Simulated Analogs of Merging Galaxy Clusters Constrain the Viewing Angle

A key uncertainty in interpreting observations of bimodal merging galaxy clusters is the unknown angle between the subcluster separation vector and the plane of the sky. We present a new method for constraining this key parameter. We find analogs of observed systems in cosmological n-body simulations and quantify their likelihood of matching the observed projected separation and relative radial velocities between subclusters, as a function of viewing angle. We derive constraints on the viewing angle of many observed bimodal mergers including the Bullet Cluster (1E 0657-558) and El Gordo (ACT-CL J0102-4915). We also present more generic constraints as a function of projected separation and relative radial velocity, which can be used to assess additional clusters as information about them becomes available. The constraints from these two observables alone are weak (typically $\gtrsim 70-75^\circ$ at 68\% confidence and $\gtrsim 55-60^\circ$ at 95\% confidence) but incorporate much more cosmological context than the classical timing argument, marginalizing over many realizations of substructure, peculiar velocities, and so on. Compared to the MCMAC code, which implements the timing argument on NFW halos, our constraints generally predict subcluster separation vectors closer to the plane of the sky. This is because in realistic mergers the subcluster velocity vectors are not entirely parallel to the separation vector (i.e, the mergers are not perfectly head-on). As a result, observation of a nonzero relative radial velocity does not exclude a separation vector in the plane of the sky, as it does in the head-on timing argument employed by MCMAC.