Type Ia Supernova Progenitors and Surviving Companions within the Symbiotic Channel

The symbiotic channel of Type Ia supernovae progenitors is crucial for explaining the observed circumstellar material in some Type Ia supernovae. While extensive numerical and observational efforts have been dedicated to exploring the progenitor system, limited emphasis has been placed on studying the surviving companions arising from the symbiotic channel. In this paper, we present a numerical study of the symbiotic systems using {\tt MESA} as potential Type Ia supernova progenitors. We conduct 1260 binary stellar evolution simulations, over a wide range of parameters, incorporating the optically thick wind model developed by Hachisu et al., and predict the post-impact evolution of these surviving companions. We classify four types of progenitor systems based on the evolutionary stage of the companion at the onset of the explosion: red giant companions, with or without prior helium flash events, and asymptotic giant branch companions, with or without the thermal pulsing phase. After the SN impact, a blue dwarf star with either a helium or carbon-oxygen core is left behind. However, if a small portion of the envelope ($\gtrsim$ 0.3\%) remains on the core of the surviving companion, the overall post-supernova evolution may remain similar to its pre-explosion state, albeit slightly fainter, making observation a challenging endeavor.