Dark matter and galaxies: using gravitational lensing to map their relative distributions
Koens, Lars Arnout
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Cosmological constraints from galaxy surveys are as accurate as our understanding of the relative distributions of dark matter and galaxies, known as galaxy bias. Weak gravitational lensing is a powerful probe of galaxy bias, since the distortion in the shapes of distant galaxies, called shear, is directly related to the dark matter distribution, which can be compared to the galaxy field. I look at the galaxy clustering amplitude relative to the dark matter field, quantified by the galaxy bias b, as well as the cross-correlation coefficient r, which tells us how correlated the positions of galaxies are with the dark matter. In this thesis I present several techniques to constrain galaxy bias through weak lensing, using both numerical simulations and observational data. The most commonly used method, using aperture statistics, is shown to be subject to serious systematics in the presence of noisy data and scale- and time dependence in the galaxy bias. A local comparison technique is introduced, where the foreground distribution is used to predict the shear in the background, to which it is compared. The technique is tested with simulations, concluding that it requires high quality data. A model fitting approach is proposed, based on the McDonald (2006) galaxy bias model. The two parameters of this model, a large scale bias, b1, and a parameter, b2, that quantifies the scale dependence of the bias, are insufficient in the presence of stochasticity. Therefore, R is introduced as an additional parameter to take this into account. I present galaxy bias constraints for two spectroscopic galaxy samples: the Baryon Oscillations Spectroscopic Survey (BOSS) and the WiggleZ Dark Energy Survey (WiggleZ), applying the traditional aperture method and the model fitting approach to the Red Sequence Cluster Lensing Survey (RCSLenS). Both techniques strongly suggest that galaxies trace mass, but in a complicated way, with differences in scale- and time dependence between the samples considered. The WiggleZ galaxy bias is found to be around b ~ 1:2, depending on redshift and scale, and has a low cross-correlation coefficient of r ~ 0:5 at small scales. The BOSS samples have higher bias with scale dependence around b ~ 2:0 and show no sign of stochasticity, finding r to be close enough to unity to be explained within a deterministic scenario. The observations are in line with previous galaxy bias measurements from lensing data. The thesis incorporates work on the X-ray Luminosity Function (XLF) of galaxy clusters, measured from the Wide Angle ROSAT Pointed Survey (WARPS). Evolution is quantified with a likelihood analysis and I conclude that it is driven by a decreasing number density of high luminosity clusters with redshift, while the bulk of the cluster population remains nearly unchanged out to redshift z ~ 1:1, as expected in a low density Universe. I conclude by investigating the impact of my galaxy bias measurements from BOSS and WiggleZ on the growth rate of structure, as extracted from Redshift Space Distortions (RSD). The imperfect correlation between the galaxy and matter field, as quantified by R and b2, leads to an underestimation of the true growth rate under the assumption of a linear bias. Therefore, in order to constrain galaxy bias and gravity simultaneously, future cosmological redshift surveys require high quality lensing data.