Exomoons of Circumbinary Planets

TL;DR

This study investigates whether exomoons can survive the inward migration of circumbinary planets within protoplanetary discs. Using population synthesis of 2000 binary–planet–moon systems and N-body integrations with disc-migration and planetary oblateness, the authors classify moon outcomes into four archetypes: smoons, ploonets, no-moon cases, and collisions. They find that moons formed within roughly 5–10% of the planet's Hill radius tend to survive full migration, about 38% become long-period ploonets, 29% remain as moons, 32% collide, and 1% eject from the system; 18% of surviving moons reside in the habitable zone. The results imply that CBPs can host habitable moons, that a population of wide, long-period ploonets could be detectable via microlensing (e.g., Roman), and that circumbinary dynamics may contribute to free-floating planetary-mass objects. These findings guide observational strategies for exomoons with future facilities and illuminate the dynamical pathways shaping moon formation in dynamically active multi-body systems.

Abstract

Confirmation of the first exomoon remains elusive. Although several exomoon candidates exist around single stars, there are currently no candidates around circumbinary planets (CBPs). Most circumbinary planets are thought to form far from the host binary and migrate through the protoplanetary disc. Therefore, an exomoon of a CBP represents a fascinating yet complex and evolving four-body system. Their existence (or absence) would shed light on the robustness of moon formation and evolution in dynamically active planetary systems. In this work, we simulate the orbital evolutions of exomoons around migrating CBPs. We show that for fully migrated CBPs, a moon is capable of surviving the migration if it is formed within $\sim5-10\%$ of the planet's Hill Radius, well within the currently proposed range at which moons are thought to settle in the planetary disc for giant planets. Even though all known CBPs are gas giants, 18\% of the surviving moons in our sample are within the habitable zone, giving credence to circumbinary habitability, albeit hosted by moons rather than planets. $38\%$ of moons escape their host planet early in the migration and become long-period CBPs (i.e a multi-planet circumbinary system). Nearly one-third of exomoons collide with their host planet, and $1\%$ are ejected from the system entirely. This last class presents another pathway for producing free-floating planetary mass objects, like those discovered recently and expected from the Roman microlensing survey.

Figures (7)

• Figure 1: Radius and orbital period of all confirmed transiting planets (black dots), compared with the 12 Kepler (blue circles) and 2 TESS (pink circles) circumbinary planets.
• Figure 2: Top: Semi-major axis of the moon with respect to the binary for three archetypal systems: a saved moon ("smoon", red), a moon-turned-planet ("ploonet", yellow), and a completely ejected moon ("no moon", blue). The three samples shown display ideal conditions and are not used in our final dataset, hence starting beyond 5 AU. Since the moon orbits a planet, its osculating semi-major axis calculated relative to the binary stars oscillates around its host planet's orbital radius, as can be seen as the thick parts in the plot. The ploonet example shows a moon that is initially orbiting the planet but eventually leaves the planet's Hill sphere after 0.8 Myr and starts to orbit the binary as a CBP. Bottom: Time evolution of $a_{\mathrm{moon}}/r_{\mathrm{Hill}}$ for the same three archetypal systems. For the retained moon (red), $a_{\mathrm{moon}}/r_{\mathrm{Hill}}$ initially increases due to $r_{\mathrm{Hill}}$ decreasing as the planet migrates inwards. At roughly 0.1 Myr, the planet reaches the disc truncation radius, so the $a_{\mathrm{moon}}/r_{\mathrm{Hill}}$ ratio plateaus at 0.26. For the ploonet (yellow) and ejected moon (blue), $a_{\mathrm{m}}$ becomes undefined about the planet once the moon moves beyond the Hill radius.
• Figure 3: Three example simulations demonstrating a saved moon, "smoon" (top), a moon-turned-planet, "ploonet" (middle) and an ejected moon, "no moon" (bottom). The distance scale is logarithmic. The depicted sizes of the stars and the planet are scaled by the body's mass. The stability limit (and corresponding error bars) pictured by the vertical purple line is 1.5 times the limit calculated via the criteria in stabLimCalculation, with the error bars taken from the same paper.
• Figure 4: Flowchart showing the four expected outcomes of a moon orbiting a circumbinary planet that migrates in towards the inner edge of the circumbinary disc (denoted by an orbital period of $P_{\rm disc}$). If the planet does not migrate completely to the disc edge, then the moon is more likely to be saved (a "smoon"), as the first bifurcation criterion is likely to be met.
• Figure 5: Results from $N$-body simulations showing how the initial moon-planet and planet-binary separation impacts the outcome. The smoon, ploonet, no moon, and collision archetypes are labeled via red, yellow, blue, and gray dots, respectively. The dot size corresponds to that planet's mass on a log scale, as depicted. As predicted, moons that are initially very close to their host planet are retained, whereas moons initially far from their host planet easily become unstable. The binary separation also plays a critical role, as a wider binary makes it more likely for a planet to retain its moon. Less massive planets did not migrate as far and were able to retain their moons, as seen by small red dots with a large $a_{\mathrm {moon}}$ to $r_{\mathrm {Hill}}$ ratio. The collisional outcome populates all regions of parameter space in which moons are ejected from their host planet.