The local bias model in the large-scale halo distribution
Abstract
We explore the biasing in the clustering statistics of haloes 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(δ) between DM fluctuations, δ, smoothed over a top-hat radius Rs at a point in the simulation and its corresponding tracer h (i.e. haloes) at the same point. This local relation can be Taylor expanded to define a linear (b1) and non-linear (b2) bias parameter. The values of b1 and b2 in the simulation vary with Rs approaching a constant value around Rs > 30-60 Mpc h-1. 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 per cent level) for the halo 2-point correlation ξ(r12) for r12 > 15 Mpc h-1, but only when we use the biasing values that we found at very large smoothing radii Rs > 30-60 Mpc h-1. We find no effect from stochastic or next-to-leading-order terms in the f(δ) expansion. However, 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 discreteness corrections (to the local model) are needed at the 10-20 per cent level. Shot-noise can be corrected with a term ?, where σ2e < 1, that is, 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 per cent systematic (and similar statistical) errors in the mass estimation when we use the halo model biasing predictions to calibrate the mass.
- Publication:
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Monthly Notices of the Royal Astronomical Society
- Pub Date:
- July 2011
- DOI:
- 10.1111/j.1365-2966.2011.18705.x
- arXiv:
- arXiv:0912.0446
- Bibcode:
- 2011MNRAS.415..383M
- Keywords:
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- large-scale structure of Universe;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- Accepted in MNRAS. Compared to first version, the paper has been completely reorganised. New figures and content added