The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

TL;DR

This paper introduces a Lagrangian bias expansion framework for modeling the matter-tracer density relationship and validates a non-Poissonian shot-noise model, improving the understanding of galaxy clustering statistics.

Contribution

It presents a new Lagrangian bias model for the matter-tracer connection and demonstrates its superiority over Eulerian models, along with a validated non-Poissonian shot-noise model.

Findings

Lagrangian bias model outperforms Eulerian in describing tracer-matter expectation.

Non-Poissonian shot-noise model accurately fits simulation data.

Framework sets the stage for improved analysis of survey data.

Abstract

We study the connection of matter density and its tracers from the PDF perspective. One aspect of this connection is the conditional expectation value $\langle \delta_{\mathrm{tracer}}|\delta_m\rangle$ when averaging both tracer and matter density over some scale. We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics. Using N-body simulations and mock galaxy catalogs we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization. For halos hosting typical luminous red galaxies, the Lagrangian model provides a significantly better description of $\langle \delta_{\mathrm{tracer}}|\delta_m\rangle$ at second order in perturbations. A second aspect of the matter-tracer connection is shot-noise, \ie the scatter of tracer density around $\langle \delta_{\mathrm{tracer}}|\delta_m\rangle$. It is well known that this noise can be significantly non-Poissonian and we validate the performance of a more general, two-parameter shot-noise model for different tracers and simulations. Both parts of our analysis are meant to pave the way for forthcoming applications to survey data.