The abundance of lensing protoclusters
  Weak gravitational lensing provides a potentially powerful method for the detection of clusters. In addition to cluster candidates, a large number of objects with possibly no optical or X-ray component have been detected in shear-selected samples. We develop an analytic model to investigate the claim of Weinberg & Kamionkowski (2002) that unvirialised protoclusters account for a significant number of these so-called "dark" lenses. In our model, a protocluster consists of a small virialised region surrounded by in-falling matter. We find that, in order for a protocluster to simultaneously escape X-ray detection and create a detectable weak lensing signal, it must have a small virial mass (~10^{13} \Msun) and large total mass (~ 10^{15} \Msun), with a relatively flat density profile outside of the virial radius. Such objects would be characterized by rising tangential shear profiles well beyond the virial radius. We use a semi-analytic approach based on the excursion set formalism to estimate the abundance of lensing protoclusters with a low probability of X-ray detection. We find that they are extremely rare, accounting for less than 0.4 per cent of the total lenses in a survey with background galaxy density n = 30 arcmin^{-2} and an intrinsic ellipticity dispersion of 0.3. We conclude that lensing protoclusters with undetectable X-Ray luminosities are too rare to account for a significant number of dark lenses. 
Anson D'Aloisio, Steven R. Furlanetto, Priyamvada Natarajan