Astronomers develop model for the distribution of inner planetary systems

Data from the Kepler space telescope, launched more than a decade ago, is still helping astronomers who study planets outside of our own solar system — exoplanets — and unravel the mysteries of planetary systems. Initially, astronomers were surprised that Kepler found so many exoplanets, including hundreds of planetary systems with multiple planets orbiting close to their host star. As astronomers developed models to explain the abundance of inner exoplanets, they encountered a new mystery: “Why did Kepler detect just one planet around so many stars, instead of planetary systems with multiple planets?"

In a recent study published in The Astronomical Journal, the team of astronomers built a model for the population of planetary systems that could explain both of these surprises. The new study combines the physics of planetary orbits and a statistical model to make predictions that could help guide astronomers as they search for additional exoplanets.

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“The Kepler mission provided such a rich and complex data set that one must combine a detailed understanding of both astrophysics and modern statistical methods to properly interpret the data. Years after the mission formally ended, we’re just beginning to understand all that it’s revealed about how common different types of planetary systems are.” said Eric Ford, professor of astronomy and astrophysics in the Eberly College of Science, director of Penn State’s Center for Exoplanets and Habitable Worlds and co-hire at the Institute for Computational Data Science (ICDS).

According to Matthias He, a doctoral student in astronomy and astrophysics, during the primary Kepler mission, the telescope carefully collected a massive amount of data, measuring the amount of light from over 160,000 stars twice an hour for over three years and recognizing fluctuations due to planets passing transiting in front of their host stars.

“One of the ways that we can find planets is to look for these periodic dips in the light curves of these stars, which indicates that a planet is orbiting around it and blocking out some of the starlight as it passes each time,” said He. “If there’s more than one planet in the system and if they all transit in front of the star, then you’ll see multiple different dips at different frequencies, so you can tell from the data that they are multi-planet systems.”

Astronomers had previously analyzed data from Kepler’s meticulous survey of this cosmic light show and found evidence that most stars host multiple sub-Neptune-size planets orbiting very close to their star. However, when astronomers calculated how often Kepler would detect only one of the planets, they significantly underestimated the number of stars for which Kepler detected a single planet. This has become known as the Kepler dichotomy, according to He. To explain this phenomena, some astronomers had suggested that many stars might have only a single planet orbiting close to their star.  Other studies proposed two distinct types of planetary systems with different formation histories. 

However, the researchers’ new model suggests that more complex correlations in the orbital configurations of multiplanet systems could better explain the Kepler data. The statistical model was inspired by the physics of how planetary systems evolve and what combinations of orbits are likely to remain stable for billions of years.

“What the initial studies of Kepler data found is that there may be a population of single planet systems that makes up a big chunk of the systems — or they could still have multiple planets but with highly inclined orbits, so only one planet is seen transiting,” said He. “What our study showed is that it is possible to have a single distribution of planetary systems that can explain both the number of single systems and multi-systems, if the degree of the mutual inclinations is correlated with the number of planets in the same system. More specifically, we found that systems with more planets tend to be more nearly co-planar, or located on the same plane, than systems with fewer planets.”

As an example, He added that our solar system — a multi-planet system — has many planets following orbits nearly in the same plane, situated within a few degrees of each other.

New Earths?

“If we assume a model of what the true distribution of planets might be, then we can simulate what Kepler would detect, and then we can compare what we get with our simulations to the actual data,” said He, whose particular focus is developing statistical models to describe the distribution of planets.

He added that using these models to search for new planets in planetary systems outside of our own is a bit like finding the faint gleam of additional needles in immense fields of haystacks, if you know how many needles are in each haystack and that they are similar. The statistical model of planetary distribution may help their colleagues strategize how to conduct future planet searches to find more exoplanets and to test models for the distributions of additional planets within a planetary system.

Future work

While Kepler provided astronomers the data to measure the frequency of Earth-size planets around nearby stars, most of the planetary systems it finds are so far away that they are hard to study in detail. Penn State recently built two precision spectrographs that will be used to search for rocky planets around nearby stars using a complementary method which detects planets as the pull of their gravity causes stars to wobble slightly. The team plans to make predictions about what additional planets radial velocity surveys are likely to find when they observe stars with one transiting planet. By comparing those predictions with actual survey data, they can test their model and improve planet formation models.

“Because we have a sense of the distribution of these systems, including the ones that don’t transit, we can take our models and better predict what types of planetary systems are out there, including the ones that could be detectable by radial velocity surveys,” said He.

To build the model, the researchers used data collected by NASA’s Kepler mission. To do this, the researchers relied on the computational power of ICDS’s Roar supercomputer.

Daniel Carrera, former assistant research professor of astronomy at Penn State’s Eberly College of Science, and Darin Ragozzine, assistant professor of Physics and Astronomy at Brigham Young University also worked with Ford and He.

NASA and the Natural Sciences and Engineering Research Council of Canada (NSERC) also supported this work.