We’re all interested in transiting planets smaller than the Neptune-sized Gliese 436b, and sure to find many of them as our methods improve. One day soon, via missions like COROT or the upcoming Kepler, we’ll be studying planets close to Earth mass and speculating on conditions there. But here’s a scenario for you: Suppose the first Earth-mass detection isn’t of a planet at all, but a moon orbiting a much larger planet? That challenging scenario comes from David Kipping (University College London) in a new paper on the detection of such moons.
I should be calling them ‘exomoons,’ the satellites of planets around other stars. It’s reasonable enough to assume they’re out there in the billions given the nature of our own Solar System. And compared to the multitude of giant planets found thus far, an Earth-mass exomoon in the habitable zone would seem to offer a far more benign environment for life. The trick, of course, is to pull off a detection, for most exomoons are going to be smaller than the Earth. Varying orbital distances will make the moon hard to spot during a transit, at times hiding the moon behind or in front of the planet. But Kipping notes that variations in the time a planet takes to transit its star could be one clue to the presence of such a moon.
It’s an interesting thought, but does it tell us enough? The transit timing variation (TTV) signal varies according to both the mass of the exomoon and its orbital separation from the planet it circles. It becomes impossible using transit timing variations alone to determine the mass of the exomoon without plugging in some value for its orbital separation. It’s a conundrum unless a secondary method can be found that works in conjunction with transit timing variations to tease out the exomoon’s parameters. Kipping finds that method in transit duration variation (TDV), which offers a signal of the same magnitude, and one that can be larger than TTV itself.
Measure multiple transits over a period of time and periodic changes in its duration are what make up the TDV value. In a recent email, Kipping said this about the relationship between TTV and TDV:
The moon and planet both orbit a common centre of mass, albeit a position very close to the planet’s centre. The effect of this is that the planet seems to wobble… As you can see, not only the position, but the velocity of the planet is shifting constantly. The spatial wobble causes TTV and the velocity wobble causes TDV. Hence, you will see why they must be 90 degrees out of phase!
Here is an animation of the process (all effects greatly exaggerated for clarity):
[kml_flashembed movie=”https://www.centauri-dreams.org/wp-content/images/wobble.swf” height=”250″ width=”400″ /]
I send you to the paper for the relevant equations, but using them Kipping is able to show that transit duration variation allows us to measure the moon’s mass without making assumptions about its orbital separation. It then becomes possible to derive the orbital period itself. A hypothetical planet identical to GJ 436b, for example, but with a 35.7 day period in a circular orbit would be in the habitable zone of the star it circles. An Earth-mass exomoon around such a world would be an achievable target. Studies of GJ 436b show that such a transit timing variation signal would be well within reach of existing instruments. From the paper:
This suggests that the detection of the exomoon should be presently possible through TTV from the ground and feasible with TDV in the near future. This illustrates that even ground-based instruments could detect an Earth-like body in the habitable zone using timing effects.
All of which points to data future observers should be gathering:
We also ?nd that current ground-based telescopes could detect a 1 [Earth mass] exomoon in the habitable zone around a Neptune-like exoplanet. The author would therefore encourage observers to produce not only their mid-transit times, but also transit durations for each transit, rather than composite lightcurve durations. This will allow constraints to be placed on the presence of exomoons around such planets.
The science of exomoons takes us yet deeper into understanding exoplanetary systems. Not only am I jazzed about the scientific implications here, but I’m reminded to ask readers for recommendations on science fiction treatments of habitable moons around gas giants. Who knows what settings may become imaginable as we begin the detection of such moons through planetary transits? The paper is Kipping, “Transit Timing Effects due to an Exomoon,” accepted by Monthly Notices of the Royal Astronomical Society and available online.
Addendum: The original paper on using transit timing variations to detect exomoons is Sartoretti and Schneider, “On the detection of satellites of extrasolar planets with the method of transits,” Astronomy and Astrophysics Supplementary Series 134 (1999), pp. 553-560 (abstract). In an email, Dr. Schneider notes that the COROT team had already begun searching for TTV signatures before the appearance of Dr. Kipping’s paper. It will be interesting to see how TTV and TDV play out in the analysis of any resulting data.