Warm Dark Haloes Accretion Histories and their Gravitational Signatures
  We study clusters in Warm Dark Matter (WDM) models of a thermally produced
dark matter particle $0.5$ keV in mass. We show that, despite clusters in WDM
cosmologies having similar density profiles as their Cold Dark Matter (CDM)
counterparts, the internal properties, such as the amount of substructure,
shows marked differences. This result is surprising as clusters are at mass
scales that are {\em a thousand times greater} than that at which structure
formation is suppressed. WDM clusters gain significantly more mass via smooth
accretion and contain fewer substructures than their CDM brethren. The higher
smooth mass accretion results in subhaloes which are physically more extended
and less dense. These fine-scale differences can be probed by strong
gravitational lensing. We find, unexpectedly, that WDM clusters have {\em
higher} lensing efficiencies than those in CDM cosmologies, contrary to the
naive expectation that WDM clusters should be less efficient due to the fewer
substructures they contain. Despite being less dense, the larger WDM subhaloes
are more likely to have larger lensing cross-sections than CDM ones.
Additionally, WDM subhaloes typically reside at larger distances, which
radially stretches the critical lines associated with strong gravitational
lensing, resulting in excess in the number of clusters with large radial
cross-sections at the $\sim2\sigma$ level. Though lensing profile for an
individual cluster vary significantly with the line-of-sight, the radial arc
distribution based on a sample of $\gtrsim100$ clusters may prove to be the
crucial test for the presence of WDM.
