Inferring the Halo Mass Function from Galaxy Clusters: Accuracy Limits Due to Redshift-Space Distortions

Measuring the abundance of dark matter halos as a function of mass – termed the halo mass function – allows us to constrain cosmological parameters of interest. One way to infer the halo mass function is through measuring the abundance of galaxy clusters as a function of optical richness in redshift surveys. However, redshift-space distortions cause errors in cluster-finding and thus place a fundamental limit on the accuracy of this method. In particular, the velocity dispersion of member galaxies stretches out a galaxy cluster in redshift-space along the line of sight, in what is known as the 'fingers-of-God' effect. The main focus of this thesis is to estimate the contribution of this effect to the accuracy limit of the cluster mass function measured from optically-selected galaxy clusters.

This study uses Monte Carlo experiments to estimate the error rate in cluster-finding due to 'fingers-of-God' confusions in an idealized model. The trade-off between two types of error – fragmentation and overmerging – is studied in detail, and presented as an intermediate result. The model is then applied to a halo catalog from a cosmological simulation. Redshift-space confusions are found to tilt the measured halo mass function towards higher masses. Under the assumptions of our setup, the effects bias the best-fit cosmological parameters by a few percent, within the range that is relevant for inferring these parameters from upcoming surveys.