2017ApJ...841...46M

The colliding cluster, CIZA J2242.8+5301, displays a spectacular, almost 2 Mpc long shock front with a radio based Mach number M≃5, that is puzzlingly large compared to the X-ray estimate of M≃2.5. The extent to which the X-ray temperature jump is diluted by cooler unshocked gas projected through the cluster currently lacks quantification. Here we apply our self-consistent N-body/hydrodynamical code (based on FLASH) to model this binary cluster encounter. We can account for the location of the shock front and also the elongated X-ray emission by tidal stretching of the gas and dark matter between the two cluster centers. The required total mass is 8.9×10¹⁴ M_☉ with a 1.3:1 mass ratio favoring the southern cluster component. The relative velocity we derive is ≃2500 km s^–1 initially between the two main cluster components, with an impact parameter of 120 kpc. This solution implies that the shock temperature jump derived from the low angular resolution X-ray satellite Suzaku is underestimated by a factor of two, due to cool gas in projection, bringing the observed X-ray and radio estimates into agreement. Finally, we use our model to generate Compton-y maps to estimate the thermal Sunyaev-Zel'dovich (SZ) effect. At 30 GHz, this amounts to ΔS_n=-0.072 mJy/arcmin² and ΔS_s=-0.075 mJy/arcmin² at the locations of the northern and southern shock fronts respectively. Our model estimate agrees with previous empirical estimates that have inferred the measured radio spectra of the radio relics can be significantly affected by the SZ effect, with implications for charged particle acceleration models.