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Stability and fates of planetary systems

One important lesson that have learnt from the thousands of exoplanets discovered to date is that planetary systems often become dynamically unstable. Instabilities can dramatically change the configuration of the planetary system, including its disruption. The observational evidence for this comes from the multi-planet systems discovered by the Kepler spacecraft that often lie close to instability edge and from the dynamical imprints in other observed systems:

- eccentric orbits observed in radial velocity surveys;

- large spin-orbit angles of hot Jupiters;

- free-floating planets (unbound orbits);

- possible large mutual inclinations between planets, etc...

Thus, in order to understand the history and the evolution of the planetary systems that we observe today it is a fundamental to assess their stability and the possible outcomes that follow after the onset of their dynamical instability.

I have worked in various aspects of this problem and I describe some of the highlights below.

Machine learning and planet stability

In Petrovich 2015c, I provided with an empirical stability boundary for widely-separated two-planet systems with eccentric and inclined orbits. I ran a large set of long-term N-body integrations and use the Support Vector Machine algorithm to provide with the an easy-to-use and accurate boundary that separates stable systems from unstable ones including collisions with the stars and ejections (see Figure).

This stability boundary performs well for a wide range of parameters and can be used (and it has been used!, see the figure below) to constrain the orbits and masses of systems with Jovian planets, typically found in radial velocity surveys.

Figure: Constraints on the third body in the K2-111 (EPIC 210894022) system taken from Figure 7 of Fridlund et al. 2017. Solid lines show the minimum masses required to repro-duce the RV trend, as a function of the third body’s orbital period and eccentricity and dotted lines show the maximum masses allowed for dynamical stability.

Related to this work, my colleague Dan Tamayo led a collaborative work within the University of Toronto (Tamayo et al. 2016) using more sophisticated machine learning algorithms to tackle a harder problem of three-planet systems where a simple functional form like the one above performs poorly.

Dynamical imprints of unstable giant planets on Kepler systems

Huang, Petrovich & Deibert 2017In we tackled a simple question: what are the dynamical consequences of having unstable non-transiting giant planets at >1 AU distances on the typical Kepler-like multi-planet systems?

This question is motivated by observations: i) giant planets are typically found at ~AU distances in eccentric orbits (signature of instabilities); ii) Kepler-like planets (typically ~2-3 Earth radii inside ~0.5 AU) are observed to have a dichotomy: single transiting planets have a broader eccentricity distribution, while multi-transiting have small eccentricities.

Final states of Kepler-like planets as a function of multiplicity and mutual inclination

We found that unstable giant planets can explain this dichotomy, specially the systems with e>0.3 that are hard to explain otherwise. Future missions like TESS, which will discover Kepler-like planets in brighter stars that more amenable for Radial Velocity follow ups, should be able to see whether the giant planets are indeed out there.

See story in New Scientist.

Past and future of some extraordinary planetary systems: TRAPPIST-1 and HL Tau

My colleagues at the University of Toronto and I use N-body integrations to learn about the history and future of recently discovered multi-planet systems:

i) In Tamayo, Rein, Petrovich, & Murray 2017 we argued that the long-term stability of the TRAPPIST-1 system is due to the resonant configuration that arose from its early orbital migration when the gas disk was present. See detailed story and other links here .

ii) In Simbulan, Tamayo, Petrovich, Rein, & Murray 2017 we argued that the young HL Tau system will likely become unstable and its final state after ~Gyr timescales shares many properties with the observed and more mature planetary systems.

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