We use the Fourth Data Release of the Sloan Digital Sky Survey to test the ubiquity of infall patterns around galaxy clusters and measure cluster mass profiles to large radii .
The Cluster And Infall Region Nearby Survey ( CAIRNS ) found infall patterns in nine clusters , but the cluster sample was incomplete .
Here , we match X-ray cluster catalogs with SDSS , search for infall patterns , and compute mass profiles for a complete sample of X-ray selected clusters .
Very clean infall patterns are apparent in most of the clusters , with the fraction decreasing with increasing redshift due to shallower sampling .
All 72 clusters in a well-defined sample limited by redshift ( ensuring good sampling ) and X-ray flux ( excluding superpositions ) show infall patterns sufficient to apply the caustic technique .
This sample is by far the largest sample of cluster mass profiles extending to large radii to date .
Similar to CAIRNS , cluster infall patterns are better defined in observations than in simulations .
Further work is needed to determine the source of this difference .
We use the infall patterns to compute mass profiles for 72 clusters and compare them to model profiles .
Cluster scaling relations using caustic masses agree well with those using X-ray or virial mass estimates , confirming the reliability of the caustic technique .
We confirm the conclusion of CAIRNS that cluster infall regions are well fit by NFW and Hernquist profiles and poorly fit by singular isothermal spheres .
This much larger sample enables new comparisons of cluster properties with those in simulations .
The shapes ( specifically , NFW concentrations ) of the mass profiles agree well with the predictions of simulations .
The mass in the infall region is typically comparable to or larger than that in the virial region .
Specifically , the mass inside the turnaround radius is on average 2.19 \pm 0.18 times that within the virial radius .
This ratio agrees well with recent predictions from simulations of the final masses of dark matter haloes .