The return of the merging galaxy subclusters of El Gordo?

Merging galaxy clusters with radio relics provide rare insights to the merger dynamics as the relics are created by the violent merger process. We demonstrate one of the first uses of the properties of the radio relic to reduce the uncertainties of the dynamical variables and determine the 3D configuration of a cluster merger, ACT-CL J0102-4915, nicknamed El Gordo. From the double radio relic observation and the X-ray observation of a comet-like gas morphology induced by motion of the cool core, it is widely believed that El Gordo is observed shortly after the first core-passage of the subclusters. We employ a Monte Carlo simulation to investigate the three-dimensional (3D) configuration and dynamics of El Gordo. Using the polarization fraction of the radio relic, we constrain the estimate of the angle between the plane of the sky and the merger axis to be $\alpha = 21~{\rm degree} \pm^9_{11}$. We find the relative 3D merger speed of El Gordo to be $2400\pm^{400}_{200}~{\rm km}~{\rm s}^{-1}$ at pericenter. The two possible estimates of the time-since-pericenter are $0.46\pm^{0.09}_{0.16}$ Gyr and $0.91\pm^{0.22}_{0.39}$ Gyr for the outgoing and returning scenario respectively. We put our estimates of the time-since-pericenter into context by showing that if the time-averaged shock velocity is approximately equal to or smaller than the pericenter velocity of the corresponding subcluster in the center of mass frame, the two subclusters are more likely to be moving towards, rather than away, from each other, post apocenter. We compare and contrast the merger scenario of El Gordo with that of the Bullet Cluster, and show that this late-stage merging scenario explains why the southeast dark matter lensing peak of El Gordo is closer to the merger center than the southeast cool core.