AGN feedback and multiphase gas in giant elliptical galaxies

Recent observations have found extended multi-phase gas in a significant fraction of massive elliptical galaxies. We perform high-resolution three-dimensional hydrodynamical simulations of two idealized elliptical galaxies -- one representing a typical galaxy characterized by initial conditions conducive to the development of thermal instability and the other one less likely to develop thermal instability -- in order to study the development of thermal instability and the formation of multi-phase structures. We analyze the interplay between radiative cooling, momentum-driven AGN feedback, star formation, and stellar feedback from both young and old stars. We find that in one class of elliptical galaxies, the entropy of the hot halo gas rises sharply as a function of radius, and the hot halo is thermally stable and run-away cooling can only happen in the very center of the galaxy. In other class of ellipticals, the hot halo gas has a cooling to free-fall time ratio close to 10, and the non-linear perturbation driven by AGN feedback can cause the hot gas to frequently precipitate into extended multi-phase filaments. Both multi- and single-phase elliptical galaxies experience cooling-driven AGN feedback cycles. Interestingly, AGN feedback maintains the multi- or single-phase nature of the halo but does not turn multi-phase galaxies into single-phase ones or vice versa. Some of the extended cold gas in the multi-phase galaxy also forms young stars. The level of star formation and its spatial distribution are in excellent agreement with {\it Hubble} observations of nearby elliptical galaxies.