Average Dark Matter Halo Sparsity Relations as Consistency Check of Mass
  Estimates in Galaxy Cluster Samples
  The dark matter halo sparsity provides a direct observational proxy of the
halo mass profile, characterizing halos in terms of the ratio of masses within
radii which enclose two different overdensities. Previous numerical simulation
analyses have shown that at a given redshift the halo sparsity carries
cosmological information encoded in the halo mass profile. Moreover, its
ensemble averaged value can be inferred from prior knowledge of the halo mass
function at the overdensities of interest. Here, we present a detailed study of
the ensemble average properties of the halo sparsity. In particular, using halo
catalogs from high-resolution N-body simulations, we show that its ensemble
average value can be estimated from the ratio of the averages of the inverse
halo masses as well as the ratio of the averages of the halo masses at the
overdensity of interests. This can be relevant for galaxy clusters data
analyses. As an example, we have estimated the average sparsity properties of
galaxy clusters from the LoCuSS and HIFLUGCS datasets respectively. The results
suggest that the expected consistency of the different average sparsity
estimates can provide a test of the robustness of mass measurements in galaxy
cluster samples.
