The HR 8799 Debris Disc: Shaped by Planetary Migration and a Possible Fifth Outermost Planet

Context. The HR 8799 system, hosting four giant planets between a warm and cold debris disc, and an extended dusty tail beyond, serves as an ideal laboratory for studying planetary formation and evolution. The debris discs have been observed across various wavelengths, and the planetary properties are well-constrained. Nonetheless, there are still open questions regarding the role of the planets in shaping the debris discs. Aims. We investigate the system's evolution with the aim of understanding how planetary migration shapes its architecture, both in terms of planets and the disc. Methods. We performed $N$-body simulations to model the HR 8799 system. We examined the orbital evolution of the known four super-Jupiter planets through the course of simple, imposed migration in a gaseous disc as they perturb an external, massless planetesimal disc. We also explore the impact of introducing a fifth planet on the dynamical and morphological aspects of the disc. Results. The planets migrate outward as a result of their imposed interactions with the gaseous disc while maintaining their resonant configuration. This outward migration excites the planetesimal disc, producing a transient scattered population. While a four-planet system partially reproduces the observed cavity between the star and the cold debris disc, the inclusion of a fifth low-mass planet appears to be crucial for better reproducing key morphological aspects of the cold debris disc. Conclusions. This model provides a novel explanation for the architecture of HR 8799. Outward planetary migration, combined with mean motion resonant interactions and a fifth, low-mass planet, can effectively replicate the observed planetary architecture and cold debris disc characteristics. Our findings underscore the potential important role of planetary migration in shaping debris discs.