Bias deconstructed: Unravelling the scale dependence of halo bias using real space measurements

TL;DR

This paper investigates the scale dependence of halo bias using real space measurements from simulations and compares them with theoretical models, successfully reconstructing bias parameters without free parameters and validating the ESP formalism.

Contribution

It introduces a parameter-free method to reconstruct scale-dependent halo bias from real space data and validates the ESP formalism against simulations.

Findings

Reconstructed linear bias agrees well with previous Fourier space estimates.

The quadratic bias reconstruction is consistent but lacks prior Fourier space comparisons.

ESP predictions accurately match the measured scale dependence of bias.

Abstract

We explore the scale dependence of halo bias using real space cross-correlation measurements in N-body simulations and in Pinocchio, an algorithm based on Lagrangian Perturbation Theory. Recent work has shown how to interpret such real space measurements in terms of k-dependent bias in Fourier space, and how to remove the k-dependence to reconstruct the k-independent peak-background split halo bias parameters. We compare our reconstruction of the linear bias, which requires no free parameters, with previous estimates from N-body simulations which were obtained directly in Fourier space at large scales, and find very good agreement. Our reconstruction of the quadratic bias is similarly parameter-free, although in this case there are no previous Fourier space measurements to compare with. Our analysis of N-body simulations explicitly tests the predictions of the excursion set peaks (ESP) formalism of Paranjape et al. (2013) for the scale dependence of bias; we find that the ESP predictions accurately describe our measurements. In addition, our measurements in Pinocchio serve as a useful, successful consistency check between Pinocchio and N-body simulations that is not accessible to traditional measurements.