The paper has been published in the Astronomical Journal!! View it here.
Kepler-80, formally KOI500, is a five planet system about 1100ly away from Earth! The cool thing about this system is that all five orbits fit inside 1/10 AU. We wanted to discover the masses of the four outer planets as well as their orbits. The data we got from the Kepler Space Telescope was only the brightness of the star; however, when a planet passes in front of (or transits) its star, the observed brightness decreases. Because the planets are so close to each other, a planet can gravitationally perturb the orbits of the other planets, causing it to transit either early or late. These transit timing variations, or TTVs, can be used to fit the orbits and masses of the planets. Unfortunately, the inner-most planet is dynamically decoupled from the other planets and has a very weak TTV signal, so we can only estimate its mass using mass-radius relationships.
We ran thousands of Levenberg-Marquardt minimizations of chi-squared using the IDL algorithm mpfit. We had a variety of different metadata sets for the TTVs. It was my job to determine which set was best for our fitting. To do this, I fit a polynomial sinusoid to each data set, and subtracted this from the data. The set with the smallest residuals was used. This was Dan Fabrycky's short cadence data.
We wanted to verify that the fitter was actually working properly, and that the results were actual best-fits and not justify parameters preferred by the fitter. In addition, we wanted to confirm that assuming circular and coplanar orbits would not grandly affect the outcome of our masses. To do this, I created multiple sets of synthetic data, and fit them under "untrue" assumptions. For example, I created a data set where the orbits all had small but non-zero eccentricities (as we think Kepler-80 is) and fit it assuming circular orbits. Of the thirteen synthetic sets that were created and fit, eleven of them returned the "true" masses within one sigma errors, and the remaining two were returned within two sigma error bars.
Another awesome thing about Kepler-80 is that it is a perfect example of a STIP (possibly even of a SUTIP). Systems with Tightly-spaced Inner Planets (STIPs) are made of 3-7 relatively small and closely packed planets. The periods of the planets fall between 1-100 days, though most are between 3 and 20 days. STIPs need to be stable, and have small mutual inclinations because of this. Some STIPs have longer-period companions (such as HD 10180, 55 Cnc, GJ163) and there seems to be a disjoint population called Systems with Ultra-Tightly-spaced Inner planets, or SUTIPs, that are more compact than STIPs and remarkably less common. Although Kepler found a plethora of STIPs, very few SUTIPs have yet to be discovered. See poster from Sagan Exoplanet Workshop 2015!
Yet another thing that makes Kepler-80 interesting is it's interlocking three-body resonances. This means that many configurations of three planets can be in a three-body resonance which is caused by the commensurabiliy of the periods that causes a repeated geometrical configuration that is stable to pertubations. Many potential three-body configurations are librarting with amplitudes of 1-2 degrees, but due to the nature of the interlocking resonances, it is difficult to tell which resonance the planets are actually in. As you can see, none of these resonances are librating around 0 or 180 degrees, which is typical of three-body resonances, but this is not the first time this has happened; KOI-730 is in a similar situation, and this is due to the torque from the other, non-resonance planets that causes the resonance center to shift from the nominal value. As a side note, although the periods are near 3:2, 3:2, and 4:3 resonance, none of these two-body resonances are librating.
It is clear in the above gifs that this system has strong 3-body resonances as well as 4-body resonances. The 3-body resonances can be seen as the 1st and 2nd planets are librating back and forth in the same region of their orbits and the 4-body resonance is seen by noting that the 1st and 2nd planets move in sync. The innermost planet is not dynamically coupled, and therefore moves about randomly in all three gifs.
Presentations and Publications
The paper has been published in AJ!! It can be seen here.
This work was presented at AAS: Division for Planetary Sciences on November 13, 2015. Here is the abstract.
Click here for the poster on STIPs from the Sagan Exoplanet Workshop 2015.