Smoons, Ploonets, and Circumbinary Planets, Oh My!

Title: Exomoons of Circumbinary Planets

Authors: Ben R. Gordon, Helena Buschermöhle, Wata Tubthong, David V. Martin, Sean Smallets, Grace Masiello, Liz Bergeron

First Author’s Institution: Department of Physics & Astronomy, Tufts University

Status: Under review at ApJ, preprint posted on Arxiv, Dec 3 2024

Do you believe in exomoons?

The concept—a moon orbiting an exoplanet—makes sense. But despite all the exoplanets we’ve discovered, only two exomoon candidates have been proposed, namely around Kepler-1625 b and Kepler-1708 b, with their validity cast into serious doubt. The difficulty of detecting exomoons comes from that with our current technology, there are limited ways to find them. These ways are direct transit detection, transit timing variations, and transit duration variations, as explained beautifully in this Astrobite. JWST, CHEOPS, and futurely Roman might be able to detect them, given their increased sensitivity.

But the discovery of exomoons remains a tantalizing prospect, as they would represent a “missing link” in planetary formation theory, and might change how we think about the habitable zone. Despite the diversity of worlds in our own solar system, from our own beautiful Earth to turbulent gas giants Jupiter and Saturn to potato-shaped lumps like the moons of Mars, we still don’t know enough to say definitively how our own Moon formed, other than that around 4.5 billion years ago, something crashed into the Earth, the resulting shrapnel becoming the Moon. Also under investigation within our solar system is whether there is life on Europa and Enceladus, moons orbiting Jupiter and Saturn respectively. Finding an exomoon would tell us a lot about formation conditions in other systems, and if we find one around a gas giant, it could be a clue as to whether Europa and Enceladus are one-offs, or whether potentially habitable moons around giant planets are more common than we think.

In the meantime, researchers have been very happy to theoretically examine exomoon formation and habitability with the use of computer and numerical simulations, which today’s authors do. They simulate the orbital evolution of exomoons around a weird and wild type of exoplanet: circumbinary planets.

Gee, exomoon! How come your system lets you have two stars?

Circumbinary planets (CBPs) are planets that orbit two stars, much like Tatooine in Star Wars. Only about 14 of these planets have been discovered through the transit method, all of them being gas giants. The authors assert that although no exomoon candidates around CBPs have been found, they might be worth considering as exomoons are thought to be more easily found around planets with longer orbital periods (already a challenge since our observations favor shorter-period planets), and CBPs tend to have longer periods compared to other transiting exoplanets we’ve found. Some of them also reside in the habitable zone, meaning that if they happened to have a exomoon we haven’t detected, that exomoon would also be in the habitable zone.

Of course, all of that assumes exomoons would survive in a CBP system in the first place—its addition to such a system sets up a “four-body problem,” a gravitational configuration whose trajectory is notoriously hard to predict without certain assumptions and which invites chaos. There’s also the issue of planetary migration, the movement of a planet away or towards a central star (or stars, in the case of CBPs) due to interactions with the protoplanetary disk. The authors of today’s paper state that most known transiting CBPs are the product of migration toward their central stars in an interchange of torques related to disk properties.

This begs the question, if CBPs migrate closer in towards their host stars, will their (hypothetical) exomoons follow as well? Let’s find out.

The Sims but for circumbinary planet exomoons

The authors use REBOUND, a software program commonly used in astrophysics to simulate objects moving under the influence of gravity, plus REBOUNDx, an add-on that includes migration options, to simulate exomoons around CBPs undergoing migration. They create two populations of CBPs: Population 1, which has no limit on planetary radius; and Population 2, which limits planetary radii to more than 3 Earth radii to match the observed population of CBPs; starting within 1 to 5 AU of their central stars, and place an exomoon the size and mass of Ganymede somewhere within the Roche limit for their respective CBP and 48% of their respective CBP’s Hill radius, the region of a nonmigrating planet where moons may be supported. The value of 48% was chosen because it is at that point that a satellite orbiting a migrating planet will fall off.

The authors then let the simulations run over a million years, keeping track of each exomoon’s parameter ɣ, which they define as the exomoon’s semi-major axis divided by the CBP’s Hill radius. This parameter turns out to determine three simulation outcomes:

• Smoon:  ɣ is less than 0.48 the whole time, letting the CBP keep its exomoon, i.e., a “successful moon.” This exomoon will follow the CBP as it migrates.
• Ploonet: as the planet migrates, its Hill radius shrinks to the point ɣ becomes more than 0.48, essentially leaving the exomoon to fend for itself, becoming a planet in its own right, a “moon turned planet,” a ploonet!
• No moon (nmoon?): the exomoon is ejected from the system altogether, which happens if ɣ exceeds 0.48 as the CBP approaches its central stars so closely that it runs the risk of becoming unstable, which can be approximated as when the orbital period of the CBP is equal to 4 times the period of debris moving in the inner edge of the protoplanetary disk.

The authors summarize these findings in a handy flowchart, shown here in Figure 1.

Figure 1 (figure 5 in the paper): A flowchart showing how one can predict whether a CBP exomoon winds up as a smoon, ploonet, or “no moon,” based on ɣ and the CBP’s orbital period compared to that of the inner protoplanetary disk.

What to make of all this? Well, there’s good news and bad news for CBP exomoon believers: the good news is that most simulated exomoons remain physically bound to the overall CBP system. The bad news is most of these exomoons continue to exist as ploonets, ceasing to be exomoons. But the smoon scenario occurs in 30% of these simulations, which is nothing to sneeze at! It also might be possible, the authors speculate, that the “no moon” outcome could explain some rogue planets we’ve detected. The authors also find that about 22% and 33% of ploonets and smoons respectively reside in the habitable zone, raising hopes for potential exomoon habitability.

You never know—the first exomoon to be detected could be around a circumbinary planet!

Featured image credit: Helena Valenzuela Widerström

Edited by: Lucas Brown