AIMS. We study and discuss the time-dependent X-ray emission predicted by hydrodynamic modeling of the interaction of a SNR shock wave with an interstellar gas cloud. The scope includes: 1) to study the correspondence between modeled and X-ray emitting structures, 2) to explore two different physical regimes in which either thermal conduction or radiative cooling plays a dominant role, and 3) to investigate the effects of the physical processes at work on the emission of the shocked cloud in the two different regimes. METHODS. We use a detailed hydrodynamic model, including thermal conduction and radiation, and explore two cases characterized by different Mach numbers of the primary shock: M = 30 in which the cloud dynamics is dominated by radiative cooling and M = 50 dominated by thermal conduction. From the simulations, we synthesize the expected X-ray emission, using available spectral codes. RESULTS. The morphology of the X-ray emitting structures is significantly different from that of the flow structures originating from the shock-cloud interaction. The hydrodynamic instabilities are never clearly visible in the X-ray band. Shocked clouds are preferentially visible during the early phases of their evolution. Thermal conduction and radiative cooling lead to two different phases of the shocked cloud: a cold cooling dominated core emitting at low energies and a hot thermally conducting corona emitting in the X-ray band. The thermal conduction makes the X-ray image of the cloud smaller, more diffuse, and shorter-lived than that observed when thermal conduction is neglected.
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