Simulations of two-temperature jets in galaxy clusters II. X-ray properties of the forward shock

Context. Forward shocks by radio jets, driven into the intracluster medium, are one of the indicators that can be used to evaluate the power of the jet. Meanwhile, high-angular-resolution X-ray observations show the Mach numbers of powerful radio jets are smaller compared to the results of theoretical and numerical studies, namely, Mobs < 2.Aims. Our aim is to systematically investigate various factors, such as projection effects and temperature non-equilibration between protons and electrons, that influence the Mach number estimate in a powerful jet.Methods. Using a two-temperature magnetohydrodynamic simulation data for the Cygnus A radio jets, whose Mach number is approximately 6, we constructed mock X-ray maps of simulated jets from various viewing angles. Furthermore, we evaluated the shock Mach number from the density-temperature jump using the same method of X-ray observations.Results. Our results demonstrate that measurements from the density jump significantly underestimate the Mach numbers, M < 2, around the jet head at a low viewing angle, <50 degrees. The observed post-shock temperature is strongly reduced by the projection effect, as our jet is in the cluster center where the gas density is high. On the other hand, the temperature jump is almost at unity, even if thermal electrons are in instant equilibration with protons. Upon comparison, we find that the shock property of our model at a viewing angle of < 55 degrees is in good agreement with the results of Cygnus A observations.Conclusions. These works illustrate the importance of the projection effect in estimating the Mach number from the surface brightness profile. Furthermore, forward shock Mach numbers could serve as a useful probe for determining viewing angles for young, powerful radio jets.