Non-local Lagrangian bias

Abstract

Halos are biased tracers of the dark matter distribution. It is often assumed that the patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in that of the dark matter. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte-Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory), and provide an analytic model which provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it -- this introduces k-dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other is due to the surrounding shear field; this affects the quadratic and higher order bias factors, and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in analyses of higher order clustering such as the halo bispectrum in Lagrangian or Eulerian space. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web -- filaments, sheets and voids.

13 pages, 6 figures; new section shows agreement with bispectrum measurements in simulations

References in corpus (8)

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Cited by in corpus (10)

• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the configuration-space clustering wedges
• Understanding higher-order nonlocal halo bias at large scales by combining the power spectrum with the bispectrum
• The Gaussian streaming model and Lagrangian effective field theory
• Halo bias in mixed dark matter cosmologies
• Tests of redshift-space distortions models in configuration space for the analysis of the BOSS final data release
• Soft-Pion Theorems for Large Scale Structure
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• Non-local bias in the halo bispectrum with primordial non-Gaussianity
• The bias of dark matter tracers: assessing the accuracy of mapping techniques
• Phenomenology of BAO evolution from Lagrangian to Eulerian Space