On the Distribution of Haloes, Galaxies and Mass

Abstract

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function $P_V(N_h|{\delta }_m)$ which gives the probability of finding $N_h$ haloes in a volume $V$ with mass density contrast ${\delta }_m$. We study the properties of this function using high-resolution $N$-body simulations, and find that $P_V(N_n|{\delta }_m)$ is significantly non-Poisson. The ratio between the variance and the mean goes from $\sim 1$ (Poisson) at $1+{\delta }_m\ll 1$ to $<1$ (sub-Poisson) at $1+{\delta }_m\sim 1$ to $>1$ (super-Poisson) at $1+{\delta }_m\gg 1$. The mean bias relation is found to be well described by halo bias models based on the Press-Schechter formalism. The sub-Poisson variance can be explained as a result of halo-exclusion while the super-Poisson variance at high ${\delta }_m$ may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behavior of the variance as a function of ${\delta }_m$. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behavior. We discuss the implications of the stochasticity in halo bias to the modelling of higher-order moments of dark haloes and of galaxies.

10 pages, 6 figures, Latex using MN2e style. Minor changes. Accepted for publication in MNRAS

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