## What Shapes the Edge of a Planetary System?

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**Title: **Can Cold Jupiters Sculpt the Edge-of-the-multis?

**Authors:** Nicole Sobski and Sarah Millholland

**Authors’ Institutions: **Wellesley College and Massachusetts Institute of Technology

**Status: **Published in *ApJ*

The Kepler mission revealed thousands of transiting exoplanets. Through this unique data set, we have come to understand much more about exoplanet demographics and the occurrence rates of different kinds of planets. In particular, we now understand that the most common type of planetary system is what we refer to as a “compact multi-planetary system.” That is to say, a system of multiple small planets (less than 4 Earth radii each) where each planet orbits in similar, short timespans (usually less than about 50 days). Studies of the full Kepler data set show that these “compact multis” are ubiquitous across the galaxy. Furthermore, these systems are shown to have a high rate of intra-system uniformity, sometimes called “peas-in-a-pod” architecture. Planets within a compact multi often have similar radii and similar spacing in their orbital periods.

But in a system of multiple transiting exoplanets of such uniformity, what causes the system to “end”? That is, what causes the pod to be filled up with peas? A new study looks into one possible force that may “sculpt” the edge of a compact multi-planet system: cold Jupiters. A cold Jupiter is a planet that has the mass of our own solar system’s Jupiter and is widely separated from its host star. The authors explore if and how the existence of a cold Jupiter at wide separation from an inner compact multi arrangement might determine how the pod gets filled with peas.

To test this, the authors needed a data set of known compact multis. They turned to the Kepler data set and selected the systems with at least four transiting planets. This left them with 279 planets in 64 systems. Next, they compiled the previously measured masses of these planets; only 60 of 279 had masses, so for the remainder they used a well-described mass–radius relationship to estimate planet masses. Planet mass is a crucial input for this study as mass is the primary parameter needed for dynamical studies, which inherently rely on gravitational forces.

To determine if and how a cold Jupiter could sculpt the edge of the inner compact system, the authors devised a dynamical study. Dynamical studies test how planets interact with each other through their gravitational influence on one another; often a researcher will test to see if a certain configuration of planets is stable or if it is unstable. In an unstable system, some or all of the planets get gravitationally kicked out of the system. Using a simulation software called the Stability of Planetary Orbital Configurations Klassifier (SPOCK), which takes in a list of planet masses and a few basic orbital parameters, the authors were able to compute the stability of the system over a specified time span. The authors added a simulated cold Jupiter (with parameters drawn from random distributions) to a planetary system with real planet masses and orbits and then determined the system’s stability over 1 billion years. For each of the 64 systems in the sample, they performed this test 10,000 times, noting the probability that the system was stable or not over that time span.

Each test resulted in one of three outcomes: unstable, fully stable, or metastable. Within the context of this study, metastable meant that the system was stable in about half of the simulations. Unstable simulations mean that the system will be ripped apart by gravitational interactions. The injected cold Jupiters that result in unstable configurations are not considered plausible edge-sculptors, then, because we *do* see planets in these systems; if the presence of a cold Jupiter made the system unstable, we wouldn’t see planets in the system. Next, the stable simulations represent injected cold Jupiters that had no effect on the inner system. These cold Jupiters exist at too wide a separation from the inner system for gravity to play a role in sculpting the edge of the pea pod. Therefore, these planets were also not considered plausible edge-sculptors. The metastable simulations, in which the odds of the system falling apart were between 30% and 70% (above 70% was considered fully stable), are the most interesting. These simulations correspond to systems in which the injected cold Jupiter had a real effect on the inner compact system and could potentially sculpt the edge of the inner compact system, as shown in Figure 1.

Therefore, the authors conclude that cold Jupiters likely do not help sculpt the edge of compact multi-planet systems. If they could, we would have found them in real data; since we don’t find them in real data, they must not exist in the compact multis studied here. Even though this experiment led to the rejection of the original hypothesis, it is nevertheless a fascinating result that tells us a bit more about the way exoplanet systems may form and evolve.

*Original astrobite edited by Lindsay DeMarchi.
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## About the author, Jack Lubin:

Jack received his PhD in astrophysics from UC Irvine and is now a postdoc at UCLA. His research focuses on exoplanet detection and characterization, primarily using the radial-velocity method. He enjoys communicating science and encourages everyone to be an observer of the world around them.