A Model for Multi-property Galaxy Cluster Statistics
  The massive dark matter halos that host groups and clusters of galaxies have
observable properties that appear to be log-normally distributed about
power-law mean scaling relations in halo mass. Coupling this assumption with
either quadratic or cubic approximations to the mass function in log space, we
derive closed-form expressions for the space density of halos as a function of
multiple observables as well as forms for the low-order moments of properties
of observable-selected samples. Using a Tinker mass function in a {\Lambda}CDM
cosmology, we show that the cubic analytic model reproduces results obtained
from direct, numerical convolution at the 10 percent level or better over
nearly the full range of observables covered by current observations and for
redshifts extending to z = 1.5. The model provides an efficient framework for
estimating effects arising from selection and covariance among observable
properties in survey samples.
