Galaxy Cluster Mass Reconstruction Project - IV. Understanding the
  effects of imperfect membership on cluster mass estimation
  The primary difficulty in measuring dynamical masses of galaxy clusters from
galaxy data lies in the separation between true cluster members from
interloping galaxies along the line of sight. We study the impact of membership
contamination and incompleteness on cluster mass estimates obtained with 25
commonly used techniques applied to nearly 1000 mock clusters. We show that all
methods overestimate or underestimate cluster masses when applied to
contaminated or incomplete galaxy samples respectively. This appears to be the
main source of the intrinsic scatter in the mass scaling relation. Applying
corrections based on a prior knowledge of contamination and incompleteness can
reduce the scatter to the level of shot noise expected for poorly sampled
clusters. We establish an empirical model quantifying the effect of imperfect
membership on cluster mass estimation and discuss its universal and
method-dependent features. We find that both imperfect membership and the
response of the mass estimators depend on cluster mass, effectively causing a
flattening of the estimated - true mass relation. Imperfect membership thus
alters cluster counts determined from spectroscopic surveys, hence the
cosmological parameters that depend on such counts.
