The orbital architecture and stability of the $\mu$ Arae planetary system

We re-analyze the global orbital architecture and dynamical stability of the $\mu$ Arae planetary system. We have updated the best-fit elements and minimal masses of the planets based on literature radial velocity (RV) measurements, now spanning 15 years. This is twice the RVs interval used for the first characterization of the system in 2006. It consists of a Saturn- and two Jupiter-mass planets in low-eccentric orbits resembling the Earth-Mars-Jupiter configuration in the Solar system, as well as the close-in warm Neptune with a mass of ~14 Earth masses. Here, we constrain this early solution with the outermost period to be accurate to one month. The best-fit Newtonian model is characterized by moderate eccentricities of the most massive planets below 0.1 with small uncertainties ~0.02. It is close but meaningfully separated from the 2e:1b mean motion resonance of the Saturn-Jupiter-like pair, but may be close to weak three-body MMRs. The system appears rigorously stable over a wide region of parameter space covering uncertainties of several $\sigma$. The system stability is robust to a five-fold increase in the minimal masses, consistent with a wide range of inclinations, from 20 to 90 deg. This means that all planetary masses are safely below the brown dwarf mass limit. We found a weak statistical indication of the likely system inclination I~20-30 deg. Given the well constrained orbital solution, we also investigate the structure of hypothetical debris disks, which are analogs of the Main Belt and Kuiper Belt, and may naturally occur in this system.