Rory's Extra-Solar Planets Page

I work on the stability and dynamics of extra-solar planetary systems, and maintain a web page listing their dynamical interactions. Many planets have been detected so far (see exoplanets.org), but I mainly work on systems with more than 1 planet since Isaac Newton solved the equations of motions for a star and 1 planet about 300 years ago. Planetary systems are chaotic and their motion can only be accurately modeled with computer simulations. Unfortunately most of the planets' orbits are poorly constrained, and my analyses of them are limited. But as time goes on the orbits keep getting better. Because of these poor constraints I focus my research on trends, similarities and differences between the systems. Specifically I have tried recently to classify systems quantitatively. I have so far identified two parameters that can characterize the interaction between two planets. These are observables of multiple planet systems which can be compiled into distribution functions. Planet formation models (see my planet formation page) can then be evaluated against these distribution functions. The first quantity is the "packing parameter", &gamma, which measures how close two planets approach each other over long timescales (~100,000 years). I normalize &gamma by the "mutual Hill radius", a measure of the gravitational power of a planet, relative to its host star. The current (Nov 2006) distribution of &gamma is in Fig. 1.

Fig. 1 - The observed distribution of packing parameters of multiple planet systems. The dashed line is a possible lower limit for dynamical stability (it is the limit for two planets on circular orbits). Most pairs with large values have 1 planet that has undergone tidal circularization. There appears to be a significant number of planets near instability.

The second quantity is a little more complicated. Over long periods of time, the shapes of orbits change. Orbits are ellipses and have long axes. We can measure the positions of these long axes over time relative to each other. This difference becomes impossible to quantify if the eccentricity of one planet reaches zero (there is no long axis!). This second quantity, &epsilon, measures how close a pair of planets comes to this particular configuration (called a "secular separatrix"). Fig. 2 shows the distribution of &epsilon .

Fig. 2 - The distribution of proximities to a secular separatrix among observed multple planet systems. There is a significant fraction of systems with small values. Values less than 0.01 are certainly near-separatrix, 0.01 - 0.1 are marginally near-separatrix. The origin of this distribution is unknown at this point, but one theory is that early on in the system's evolution, an additional planet was ejected from the system, leaving the remaining planets with this type of motion.

The large fraction of systems near instability (Fig. 1) led to the Packed Planetary Systems (PPS) hypothesis that I developed along with Sean Raymond, Thomas Quinn and Richard Greenberg. But if you examine Fig. 1 closely there are a few planetary pairs that have pretty large gaps between them (&gamma is big). These gaps might be smaller, due to observational errors (indeed the masses of the bodies are not well known at all, so &gamma could, in principle, be arbitrarily small), or, more tantalyzing, they may hold extra planets! One system that Sean and I focused on was 55 Cnc. The outer two planets in this system have a very wide gap (&gamma = 17). We ran simulations that tried to find where extra planets might be. Fig. 3 shows the most likely orbits of saturn-mass objects in this system.

Fig. 3 - The most likely location of a putative saturn-mass planet in the 55 Cnc system. The dashed lines designate the habitable zone. If a satellite like Europa was in orbit about a gas giant planet in that location, it would have a liquid water surface.

Sean and I, along with Nathan Kaib, found that 55 Cnc is an ideal place for a habitable planet (right mass, orbit and water content). In Fig. 4 we show results for 10 simulations of terrestrial planet formation in this system. The dashed lines are the habitable zone, and color corresponds to water content. about 30% of the simulations we ran produced habitable planets. But don't write your congressman about a mission to this planet just yet. 55 Cnc is about 41 light years away, so we won't be visiting any time soon.

Fig. 4 - Possible orbits and compositions of putative terrestrial planets in 55 Cnc. Orange and green planets (note the color of the Earth in the Solar System row) with horizontal lines inside the dashed vertical lines would probably be habitable (they'd have liquid water on the surface, if they had an atmosphere like the Earth's.) Also note that a lot of planets form in the habitable zone, but without enough water initially. If a later source could douse these planets with water (like comets), they might become habitable.

This latter work received a lot of press. I was interviewed live by Ted Simons on KTAR radio, Phoenix. You can hear the whole interview here (for the record, 55 Cnc is in the constellation Cancer; the danger of live radio I guess). So what does all this mean? Extrasolar planets are telling us a lot about how planets form, and how our Solar System fits into the Universe. Research like this can tell us where to find habitable planets and life, maybe even intelligent life!


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