Orbital Stability and Secular Dynamics of the Proxima Centauri Planetary System

The two innermost planets of the Proxima Centauri system are separated by just 0.02 au, inducing strong gravitational interactions between them. We assess this interaction by leveraging fast orbital stability indicators and find that orbital stability is very likely if the initial eccentricities of planets b and d are less than $\sim 0.2$, but cannot confirm stability at larger values. We find that stability is not strongly affected by the true masses of the planets or by the distant planet c. However, mutual inclinations between 95$^\circ$ and 142$^\circ$ often result in unstable motion. We further explore the long-term evolution of the orbits in these stable regions of parameter space and find that circularization can take over 5 Gyr. This tidal evolution could support surface energy fluxes in excess of 1 W m$^{-2}$ for over 1 Gyr, possibly affecting planet b's habitability.