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 \degree \pm ^ { 9 } _ { 11 } .
We find the relative 3D merger speed of El Gordo to be 2400 \pm ^ { 400 } _ { 200 } ~ { } \kilo \meter~ { } \second ^ { -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 .