Comparing halo bias from abundance and clustering

TL;DR

This paper models halo abundance and bias using large simulations, revealing significant variations among models, but also universal relations, with implications for cosmological measurements and galaxy clustering analyses.

Contribution

It introduces improved fitting methods for halo mass functions and establishes universal relations between bias parameters, highlighting model variations and their impact.

Findings

Strong variation in mass function fits at low and high masses.

Universal relations between bias parameters with simple fits.

Bias prediction discrepancies impact growth and mass calibration.

Abstract

We model the abundance of haloes in the $\sim(3 \ \text{Gpc}/h)^3$ volume of the MICE Grand Challenge simulation by fitting the universal mass function with an improved Jack-Knife error covariance estimator that matches theory predictions. We present unifying relations between different fitting models and new predictions for linear ($b_1$) and non-linear ($c_2$ and $c_3$) halo clustering bias. Different mass function fits show strong variations in their performance when including the low mass range ($M_h \lesssim 3 \ 10^{12} \ M_{\odot}/h$) in the analysis. Together with fits from the literature we find an overall variation in the amplitudes of around $10$% in the low mass and up to $50$% in the high mass (galaxy cluster) range ($M_h > 10^{14} \ M_{\odot}/h$). These variations propagate into a $10$% change in $b_1$ predictions and a $50$% change in $c_2$ or $c_3$. Despite these strong variations we find universal relations between $b_1$ and $c_2$ or $c_3$ for which we provide simple fits. Excluding low mass haloes, different models fitted with reasonable goodness in this analysis, show percent level agreement in their $b_1$ predictions, but are systematically $5-10$% lower than the bias directly measured with two-point halo-mass clustering. This result confirms previous findings derived from smaller volumes (and smaller masses). Inaccuracies in the bias predictions lead to $5-10$% errors in growth measurements. They also affect any HOD fitting or (cluster) mass calibration from clustering measurements.