We perform simulations for future Cherenkov Telescope Array (CTA) observations of RX~J1713.7$-$3946, a young supernova remnant (SNR) and one of the brightest sources ever discovered in very-high-energy (VHE) gamma rays. Special attention is paid to explore possible spatial (anti-)correlations of gamma rays with emission at other wavelengths, in particular X-rays and CO/H{sc i} emission. We present a series of simulated images of RX J1713.7$-$3946 for CTA based on a set of observationally motivated models for the gamma-ray emission. In these models, VHE gamma rays produced by high-energy electrons are assumed to trace the non-thermal X-ray emission observed by {it XMM-Newton}, whereas those originating from relativistic protons delineate the local gas distributions. The local atomic and molecular gas distributions are deduced by the NANTEN team from CO and H{sc i} observations. Our primary goal is to show how one can distinguish the emission mechanism(s) of the gamma rays (i.e., hadronic vs leptonic, or a mixture of the two) through information provided by their spatial distribution, spectra, and time variation. This work is the first attempt to quantitatively evaluate the capabilities of CTA to achieve various proposed scientific goals by observing this important cosmic particle accelerator.
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