The mass accretion rate of galaxy clusters: a measurable quantity

We are interested in investigating the growth of structures at the nonlinear scales of galaxy clusters from an observational perspective: we explore the possibility of measuring the mass accretion rate of galaxy clusters from their mass profile beyond the virial radius. We derive the accretion rate from the mass of a spherical shell whose infall velocity is extracted from $N$-body simulations. In the redshift range $z=[0,2]$, our prescription returns an average mass accretion rate within $20-40 \%$ of the average rate derived from the merger trees of dark matter haloes extracted from $N$-body simulations. Our result suggests that measuring the mean mass accretion rate of a sample of galaxy clusters is actually feasible, thus providing a new potential observational test of the cosmological and structure formation models.