#gj581

Our N-body simulations show that the innermost planet of the GJ 581 system (planet E) needs to have an eccentricity below .2. Any higher and planets E and B get so close to each other that they can interact and make the system unstable. Last time I posted some chi^2 maps that show where the best fits to the radial velocity data are. 

It all boils down to this: The simulations say eccentricity of planet E should be below 0.2 and the radial velocity measurements say an eccentricity of ~ 0.3 best explains the data. How far away from the best fit value can we go before we are being unreasonable?

Using an F-test we can compare different models where the only variation is the eccentricity of E. The F-Test will tell us how likely it is that the models are the same.

After some talking with the maintainer of Systemic I got a script to make chi squared maps. What you see is a plot of how the chi squared value changes when you change orbital parameters of planet e.

I was also able to recreate the Eccentricity of E vs Chi^2, Stellar Jitter, and RMS plots in a much less tedious way!

I started from the best fit I could get in systemic chi sqr ~ 2.7 and let the eccentricity, mean anomaly, and longitude of periastron vary. Below are the plots:

Sometimes during simulations the eccentricities of the planets will shift. I wanted to see if the change in eccentricity had anything to do with how long the simulation would last.

Here are the plots:

For the most part the planets didn't change their eccentricities during their simulated lifetime. I filtered out all the runs with no change:

I've figured out how to pick out the runs where the orbits of E and B intersect.

Out of about 22,000 runs, the orbits of E and B intersect only 200 times. Here is the contour plot of those doomed Mercury runs.