Stability of a cluster-disrupted mean-motion resonance (chain) in HR 8799 and PDS 70

Context. HR 8799 is a planetary system in which four observed planets potentially form a mean-motion resonance chain. Although they potentially form a resonance chain, it is not clear from the observations whether they are in mean-motion resonance. Similarly, PDS 70 is a planetary system in which two observed planets are potentially in mean-motion resonance. Aims. We study the stability of HR 8799 and PDS 70 under external perturbations to test how they respond under resonance and under mean-motion resonance. Methods. We integrated the equations of motion of the planets in HR 8799 and PDS 70 beginning with a system either in resonance or in mean-motion resonance and studied the stability of HR 8799 and PDS 70 in isolation and in a star cluster. In the star cluster, we accounted for the effects of passing stars. The dynamics of the star cluster were resolved using the Lonely Planets module in AMUSE. Results. HR 8799 and PDS 70 in mean-motion resonance are stable, whereas in non-resonance they dissolve on timescales of 0.303 ± 0.042 Myr and 1.26 ± 0.25 Myr, respectively. In a cluster, the non-resonant planetary system of HR 8799 is slightly more stable than in isolation but still dissolves on a timescale of 0.300 ± 0.043 Myr, whereas the resonant planetary system remains stable for at least 0.71 Myr. In contrast, the non-resonant planetary system of PDS 70 is approximately as stable in a cluster as in isolation and dissolves on a timescale of 1.03 ± 0.20 Myr, whereas the resonant PDS 70 planetary system remains stable for at least 0.83 Myr. Conclusions. Considering the more stable solutions of mean-motion resonance for HR 8799, we argue that the planetary system was born in mean-motion resonance and that the mean-motion resonance has been preserved. If HR 8799 was not born in resonance, then the probability of its survival until the present day is negligible. Similarly, we argue that the planetary system of PDS 70 was probably born in mean-motion resonance and that the mean-motion resonance has been preserved. We also find it possible for planetary systems with a broken mean-motion resonance chain to survive longer in a perturbing cluster environment than in isolation.