  Asymptotic Giant Branch (AGB) winds from evolved stars not only provide a
non-trivial amount of mass and energy return, but also produce dust grains in
massive elliptical galaxies. Due to the fast stellar velocity and the high
ambient temperature, the wind is thought to form a comet-like tail, similar to
Mira in the Local Bubble. Many massive elliptical galaxies and cluster central
galaxies host extended dusty cold filaments. The fate of the cold dusty stellar
wind and its relation to cold filaments are not well understood. In this work,
we carry out both analytical and numerical studies of the interaction between
an AGB wind and the surrounding hot gas. We find that the cooling time of the
tail is inversely proportional to the ambient pressure. In the absence of
cooling, or in low pressure environments (e.g., the outskirts of elliptical
galaxies), AGB winds are quickly mixed into the hot gas, and all the AGB winds
have similar appearance and head-to-tail ratio. In high pressure environments,
such as the Local Bubble and the central regions of massive elliptical
galaxies, some of the gas in the mixing layer between the stellar wind and the
surrounding hot gas can cool efficiently and cause the tail to become longer.
Our simulated tail of Mira itself has similar length and velocity to that
observed, and appears similar to the simulated AGB tail in the central regions
of massive galaxies. We speculate that instead of thermal instability, the
induced condensation at the mixing layer of AGB winds may be the origin of cold
filaments in massive galaxies and galaxy clusters. This naturally explains the
existence of dust and PAH in the filaments.
