Modelling the cometary structure of the planetary nebula HFG1 based on the evolution of its binary central star V664 Cas

HFG1 is the first well-observed planetary nebula (PN) which reveals a cometary-like structure. Its main morphological features consist of a bow-shaped shell, which surrounds the central star, accompanied by a long collimated tail. In this study, we perform two-dimensional hydrodynamic simulations modelling the formation of HFG1 from the interaction of the local ambient medium with the mass outflows of its asymptotic giant branch (AGB) progenitor star. We attribute the cometary appearance of HFG1 to the systemic motion of the PN with respect to the local ambient medium. Due to its vital importance, we re-estimate the distance of HFG1 by modelling the spectral energy distribution of its central star, V664 Cas, and we find a distance of 490 ± 50 pc. Our simulations show that none of our models with time invariant stellar wind and ambient medium properties are able to reproduce simultaneously the extended bow shock and the collimated tail observed in HFG1. Given this, we increase the complexity of our modelling considering that the stellar wind is time variable. The wind description is based on the predictions of the AGB and post-AGB evolution models. Testing a grid of models, we find that the properties of HFG1 are best reproduced by the mass outflows of a 3 M⊙ AGB star. Such a scenario is consistent with the current observed properties of V664 Cas primary star, an O-type subdwarf, and bridges the evolutionary history of HFG1 central star with the observables of the PN. We discuss the implications of our study in the understanding of the evolution of AGB/post-AGB stars towards the formation of O-type subdwarfs surrounded by PNe.