The quest for Magrathea planets. II. Orbital stability of exoplanets formed around double white dwarfs

Abstract

Planetary formation might occur at different stages of the stellar evolution of compact binaries. In recent years, the formation of second-generation planets has been tested in circumbinary discs formed by the ejection of stellar material from double white dwarf (DWD) binaries. In these environments, planets ranging from sub-Neptunian to giant masses can form and migrate to within 1 au of the central binary. Nevertheless, studies on the orbital stability of such systems have yet to be undertaken. In this work, we use N-body simulations to study the stability of multi-planet systems formed around compact DWDs in both resonant and non-resonant configurations over timescales of a few million years. We track the occurrence of catastrophic events and employ a variety of metrics, e.g., orbital spacing, centre-of-mass variations and Normalized Angular Momentum Deficit, to explore the outcomes of their evolution. Furthermore, we evaluate the potential for detecting these systems in their final configurations with the Laser Interferometer Space Antenna (LISA) mission by measuring the overall gravitational-wave frequency shift amplitude induced by their planets. Our results show that planets orbiting DWDs can be stable over the studied timescales. While planetary systems starting with two-planets are more likely to survive unaltered, planetary systems with three, four or five planets, experience catastrophic events that cause them to lose some of their original planets, ending up hosting only two surviving planets in the majority of cases. This increases the number of two-planet systems by 122% with respect to their initial abundance and creates a single-planet population amounting to 7% of the totality of systems. The majority of these single-planet systems are potential candidates for LISA. Concerning multi-planet systems, a handful of systems could be detected.