Today’s post is part two completing the series by guest blogger Darin Ragozzine. Darin is a Caltech Ph.D. and currently a postdoc at the Smithsonian Astrophysical Observatory. Expert on planetary orbital dynamics and transit light curves. Member of the Kepler TTV/Multiples Working Group and Kepler Science Team Collaborator, co-author on Kepler-9, 11, and multiple other Kepler Team papers. And occasional PH user and commenter.
Last time, I introduced the idea that systems of multiple transiting planets were the most valuable systems for understanding the formation, evolution, and dynamics of planetary systems. If transiting planets are sweet, then multiple transiting planets around the same star are wicked awesome, as we’d say here in Boston. Detailed investigations by the Kepler Team into some of these systems has illustrated their value, discussed more in a technical paper here.
The Kepler-9 system has two Saturn-like transiting planets with periods of about 19 and 38 days orbiting a sun-like star, with an additional super-Earth oribting every 1.56 days, known as planets b, c, and d, respectively. The two larger planets are perturbing one another’s orbits, with the strength of the perturbation amplified by the fact that the ratio of the periods is very near 2. This means that the maximum gravitational force between the planets (when they come closest to one another) always happens at a similar point in the orbit and this “resonance” allows for the usually weak planet-planet perturbations to add coherently in an observable way. When there are no perturbations to the gravity between the star and planet, the transits occur exactly periodically. When another planet is introduced, it will pull and push on the transiting planet causing it to transit slightly earlier and later than the perfect periodicity. This is illustrated in an animation on the Kepler website (here).
The importance of the non-periodic transit times, called transit time variations or TTVs, was predicted by dynamicists in 2005, but not really seen until Kepler-9, when transits were hours off the predicted times. Furthermore, when one planet’s period was getting longer, the other’s period was getting shorter, exactly what you would expect if the two planets were interacting. (Don’t worry, after a couple of years, this trend will reverse and the planets are stable for a very long time in this dance.) The fantastic thing about TTVs is that they measure the mass of the planet without anything more than just the Kepler lightcurve. (Usually radial velocity or other hard measurements are required to measure planet masses.) I want to make sure that Planet Hunters understand this because you should NOT give up if the transits or eclipses aren’t exactly periodic (though they should be relatively close). I also want to point out that where radial velocity measurements are currently unable to measure the mass of Earth-size planets in the habitable zone of a Sun-like star, TTVs may be up to this challenge (though it requires favorable circumstances). I should point out that the majority of multi-transiting systems will have TTVs that are too weak even for Kepler to detect (see http://arxiv.org/abs/1102.0544).
This method of TTVs was also critical for understanding the six (six!) transiting planets orbiting around Kepler-11. Minute deviations from the periodic times, measurable only because Kepler is so amazingly precise, allowed us to measure masses for the five inner planets. The importance of this for Kepler-9 and Kepler-11 is to point out that interpreting the TTV signal was only possible because all of the planets were transiting. Although it is possible (and exciting) to detect the presence of a non-transiting planet because of its TTV perturbations on a known transiting planet, this is hard to do with confidence, even with Kepler data. When the perturbing planet is also transiting you know more-or-less exactly where it is and that makes it so much easier to interpret. Hence, TTV interpretation is where systems with multiple transiting planets are extra valuable.
Other really useful aspect of multi-transiting systems is that they have a much stronger chance of being real planets than “false positives”… there’s no way to explain the 6 fabulous periodic dips in Kepler-11 besides 6 transiting planets. Furthermore, multi-transiting systems allow researchers to do more precise “comparative planetology” between planets in the same system. I’d take 2 transiting planets in the same system over 10 transiting planets in different systems, especially when it comes to understanding planet formation (but I’m biased). For the two planets in Kepler-9, a paper has already come out that shows how having the two planets in the same system makes their interior composition easier to interpret.
Finally, using the large sample of multiple transiting planet candidate systems from Kepler, I was able to find that the majority of these systems are explainable by a population of multiple small planets in orbits with only small tilts between them. While precise radial velocities have started to reveal this population, Kepler blew the lid off of this population and also showed that they were nearly coplanar… which is, again, only possible because of these systems with multiple transiting planets. This is just a taste of the large amount of interesting science we were able to do with the multiple systems from Kepler. For a technical look, you can see our paper on these systems.
Of course, the Kepler team is adept at identifying multi-transiting candidates and has access to more than the public data used by PH. However, there are still many examples where multiple transiting planets can be easily seen in the data available to PH. Therefore, DO NOT STOP when you have identified one transiting planet candidate or an eclisping binary. Look for multiple signals! You could especially scour the stars with known planet candidates (from Kepler or PH) for additional dips that might be due to an extra valuable additional planet. Again, I’d take another good candidate in a system with another candidate over 10 single-candidate systems (though I’m biased). Furthermore, I encourage the PH Science Team to treat these with extra care given their usefulness. Note that even if one or both of the periodic signals is due to an eclipsing binary, it is still very interesting for further study.
Now, based on what we’ve seen from the population of multiple transiting planet candidates (see http://arxiv.org/abs/1102.0543), I can give you some tips on searching for additional planets. Longer-period planets in the same system will have longer transits, in general. We’ve also found that the sizes of the planets actually tend to be similar or maybe a bit larger, so the depths is likely to be similar even if the period is longer. Interior (shorter-period) planets are more likely than exterior planets from geometric arguments. A fraction of additional planets will be located near periods 0.48-0.5, 0.63-0.69, 1.45-1.55 and 2.00-2.05 times longer than known planets. Also note that planets at the same period are possible, though the best candidate for this “Trojan” configuration, KOI-730, has a much stronger interpretation in a non-Trojan configuration, so we no longer think that any of the identified Kepler candidates have this signature.
So, go get ’em! I see that the #multitransit tag has not been used, so if you see anything that looks like a really good multi-transiting planet candidate, please apply. I will note that the #trinary tag has been used on objects that look like variable/pulsating stars, which can have multiple periods of variability, not on systems with multiple transiting planet candidates. Also remember that eclipsing binaries will often have two dips, one large and one small (but sometimes the same) that occur with the same period. For understanding eclipsing binary and transiting planet light curves (and a variety of other astrophysical phenomena) I highly recommend the labs run by Kevin Lee at U Nebraska-Lincoln.
The #phmulti, #multiple, and #multipletransit tags have also been used, sometimes correctly, to identify these systems. We are not here discussing multiple transits by the same body… those are great since they allow us to identify the candidates in the first place, but the presence of multiple transit dips by the same planet (same period, depth, shape, etc.) is not so exciting. For an example of a multi-transiting system in PH, see Kepler favorite, KOI-70, a 4 planet candidate system on Planet Hunters Talk .
Thank you for your planet hunting and let’s find those multi-transiting systems!
Darin