Recent progress in the three-dimensional modeling of supernovae (SN) has shown the importance of asymmetries for the explosion. This calls for a reconsideration of the modeling of the subsequent phase, the supernova remnant (SNR), which has commonly relied on simplified ejecta models. In this paper we bridge SN and SNR studies by using the output of a SN simulation as the input of a SNR simulation carried on until 500~yr. We consider the case of a thermonuclear explosion of a carbon-oxygen white dwarf star as a model for a Type Ia SN; specifically we use the N100 delayed detonation model of Seitenzahl et al 2013. In order to analyze the morphology of the SNR, we locate the three discontinuities that delineate the shell of shocked matter: the forward shock, the contact discontinuity, and the reverse shock, and we decompose their radial variations as a function of angular scale and time. Assuming a uniform ambient medium, we find that the impact of the SN on the SNR may still be visible after hundreds of years. Previous 3D simulations aiming at reproducing Tychos SNR, that started out from spherically symmetric initial conditions, failed to reproduce structures at the largest angular scales observed in X-rays. Our new simulations strongly suggest that the missing ingredient was the initial asymmetries from the SN itself. With this work we establish a way of assessing the viability of SN models based on the resulting morphology of the SNR.
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