We started finding a lot of ‘hot Jupiters’ in the early days of planet hunting simply because, although their existence was not widely predicted, they were the most likely planetary types to trigger our radial velocity detection methods. These star-hugging worlds produced a Doppler signal that readily showed the effects of planet on star, while smaller worlds, and planets farther out in their orbits, remained undetected.

David Kipping (Columbia University) uses hot Jupiters as an analogy when describing his own indefatigable work hunting exomoons. We already have one of these – Kepler-1625 b-i – but it remains problematic and unconfirmed. If this turned out to be the first in a string of exomoons, we might well expect all the early finds to be large moons simply because using transit methods, these would be the easiest to detect.

Kepler-1625 b-i is problematic because the data could be showing the effects of other planets in its system. If real, it would be a moon far larger than any in our system, a Neptune-sized object orbiting a gas giant. In any case, its data came not from Kepler but from Hubble’s Wide Field Camera 3, and with but a single transit detection. In a new paper in Nature Astronomy , Kipping describes it as an ‘intriguing hint’ and is quick to point out how far we still are from confirming it.

This ‘hint’ is intriguing, but it’s also useful in making the case that what exomoon hunters need is an extension of the search space. While the evidence for Kepler-1625 b-i turned up in transit timing variations that indicated some perturbing effect on the planet, how much more useful would such variations be if detected in a survey of gas giants focusing on long-period, cool worlds, of which there is a small but growing catalog? These planets are harder to find transiting because, being so much farther from their star, they move across its surface as seen from Earth only in cycles measured in years. That means, of course, that as time goes by, we’ll find more and more of them.

But we now have a sample of 73 cool worlds that Kipping and colleagues analyze, bringing their exomoon detection toolkit to bear. The method of their selection homes in on worlds with a radius no less than half that of Jupiter, and with either a period of more than 400 days or an equilibrium temperature less than 300 K. A final qualifier is the amount of stellar radiation received from the star. Of the initial 73 worlds, three had to be rejected because the data on them proved inadequate for assessment.

So we have 70 gas giants and a deep dive into their properties, looking for any traces of an exomoon. The team sought planets in near-circular orbits, knowing that eccentric orbits would lower the stability needed to produce a moon, also looking for at least two transits (or preferably more), where transit timing variations could be detected. The model of planet plus moon needed to stand out, with the authors insisting that it be favored over a planet-only model by a factor of no less than 10; Kipping describes this as “the canonical standard of strong evidence in model selection studies.”

Out of the initial screening criteria, 11 planets emerged and were subjected to additional tests, refitting their light curves with other models to examine the robustness of the detection. Only three planets survived these additional checks, and only one emerged with a likely exomoon candidate: KIC-8681125.01. KIC stands for Kepler Input Catalog, a designation that changes when a planet is confirmed, as this one subsequently has been. Thus our new exomoon candidate: Kepler 1708-b-i.

Image: The discovery of a second exomoon candidate hints at the possibility that exomoons may be as common as exoplanets. Just as our Solar System is packed with moons, we can expect others to be, and it seems reasonable that we would detect extremely large exomoons before any others. Image credit: Helena Valenzuela Widerström.

We know all too little about this candidate other than the persistence of the evidence for it. Indeed, in a Cool Worlds video describing the effort, Kipping gets across just how firmly his team tried to quash the exomoon hypothesis, motivated not only by the necessary rigors of investigation but also by frustration born of years of unsuccessful searching. Yet the evidence would not go away. Let me quote from the paper on this:

The Bayes factor of the planet-moon model against the planet only is 11.9, formally passing our threshold of 10 (strong evidence on the Kass and Raftery scale). Inspection of the maximum-likelihood moon fit, shown in Fig. 2, reveals that the signal is driven by an unexpected decrease in brightness on the shoulder of preceding the first planetary transit, as well as a corresponding increase in brightness preceding the egress of that same event. The time interval between these two anomalies is approximately equal to the duration of the planetary transit, which is consistent with that expected for an exomoon . The second transit shows more marginal evidence for a similar effect. The planet-moon model is able to well explain these features, indicative of an exomoon on a fairly compact orbit, to explain the close proximity of the anomalies to the main transit…

That ‘pre-transit shoulder’ shouldn’t happen, and it turns up in all the models used. It looks remarkably like the signature of an exomoon. Here’s the figure mentioned above:

Image: This is Figure 2 from the paper. Caption: Transit light curves of Kepler-1708 b. The left/right column shows the first/second transit epoch, with the maximum-likelihood planet-moon model overlaid in solid red. The grey line above shows the contribution of the moon in isolation. Lower panels show the residuals between the planet-moon model and the data, as well as the planet-only model. BJD, barycentric Julian date; UTC, coordinated universal time. Credit: Kipping et al.

I won’t go through the complete battery of tests the team used to hammer away at the exomoon hypothesis – all the details are available in the paper – but as you would imagine, starspots were considered and ruled out, the moon model fit the data better than all alternatives, the transit signal to noise ratio was strong, and the pre-transit ‘shoulder’ is compelling. Numerous different algorithms for light curve analysis were applied to the modeling of this dataset. Indeed, the paper’s discussion of methods is itself an education in lightcurve analysis.

Describing Kepler 1708-b-i as “a candidate we cannot kill,” Kipping and team present a moon candidate that is 2.6 times larger than Earth and 12 planetary radii from its host planet, which happens to be about the distance of Europa from Jupiter. The exomoon’s mass is unknown, but constrained to be less than 37 Earth masses. The F-class host star, around which the planet orbits every 737 days, is some 5500 light years from Earth.

How such a moon might form raises a host of questions:

There are several broad scenarios for moon formation: planet-planet collisions, formation of moons within gaseous circumplanetary disks (for example the Galilean moons) or direct capture—either by tidal dissipation or pulldown during the growth of the planet. For a gaseous planet, the first scenario is unlikely to produce a debris disk massive enough to form a moon this large. The moon is also at the extreme end of the mass range produced by primordial disks in the traditional core-collapse picture of giant-planet formation, but is easier in the case where planets form by disk instability. Such models also naturally produce moons on low-inclination orbits. Direct capture by tidal dissipation is also possible, although the parameter range for capture without merger is limited. Pulldown capture can produce large moons within ~10 Jupiter radii, with a wide range of inclinations depending on the timescale for planetary growth.

In our own system, of course, we see no moons at Venus or Mercury, and it’s worth asking whether moons are rare for planets close to their host stars. Be that as it may, the supposition here is that if Neptune-sized moons do exist, they’ll constitute the bulk of our early catalog of exomoons, just as hot Jupiters dominated our early exoplanet finds. Indeed, it’s hard to see how anything smaller could be found in Kepler data.

This exomoon candidate is smaller than the previous candidate – Kepler-1625 b-i – and on a tighter orbit. While both these discoveries retain their candidate status, they hint at the possibility that large moons like these may begin turning up in JWST or PLATO data. The authors call for follow-up transit photometry for both Kepler-1708 b-i and Kepler-1625 b-i, adding “we can find no grounds to reject Kepler-1708 b-i as an exomoon candidate at this time, but urge both caution and further observations.”

The paper is Kipping et al., “An exomoon survey of 70 cool giant exoplanets and the new candidate Kepler-1708 b-i,” Nature Astronomy 13 January 2022 (full text).