The mass accretion rate of galaxy clusters: a measurable quantity

We explore the possibility of measuring the mass accretion rate (MAR) of galaxy clusters from their mass profiles beyond the virial radius $R_{200}$. We derive the accretion rate from the mass of a spherical shell whose inner radius is $2R_{200}$, whose thickness changes with redshift, and whose infall velocity is assumed to be equal to the mean infall velocity of the spherical shells of dark matter halos extracted from $N$-body simulations. This approximation is rather crude in hierarchical clustering scenarios where both smooth accretion and aggregation of smaller dark matter halos contribute to the mass accretion of clusters.Nevertheless, in the redshift range $z=[0,2]$, our prescription returns an average MAR within $20-40 \%$ of the average rate derived from the merger trees of dark matter halos extracted from $N$-body simulations. The MAR of galaxy clusters has been the topic of numerous detailed numerical and theoretical investigations, but so far it has remained inaccessible to measurements in the real universe. Since the measurement of the mass profile of clusters beyond their virial radius can be performed with the caustic technique applied to dense redshift surveys of the cluster outer regions, our result suggests that measuring the mean MAR of a sample of galaxy clusters is actually feasible. We thus provide a new potential observational test of the cosmological and structure formation models.