| Abstract
| - Context. The observations of the synchrotron emission from the supernova remnant (SNR) SN 1006 indicate a bilateral morphology, which is mainly characterized by two opposite bright limbs with knots and filaments along the boundary of the remnant. The morphology is not strictly circular with disturbances and bumps at the rim of the remnant. For instance, one big bump is located on the northeastern (NE) limb and several relatively small ones on the southwestern (SW) limb on the detected morphologies from the observations in the radio and X-rays. Aims. The generation of the asymmetric morphology of non-thermal X-rays for SN 1006 is investigated through three-dimensional (3D) magnetohydrodynamic simulations. Moreover, the density distribution of the ambient material can be investigated by comparing the resulting synchrotron morphology with the detected images of the hard X-ray emission. Methods. First, the remnant was simulated as a supernova explosion evolved in a turbulent plasma with a relatively small amplitude for the turbulence. In the model, several spherical cavities with lower densities compared with the background plasma were employed to reproduce the detected bumps at the bright limbs. Second, the effect of the modification on the morphology of the remnant due to efficient cosmic ray acceleration was investigated by adopting a lower adiabatic index. Results. If we assume that the injection efficiency of electrons into the diffusive shock acceleration process at the shock follows the quasi-parallel scenario, the hard X-ray morphology of SN 1006 with bumps in the bright NE and SW regions can be generally reproduced by employing cavities in the background medium in the non-modification scenario. Furthermore, in the modification case with a lower adiabatic index of 1.2 for the remnant evolved in a uniform medium, bubbles can be produced with relatively small extensions on the SNR boundary that result from the hydrodynamical instabilities that in turn overtake the forward shock. Conclusions. The SNR propagating in the turbulent medium with a relatively small amplitude can reproduce the knotty and filamentary morphology of the remnant better than what evolved in the uniform environment; moreover, the big bump on the NE limb can be explained as the result of a lower-density region, which has a radius of about 2.5 pc and a density of about 0.4 times of the general ambient medium, swept by the shock front, and the other smaller ones on the SW limb can either be reproduced with smaller regions with lower densities swept by the shock or be explained as the protrusions in the scenario of the efficient cosmic ray acceleration when the instability fingers effectively overtake the forward shock.
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