The Mass Accretion Rate of Clusters of Galaxies: CIRS and HeCS

We use a new spherical accretion recipe tested on N-body simulations to measure the observed mass accretion rate (MAR) of 129 clusters in the CIRS and HeCS. The observed clusters cover the redshift range $0.01 < z < 0.30$ and the mass range $\sim 10^{14}-10^{15}h^{-1}\text{M}_\odot$. Based on three-dimensional mass profiles of simulated clusters reaching beyond the virial radius, our recipe returns MARs that agree with MARs based on merger trees. We adopt this recipe to estimate the MAR of real clusters based on measurement of the mass profile out to $\sim 3R_{200}$. We use the caustic method to measure the mass profiles to these large radii. We demonstrate the solidity of our estimates by applying the same approach to a set of mock redshift surveys of a sample of 2000 simulated clusters with median mass $M_{200}= 10^{14} {\,h^{-1}\rm{M_{\odot}}}$, and a sample of 50 simulated clusters with median mass $M_{200}= 10^{15} {\,h^{-1}\rm{M_{\odot}}}$: the median MARs based on the caustic mass profiles of the simulated clusters are unbiased and agree within $17\%$ with the median MARs based on the real mass profile of the clusters. The MAR of the CIRS and HeCS clusters increases with the mass and the redshift of the accreting cluster, in excellent agreement with the growth of clusters in the $\Lambda$CDM model.