Mass accretion rates of the HectoMAP clusters of galaxies
  We estimate the mass accretion rate (MAR) of the 346 clusters of galaxies in
the HectoMAP Cluster Survey. The clusters span the redshift range $0.17-0.42$
and the $M_{200}$ mass range $\approx (0.5 - 3.5)\cdot 10^{14} M_\odot$. The
MAR estimate is based on the caustic technique along with a spherical infall
model. Our analysis extends the measurement of MARs for 129 clusters at $z<0.3$
from the Cluster Infall Regions in the Sloan Digital Sky Survey (CIRS) and the
Hectospec Cluster Survey (HeCS) to redshift $z \sim 0.42$. Averaging over
redshift, low-mass clusters with $M_{200}\sim 0.7\cdot 10^{14} M_\odot$ accrete
$\sim 3\cdot 10^4 M_\odot$yr$^{-1}$; more massive clusters with $M_{200}\sim
2.8\cdot 10^{14} M_\odot$ accrete $\sim 1\cdot 10^5 M_\odot$yr$^{-1}$. Low- and
high-mass clusters increase their MAR by $\sim 46\%$ and $\sim 84\%$,
respectively, as the redshift increases from $z\sim 0.17-0.29$ to $z\sim
0.34-0.42$. The MARs at fixed redshift increase with mass and MARs at fixed
mass increase with redshift in agreement with $\Lambda$CDM cosmological model
for hierarchical structure formation. We consider the extension of MAR
measurements to $z \sim 1$.
