Exomoons continue to be elude us, though they’re under intense study. One detection strategy is called Orbital Sampling Effect, as explained in the article below. I’ll let Michael Hippke describe it, but the intriguing fact is that we can work with these methods using existing datasets to refine our techniques and actively hunt for candidates. Michael is a researcher based in Düsseldorf, Germany. With a background in econometrics, statistics and IT, he mastered data analysis at McKinsey & Company, a multinational management consulting firm. These days he puts his expertise to work in various areas of astrophysics, and most recently appeared here in our discussion of his paper on Fast Radio Bursts (see Fast Radio Bursts: SETI Implications?).

by Michael Hippke


Our own Solar System hosts 8 planets (plus Pluto and other “dwarf planets”), but 16 large moons with radii over 1,000km. And we have detected thousands of exoplanets – planets orbiting other stars – but not a single exomoon. The question of their existence is interesting, as some exomoons might in fact be habitable. Lately, there has been some speculation that, overall, there might be more habitable moons than planets in the universe. Consequently, we really want to know more about moons!

Moons are, by definition, smaller than their host planets, and thus harder to detect. Various search methods have been proposed – with the HEK project (Hunt for Exomoons with Kepler), led by David Kipping, being the most prominent team. A novel, promising method has been developed by René Heller in 2014, dubbed the “orbital sampling effect” (OSE). As with exoplanet transits, this method stacks many (dozens or ideally hundreds) of planet transits, and searches for the signature of a moon in this stack. While planet transit shapes are rather simple, the moon curves turn out the be very complex.


Image: A star with a transiting planet and its moon. The angled area shows the inclination of the moon orbit. Orbit positions beyond the dashed line are not undergoing transit, and are thus not observable.

In my recent work, I have processed data from the Kepler space telescope to search for this effect. I also worked with the “scatter peak,” an exomoon detection method described by Attila Simon (Konkoly Observatory, Hungary) and team in 2012. It is based on the fact that the geometrical exomoon configuration is very likely different during every exoplanet transit: On some transits, the moon might be ahead of the planet, on other transits behind it. When stacking many transits, at a given phase folded time, one gets a flux loss in some cases, and not in others. This results in increased scatter (photometric noise) when compared to out-of-transit times.

While the sole use of the scatter peak is problematic due to stellar noise, it can be used to confirm or reject certain signals. Not surprisingly, the struggle against stellar noise, instrumental jitter and other glitches has required the development of a complex statistical framework. While the Kepler data quality is at the very limit for exomoon hunting, a few very interesting results could be achieved.

The first result is sensitivity. What moons can we detect with Kepler and the OSE? Learning the answer to this will be useful for the assessment of future time-series photometry space missions, such as TESS or PLATO 2.0. With Kepler, the limit seems to be about 0.3 — 0.4 Earth radii for a moon to be detected, which is about the size of Ganymede. In many cases, where the host stars are dimmer, or noisier, only larger moons can be detected. Despite these limitations, my work shows that the OSE is a promising method, which will one day, with better data quality and/or processing, likely succeed and find moons!


Image: The smallest radii detectable with the OSE in Kepler data are ~0.4 Earth radii. In many cases, the data and method only allows for the detection of larger moons. These are calculated limits, not real observations.

The second result is the ‘average moon’ effect. While no single moon could be detected, it is possible to “super-stack” a larger sample of planet-OSEs to estimate the average moon size in different samples. For very short-period planets with orbits shorter than about 15 days, no moons are seen. This is in agreement with stability arguments: The closer the planet to the star, the more the star “pulls” on the moon and tries to swallow it. The critical distance is not perfectly clear, but believed to be at ~15-day orbits. In my analysis, I find that the average moon signal comes up for periods over 35 days. In the sample of 35- to 80-day orbits, I find an average moon radius of about 2,000km (roughly like our moon). This estimate doesn’t tell how many planets actually have moons, or how many multiple moon systems are included in this average. It is for future studies (and telescopes) to determine this. But it is exciting that one can try.

The third result is about individual candidates. A small sample of planets shows prominent OSE-like signals justifying an in-depth analysis. It must be clearly said that, very likely, all of these will turn out to be false-positives. For some cases, it might even be possible to show that they cannot be moons, for example because some configurations are not stable over longer time frames. But this is not a bad result, for when we find false-positives, we can add the detection mechanism for these to our algorithm, and improve future searches.


Image: Planet transit (straight line), moon effect due to the OSE (dashed line) and real datapoints (dots with error bars). In this case of Kepler-264b, the data are in favour of a moon interpretation, although this cannot be considered a detection, as detailed in the paper.

Personally, I would expect that the first moon(s) that will be found will be at the long (large/massive) end of exomoon distribution, as was the case for exoplanets. This comes from a selection bias: Large things are easier to see, and will thus be detected first. It will not mean that all moons are giants, as not all planets are Hot Jupiters (which were the first planets detected). Interesting times are ahead!

For more information, the paper is Hippke, “On the detection of Exomoons: A search in Kepler data for the orbital sampling effect and the scatter peak.” It has been accepted by the Astrophysical Journal for publication. A preprint is available.