We use state of the art hydrodyamical simulations from the Sherwood, EAGLE and Illustris projects to examine the signature of $M_{ \rm z=0}\simeq 10^{ 14}M_{ \odot}$ protoclusters observed in Ly-$\alpha$ absorption at $z\simeq 2.4$. We find there is a weak correlation between the mass overdensity, $\delta_{ \rm m}$, and the Ly-$\alpha$ effective optical depth relative to the mean, $\delta_{ \tau_\textrm{ eff}}$, averaged over $15~h^{ -1}\rm\,cMpc$ scales, although scatter in the $\delta_{ \rm m}$--$\delta_{ \tau_\textrm{ eff}}$ plane means it is not possible to uniquely identify large scale overdensities with strong Ly-$\alpha$ absorption. Although all protoclusters are associated with large scale mass overdensities, most sight lines through protoclusters in a $\sim 10^{ 6}$ $\rm cMpc^{ 3}$ volume probe the low column density Ly-$\alpha$ forest. A small subset of sight lines that pass through protoclusters exhibit coherent, strong Ly-$\alpha$ absorption on $15h^{ -1}\rm\,cMpc$ scales, although these correspond to a wide range in mass overdensity. Assuming perfect removal of contamination by Ly-$\alpha$ absorbers with damping wings, more than half of the remaining sight lines with $\delta_{ \tau_{ \rm eff}}>3.5$ trace protoclusters. It is furthermore possible to identify a model dependent $\delta_{ \tau_{ \rm eff}}$ threshold that selects only protoclusters. However, such regions are rare: excluding absorption caused by damped systems, less than 0.1 per cent of sight lines that pass through a protocluster have $\delta_{ \tau_{ \rm eff}}>3.5$, meaning that any protocluster sample selected in this manner will also be highly incomplete. On the other hand, coherent regions of Ly-$\alpha$ absorption also provide a promising route for identifying and studying filamentary environments at high redshift.
Categories: astro-ph.CO astro-ph.GA