With the goal of understanding why X-rays have been reported near some high velocity clouds, we perform detailed 3 dimensional hydrodynamic and magnetohydrodynamic simulations of clouds interacting with environmental gas like that in the Galaxys thick disk/halo or the Magellanic Stream. We examine 2 scenarios. In the first, clouds travel fast enough to shock-heat warm environmental gas. In this scenario, the X-ray productivity depends strongly on the speed of the cloud and the radiative cooling rate. In order to shock-heat environmental gas to temperatures of > or = 10^6 K, cloud speeds of > or = 300 km/s are required. If cooling is quenched, then the shock-heated ambient gas is X-ray emissive, producing bright X-rays in the 1/4 keV band and some X-rays in the 3/4 keV band due to O VII and other ions. If, in contrast, the radiative cooling rate is similar to that of collisional ionizational equilibrium plasma with solar abundances, then the shocked gas is only mildly bright and for only about 1 Myr. The predicted count rates for the non-radiative case are bright enough to explain the count rate observed with XMM-Newton toward a Magellanic Stream cloud and some enhancement in the ROSAT 1/4 keV count rate toward Complex C, while the predicted count rates for the fully radiative case are not. In the second scenario, the clouds travel through and mix with hot ambient gas. The mixed zone can contain hot gas, but the hot portion of the mixed gas is not as bright as those from the shock-heating scenario.
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