The new paper in Science Advances Evidence for a large exomoon orbiting Kepler-1625b (open access!) uses a sophisticated combination of occultation light curve simulation, signal processing and statistical analysis to show that there is a significant chance that they have identified an exomoon, a moon orbiting an exoplanet.

But it's too sophisticated for me to understand how this Hubble data indicates a potential moon. Terms like "detrending", "Markov chain Monte Carlo", and "Bayesian evidences" are beyond me.

Is it possible to choose one of those plots and add an arrow to say "this blip here, this is Kepler-1625b potential moon"? If not, is it possible to at least explain in a simple way what it is from this analysis that has led them to believe there may be a moon there?


Exomoons are the natural satellites of planets orbiting stars outside our solar system, of which there are currently no confirmed examples. We present new observations of a candidate exomoon associated with Kepler-1625b using the Hubble Space Telescope to validate or refute the moon’s presence. We find evidence in favor of the moon hypothesis, based on timing deviations and a flux decrement from the star consistent with a large transiting exomoon. Self-consistent photodynamical modeling suggests that the planet is likely several Jupiter masses, while the exomoon has a mass and radius similar to Neptune. Since our inference is dominated by a single but highly precise Hubble epoch, we advocate for future monitoring of the system to check model predictions and confirm repetition of the moon-like signal.

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"Detrending" refers to removing systematic effects that are caused by the spacecraft, detector or the environment and which are not part of the particular star. The systematic trends can be caused by a large variety of things; the main ones affecting Kepler are drifts in position and focus, thruster firings to compensate for angular momentum build up in the reaction wheels and the roll of the spacecraft every quarter. Because these trends are systematic and affect all the stars that Kepler sees in a similar way, the effects can be modeled and the trends removed - detrending. There are some examples in slide 15 and 16 of this Kepler workshop presentation which shows the "raw" brightness measurements (labeled 'SAP') and the detrended data on the right (labeled 'PDC').

You can see examples of this in the Supplementary Materials. On page 47 in Figure S2, you can see the data before detrending and you can see the dips caused by the transiting exoplanet (Kepler-1625b) but these are superimposed on long-term upwards or downwards slopes or curves. Detrending removes these effects (which will be common to all the stars, not just to Kepler-1625b's star) allowing you to get corrected flat light curves, enabling the search for the much smaller exomoon signal.

The evidence for the exomoon is in two parts. The timing of the planet transit that was observed by HST in October 2017 was 77.8 minutes early compared to the predicted time from the Kepler transits. This is shown (but not very well) in Figure S12 in the Supplementary Materials. If there was no exomoon or anything else tugging on Kepler-1625b, we would have expected the HST transit (the data point at transit epoch 7) to be on the extended black prediction line at an O-C value (y axis) of +77.8 minutes, ( off the top of their plot as it scaled). The second piece of evidence is that is if the transit is early, then they should expect to see the shallower/smaller transit of the exomoon after the transit as it would be on the other side of the orbit with the exoplanet. This is what they show in the bottom half of Figure 4; no matter which detrending method they use for the HST data, they see a small shallow dip after the main transit is over, centered around a time (x value) of 3056.25. This gives more confidence that the exomoon interpretation is real and not an artifact of the detrending process.

Modified Figure 4 of paper show proposed exomoon transit

What they are saying after Table 1 is that the Δχ2 (the measure of the change in the goodness of fit of the model as you add extra things to the model) is better with the moon models (models Z and M) over one that just accounts for the transit timing variations (model T). This is because the presence of the exomoon is predicted to cause changes in the length and depth of the exoplanet transit but these are harder to measure than the change in timing.

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    It was some weird JavaScript-y plot thing so this didn't seem that easy but it's there now (Couldn't figure out quickly how to get arrowed straight lines in GIMP, so you'll have to manage without out... ;-) – astrosnapper Oct 4 at 18:17
  • – uhoh Oct 4 at 18:23
  • I've added the annotated version of Figure 4, I hope you don't mind. "Is it possible to choose one of those plots and add an arrow to say 'this blip here, this is Kepler-1625b potential moon'?" – uhoh Dec 5 at 8:46

Monte Carlo refers to a technique of running multiple simulations, each with the input data very slightly changed, usually one variable at a time. After teens or hundreds of thousands of simulations you end up with a probability plot - if these trend towards a particular distribution you can gain confidence that the data is correct.

Bayesian analysis looks more at similarities (which is why it is often used for identifying spam: if it looks more like these thousand examples of spam than those thousand valid emails then it probably is spam)

So this work uses probability theory, and the specific tools mentioned to provide a likelihood measure. And in this case, the balance of probability from the data is that it is an exomoon.

So there will not be a blip that looks like a moon - there will be a vast cloud of data that happens to be more similar to possible models of data expected from an exomoon than from other alternatives considered.

  • Thanks! So somewhere within Table 1 there's a $\Delta \chi^2$ that says "there may be a moon"? – uhoh Oct 4 at 7:23
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    Lol - that is a way of looking at it. I see it more as that Delta is slightly closer to exomoon than all these other possibilities... – Rory Alsop Oct 4 at 7:31

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