A Consistent Comparison of Bias Models using Observational Data

TL;DR

This paper compares five models of dark matter halo bias using observational data from QSOs and galaxies across different redshifts, identifying the most accurate models and estimating typical halo masses.

Contribution

It provides a consistent comparison of bias models with observational data and identifies the best-fitting models using statistical criteria.

Findings

The Basilakos & Plionis bias model best fits the data.

The Tinker et al. model is statistically equivalent to the best model.

Average halo masses are estimated for QSOs and galaxies.

Abstract

We investigate five different models for the dark matter halo bias, ie., the ratio of the fluctuations of mass tracers to those of the underlying mass, by comparing their cosmological evolution using optical QSO and galaxy bias data at different redshifts, consistently scaled to the WMAP7 cosmology. Under the assumption that each halo hosts one extragalactic mass tracer, we use a $\chi^2$ minimization procedure to determine the free parameters of the bias models as well as to statistically quantify their ability to represent the observational data. Using the Akaike information criterion we find that the model that represents best the observational data is the Basilakos & Plionis (2001; 2003) model with the tracer merger extension of Basilakos, Plionis & Ragone-Figueroa (2008) model. The only other statistically equivalent model, as indicated by the same criterion, is the Tinker et al. (2010) model. Finally, we find an average, over the different models, dark matter halo mass that hosts optical QSOs of: $M_h\simeq 2.7 (\pm 0.6) \times 10^{12} h^{-1} M_{\odot}$, while the corresponding value for optical galaxies is: $M_h\simeq 6.3 (\pm 2.1) \times 10^{11} h^{-1} M_{\odot}$.