Probabilistic Lagrangian bias estimators and the cumulant bias expansion
arxiv(2024)
摘要
The spatial distribution of galaxies is a highly complex phenomenon currently
impossible to predict deterministically. However, by using a statistical
bias relation, it becomes possible to robustly model the average
abundance of galaxies as a function of the underlying matter density field.
Understanding the properties and parametric description of the bias relation is
key to extract cosmological information from future galaxy surveys. Here, we
contribute to this topic primarily in two ways: (1) We develop a new set of
probabilistic estimators for bias parameters using the moments of the
Lagrangian galaxy environment distribution. These estimators include spatial
corrections at different orders to measure bias parameters independently of the
damping scale. We report robust measurements of a variety of bias parameters
for haloes, including the tidal bias and its dependence with spin at a fixed
mass. (2) We propose an alternative formulation of the bias expansion in terms
of "cumulant bias parameters" that describe the response of the logarithmic
galaxy density to large-scale perturbations. We find that cumulant biases of
haloes are consistent with zero at orders n > 2. This suggests that: (i)
previously reported bias relations at order n > 2 are an artefact of the
entangled basis of the canonical bias expansion; (ii) the convergence of the
bias expansion may be improved by phrasing it in terms of cumulants; (iii) the
bias function is very well approximated by a Gaussian – an avenue which we
explore in a companion paper.
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