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Accurate measurement of the cluster mass function is a crucial element in efforts to constrain structure formation models, the normalization of the matter power spectrum and the cosmological matter density, and the nature and evolution of dark energy. Large weak lensing surveys of  ∼20 000  galaxy clusters and groups will be key tools in the observational pursuit of that goal; first‐generation surveys such as those using the Sloan Digital Sky Survey (SDSS) are already beginning to calibrate previous measurements of the mass function from X‐ray observations and to extend existing constraints down to galaxy group scales. These weak lensing studies proceeded by stacking the lensing signals of many clusters and groups binned by mass‐correlated observables such as richness and luminosity; typically such analyses ignore the triaxial structure of dark matter haloes on the assumption that the averaging of many shear signals within each mass bin makes its effects (as large as factors of two in mass model parameter estimates from individual clusters) negligible. We test this assumption utilizing a population of 15 000 analytic triaxial dark matter haloes spanning 2 dex in mass, and find that triaxiality can bias 3D virial mass estimates compared to those for a spherical population by a few per cent if suboptimal mass estimators are used. This bias affects not only direct lensing constraints on the mass function but can also affect the scatter and normalization of the mass‐observable relations derived from lensing that are so crucial to constraining the cluster mass function with large samples. However, we demonstrate that a careful choice of mass estimator can remove the bias very effectively if the lensing signals from a sufficient number of triaxial haloes are averaged together, and further quantify that sufficient number for adequate shape averaging. We thus show that by choosing observable bins to contain an adequate number of haloes and by utilizing a carefully chosen 3D mass estimator stacked weak‐lensing analyses can give unbiased constraints on the triaxial mass function.

Cosmology with the cluster mass function: mass estimators and shape systematics in large weak lensing surveys