Exploring the circumstellar environment of Tycho's supernova remnant--I. The hydrodynamic evolution of the shock

Among Type Ia supernova remnants (SNRs), Tycho's SNR has been considered as a typical object from the viewpoints of its spectroscopic, morphological and environmental properties. A recent reanalysis of Chandra data shows that its forward shock is experiencing a substantial deceleration since around 2007, which suggests recent shock interactions with a dense medium as a consequence of the cavity-wall environment inside a molecular cloud. Such a non-uniform environment can be linked back to the nature and activities of its progenitor. In this study, we perform hydrodynamic simulations to characterize Tycho's cavity-wall environment using the latest multi-epoch proper motion measurements of the forward shock. A range of parameters for the environment is explored in the hydrodynamic models to fit with the observation data for each azimuthal region. Our results show that a wind-like cavity with $\rho(r)\propto r^{-2}$ reconciles with the latest data better than a uniform medium with a constant density. In addition, our best-fit model favors an anisotropic wind with an azimuthally varying wind parameter. The overall result indicates a mass-loss rate which is unusually high for the conventional single-degenerate explosion scenario.