The supernova remnant SN 1006 is a source of high-energy particles and its southwestern limb is interacting with a dense ambient cloud, thus being a promising region for gamma-ray hadronic emission. We aim at describing the physics and the nonthermal emission associated with the shock-cloud interaction to derive the physical parameters of the cloud (poorly constrained by the data analysis), to ascertain the origin of the observed spatial variations in the spectral properties of the X-ray synchrotron emission, and to predict spectral and morphological features of the resulting gamma-ray emission. We performed 3-D magnetohydrodynamic simulations modeling the evolution of SN 1006 and its interaction with the ambient cloud, and explored different model setups. By applying the REMLIGHT code on the model results, we synthesized the synchrotron X-ray emission, and compared it with actual observations, to constrain the parameters of the model. We also synthesized the leptonic and hadronic gamma-ray emission from the models, deriving constraints on the energy content of the hadrons accelerated at the southwestern limb. We found that the impact of the SN 1006 shock front with a uniform cloud with density 0.5 cm^-3 can explain the observed morphology, the azimuthal variations of the cutoff frequency of the X-ray synchrotron emission, and the shock proper motion in the interaction region. Our results show that the current upper limit for the total hadronic energy in the southwestern limb is 2.5e49 erg.
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