Our final talk session of the day is on Multiple Planet Systems, and is chaired by PSU Postdoc Thomas Beatty.
Precise Planetary Masses, Radii and Orbital Eccentricities of Sub-Neptunes from Transit Timing (Daniel Jontof-Hutter, PSU)
Kepler’s period-radius diagram shows us that sub-Neptune planets are really common, which is interesting because we don’t see any of those planets in our own solar system. We have been able to characterize a few planets using RV as well, and some with transit timing variations. With TTVs we are looking at the very slight variations in a planetary orbital period due to slight gravitational tugs on the planet from other planets in the system.
To characterize TTV transiting planets (Kepler-79 in particular), they can assume that all of the planets are co-orbital (they have the same inclinations). They also assume that there are no non-transiting perturbing planets, since the timing variations closely match what they’d expect for that system with just the transiting planets. They can use TTVs to get the masses of these planets and very good constraints on their eccentricities. This is remarkable because the eccentricities are much lower than would be detectable using RV measurements (RV doesn’t give accurate eccentricities below ~0.1). These eccentricities are 0.2% to 2%, and are still detectable.
TTVs also allow them to characterize the star Kepler-79 very well, with only 2% errors. Knowing the star really well, they can characterize the planets very well. Planet d in the system has a super-Earth mass, but a density of only 0.1 g/cm^3, comparable to atmospherics density on Earth’s surface! This means that the planet must have a much larger radius. When we compare the sample of planets characterized by RV to those by TTV, we see that TTV is looking at a very different sample of planets. Each method has their own biases, so they are finding different types of planets. With TTVs we can find super-Earth massed planets at up to 200 day orbital period, but just because they are super-Earth mass, doesn’t mean that they are rocky! They can have a huge range of bulk densities.
On the Origin and Evolution of the Kepler-36 System (Thomas Rimlinger, UMD)
Kepler-36 is a Sun-like star with two planets in a 7:6 mean-motion orbital resonance, one a super-Earth and one a sub-Neptune. This is a very unusual orbital configuration: one is high density, one is low density; they are very tightly packed; this resonance is very rare. How did this happen? Most planet formation models can’t do this.
Theory: protoplanets form far out and migrate inwards, are bombarded by Mars-sized embryos, one gets its mantle stripped, one gets mass accreted. However, few simulations result in a 7:6 resonance. This makes this particular method very unlikely, because there are a few serendipitous things that must happen to make this system via this method.
Their method: take this theory above, and modify it. Their method would not require mantle stripping, originally starting in the strange 7:6 resonance, the planets don’t have to swap places. They would start in the outer parts in a 2:1 resonance, and migrate inwards. The inner planet then just sweeps up leftover rocky material to become the super-Earth, and the outer one is left as a lower density material. They modeled this in a simulation and were able to accurately replicate this system with minimal fine-tuning of the model.
Spacing of Kepler Planets: Sculpting by Dynamical Instability (Bonan (Michael) Pu, University of Toronto)
What can the orbits of multiplanet systems tell us about their formation? There are some systems, like Kepler-11, that have many many planets packed into a very small space. These systems are also so-called “dynamically cold,” with low eccentricities, no real variations, similar inclinations. Looking at the distributions of Kepler multiplanet systems, we see two distinct families of multiplanet systems: those with many planets that are dynamically “cold” and those with fewer planets that are dynamically “hot”, that have the freedom to have large eccentricities, inclinations, or more widely spaced orbits.
Are these many planet, cold systems really stable over long times? They simulated a Kepler-11 type system - planets that are all super-Earths and tightly spaced - and dynamically ran the system to see how long something like that could survive. At planetary spacing of about 11 times the Hill Radius, all of the simulation runs survived for the full simulation time (1 billion years). At that spacing, they found that inclined and eccentric orbits destabilized the systems within 1 million years. You would need to increase the spacing even more to stabilize those systems.
They conclude that some of the Kepler multiplanet systems are at the edge of stability, and so they must have been “sculpted” over eons. There must have once been many more multiplanet systems that developed in unstable formations and dynamically evolved to their lower-number planet states.
Implications for the False-Positive Rate in Kepler Planet Systems From Transit Duration Ratios (Robert C. Morehead, PSU)
This talk only applies to the multiple planet systems detected by Kepler. As a reminder, Kepler has very low-resolution CCDs: each pixel is 4 arcseconds wide. And so there is a lot of room in the Kepler photometry for false-positive, blend scenarios, and binary star systems. When we look at these stars at higher resolution we can find out more about them, but we can’t do that for everything.
The ratio of transit duration can probe whether two planets orbit the same star. This is especially useful for systems where we know there is more than one star, or when we suspect that there is a blending scenario going on. The orbit’s eccentricity and the impact parameter affect transit duration ratio. We expect mostly that these systems have co-planar planets, since they are all transiting. They use simulations to calculate the likelihood of the observed duration ratio under different scenarios: all around one star, and a suite of false-positive scenarios.
They find that most multiplanet systems have a high probability of being associated with the same star. Now, the problem with this is that the parameters used here are the original Kepler stellar parameters, ignoring any followup observations made. So, while they conclude that most multis are likely around the same star, there is always the chance that there is a blended source and therefore a more complicated system than one might originally think.
This concludes our science talks for the day. After this we have another poster pop session and our poster session, followed by dinner.