2.6 at 1 h^-1 Mpc to 1.2 at 30 h^-1 Mpc. Including the dependence of the galaxy density on local gas temperature as well as on local mass density can fully account for this scale dependence. Galaxy density depends on temperature because gas that is too hot cannot cool to form galaxies; this causes scale dependence of b(R) because local gas temperature is related to the gravitational potential and thus contains information about the large-scale density field. We show that temperature dependence generally causes b(R) to vary on quasi-linear and nonlinear scales, indicating that scale dependence of bias may be a generic effect in realistic galaxy formation scenarios. We find that the relationship between the galaxy and mass density fields is also a function of galaxy age. On large scales, the older galaxies are highly biased (b ≈ 1.7) and highly correlated (r ≡ δδ_g/σσ_g ≈ 1.0) with the mass density field; younger galaxies are not biased (b ≈ 0.8) and are poorly correlated (r ≈ 0.5) with the mass. We argue that linear bias is inadequate to describe the relationship between galaxies and mass. We present a more physically based prescription that better fits our results and reproduces the scale dependence of the bias: ρ_g/ρ_g = L(ρ/ρ)^M(1 + T/40,000 K)^N, where L = 1.23, M = 1.9, and N = -0.66.