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Forward shocks by radio jets, driven into the intracluster medium, are one ofthe indicators that can be used to evaluate the power of the jet. Meanwhilehigh-angular-resolution X-ray observations show the Mach numbers of powerfulradio jets are smaller compared to that of theoretical and numerical studies,$\mathcal{M_{\rm obs}} < 2$. Our aim is to systematically investigate variousfactors, such as projection effects and temperature non-equilibration betweenprotons and electrons, that influence the Mach number estimate in a powerfuljet. Using two-temperature magnetohydrodynamic simulation data for the Cygnus Aradio jets, whose Mach number is approximately 6, we construct mock X-ray mapsof simulated jets from various viewing angles. Further, we evaluate the shockMach number from density/temperature jump using the same method of X-rayobservations. Our results demonstrate that measurements from density jumpsignificantly underestimate the Mach numbers, $\mathcal{M} < 2$, around the jethead at a low viewing angle, $\lessapprox 50^{\circ}$. The observed post-shocktemperature is strongly reduced by the projection effect, as our jet is in thecluster center where the gas density is high. On the other hand, thetemperature jump is almost unity, even if thermal electrons are in instantequilibration with protons. Upon comparison, we find that shock property of ourmodel at viewing angle of $<$ $55^{\circ}$ is in a good agreement with that ofCygnus A observations.

Simulations of two-temperature jets in galaxy clusters: II. X-ray property of forward shock