  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.
