The impact of cluster mergers on arc statistics

We study the impact of merger events on the strong lensing properties of galaxy clusters. Previous lensing simulations were not able to resolve dynamical time-scales of cluster lenses, which arise on time-scales that are of the order of a Gyr. In this case study, we first describe qualitatively with an analytic model how some of the lensing properties of clusters are expected to change during merging events. We then analyse a numerically-simulated lens model for the variation in its efficiency for producing both tangential and radial arcs while a massive substructure falls on to the main cluster body. We find that: (i) during the merger, the shape of the critical lines and caustics changes substantially; (ii) the lensing cross-sections for long and thin arcs can grow by one order of magnitude and reach their maxima when the extent of the critical curves is largest; (iii) the cross-section for radial arcs also grows, but the cluster can efficiently produce these kind of arcs only while the merging substructure crosses the main cluster centre, and (iv) while the arc cross-sections pass through their maxima as the merger proceeds, the X-ray emission of the cluster increases by a factor of similar to5. Thus, we conclude that accounting for these dynamical processes is very important for arc statistics studies. In particular, they may provide a possible explanation for the arc statistics problem.