The Local Bias Model in the Large Scale Halo Distribution

TL;DR

This study investigates the local bias model in large-scale halo clustering, demonstrating its effectiveness at predicting two-point correlations with minimal stochastic effects, while highlighting discrepancies in three-point functions and mass estimation errors.

Contribution

It provides a detailed analysis of the local bias relation in large-scale simulations, quantifies bias parameters at large smoothing scales, and compares local bias predictions with halo model estimates.

Findings

Bias parameters b1 and b2 stabilize at large smoothing scales (>30-60 Mpc/h).

Local bias model predicts two-point correlation with about 1% accuracy at large scales.

Discrepancies observed in three-point functions and mass estimation errors of 5-10%.

Abstract

We explore the biasing in the clustering statistics of halos as compared to dark matter (DM) in simulations. We look at the second and third order statistics at large scales of the (intermediate) MICEL1536 simulation and also measure directly the local bias relation h = f({\delta}) between DM fluctuations, {\delta}, smoothed over a top-hat radius Rs at a point in the simulation and its corresponding tracer h (i.e. halos) at the same point. This local relation can be Taylor expanded to define a linear (b1) and non-linear (b2) bias parameters. The values of b1 and b2 in the simulation vary with Rs approaching a constant value around Rs > 30 - 60 Mpc/h. We use the local relation to predict the clustering of the tracer in terms of the one of DM. This prediction works very well (about percent level) for the halo 2-point correlation {\xi}(r_12) for r_12 > 15 Mpc/h, but only when we use the biasing values that we found at very large smoothing radius Rs > 30 - 60 Mpc/h. We find no effect from stochastic or next to leading order terms in the f({\delta}) expansion. But we do find some discrepancies in the 3-point function that needs further understanding. We also look at the clustering of the smoothed moments, the variance and skewness which are volume average correlations and therefore include clustering from smaller scales. In this case, we find that both next to leading order and discreetness corrections (to the local model) are needed at the 10 - 20% level. Shot-noise can be corrected with a term {\sigma}e^2/n where {\sigma}e^2 < 1, i.e., always smaller than the Poisson correction. We also compare these results with the peak-background split predictions from the measured halo mass function. We find 5-10% systematic (and similar statistical) errors in the mass estimation when we use the halo model biasing predictions to calibrate the mass.