# DDA 2015 – Dynamical stability of imaged planetary systems in formation – Applicaon to HL Tau

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Daniel Tamayo (U. Toronto)

#### Abstract

A recent ALMA image revealed several concentric gaps in the protoplanetary disk surrounding the young star HL Tau. We consider the hypothesis that these gaps are carved by planets, and present a general framework for understanding the dynamical stability of such systems over typical disk lifetimes, providing estimates for the maximum planetary masses. We argue that the locations of resonances should be significantly shifted in disks as massive as estimated for HL Tau, and that theoretical uncertainties in the exact offset, together with observational errors, imply a large uncertainty in the dynamical state and stability in such disks. An important observational avenue to breaking this degeneracy is to search for eccentric gaps, which could implicate resonantly interacting planets. Unfortunately, massive disks should also induce swift pericenter precession that would smear out any such eccentric features of planetary origin. This motivates pushing toward more typical, less massive disks. For a nominal non-resonant model of the HL Tau system with five planets, we find a maximum mass for the outer three bodies of approximately 2 Neptune masses. In a resonant configuration, these planets can reach at least the mass of Saturn. The inner two planets’ masses are unconstrained by dynamical stability arguments.

#### Notes

• Manyexoplanetary systems are highly eccentric
• Can we back out what the ICs might have been?
• HL Tau
• age ~1 Myr
• Outer gaps are too close to contain giant planets
• but if planet-cleared, must be giants, not smaller
• dynamically unstable for larger planets
• But outer 3 gaps are near 4:3MMR chain
• can put planets there (at least for 1 Myr)
• Solution(?)
• Grow the planets in situ in resonance
• Conclusions
• Giant planets could be possible explanation for the gaps
• Precession from massive disks can significantly alter locations of resonances
• $\phi = \lambda_1 – \lambda_2 – \varpi_{12}$
• $\dot{\phi} = n_1 – n_2 – \dot{\varpi}_{12}$
• Hal Levison: can’t grow planets that fast, so something else must be going on here.