We determined &upsilon And's proximity to instability by running a lot of simulations and determining what types of orbits are stable or unstable. This approach was necessary because there was no easy way to determine stability due to the chaotic nature of planetary systems.
I expanded my investigations as more planetary systems were discovered, and found that many systems show similar behavior (Barnes & Quinn 2004). In fact, if I were an alien astronomer looking at our Solar System with the same approach we use, I would think the Solar System also seemed to lie near stability.
That was the situation in 2004 when I received my Ph.D. When I moved back to Tucson, my collaboration with Richard Greenberg led us to investigating why systems are close to instability, and searching for a way to measure how close planetary systems are to instability. It turns out for two-planet systems (which is the case for the majority of systems), there is an analytic description of a type of stability known as Hill stability. This type of stability is a little funny, and at first glance appears to not be that useful (a system is "Hill stable" even if the outer planet can be ejected), and we'd prefer to understand stability in a more generic way (i.e. "stable" means no planets are ejected). Well, it turns out that the old equation for Hill stability (derived in the early 80's) does a remakarbly good job of predicting the boundary of stability (Barnes & Greenberg 2006b). We had taken our first step toward quantifying the stability of a planetary system.
The Hill stability equation only applies to systems with only two planets that are not in a resonance. So next Rick and I turned to understanding how the Hill equation was related to the stability boundary in the presence of a mean motion resonance. It turns out that resonances provide stable orbits beyond the boundary predicted by Hill stability theory (Barnes & Greenberg 2007b). This relationship is shown in Fig. 1. We also found that all but one resonant system's best-fit placed it in this region that would normally be considered unstable.
Fig. 1 - Comparison of numerically determined stability boundaries (whiter regions are more stable) with that of the Hill stability equation (the contour lines). e is eccetricity and Pc/Pb is the ratio of orbital periods. Click here for a full resolution version.
The large fraction of systems that appear to lie near instability made us wonder about the few that aren't near instability. The nature of the detection method is that smaller planets can be harder to find. This observation led to the Packed Planetary Systems (PPS) hypothesis that I developed along with Sean Raymond, Thomas Quinn and Richard Greenberg. That hypothesis proposes that when there are gaps large enough for a planet to be on a stable orbit, there is a planet there. Our work to identify where other planets may be is described in more detail in the astrobiology page. The next step in understanding the stability of planetary systems is to determine stability boundaries in systems of more than two planets. We think we know the answer, and I am actively trying to prove it right now (things look very promising). Check back later to see how it's coming along.
Last Update: 31 July 2007