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Kyle Pearson committed Oct 24, 2023
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# N-body Retrievals

Coming soon to EXOTIC...

In the meantime checkout: https://github.com/pearsonkyle/Nbody-ai
## Prior estimate

The lomb-scargle periodogram from our ephemeris fitting code can be used to estimate a prior for an N-body retrieval. Transit timing variations (TTV) alone are not sufficient to uniquely constrain a single solution, instead multiple modes can exist which give the same amplitude/periodicity of perturbation. The distinguishing factor will rely on radial velocity measurements but none the less this approach can help limit the search space for potential planets. Below is a figure highlighting results from a grid of N-body simulations where we construct a mask based on the amplitude and periodicity found in the O-C diagram. The mask is used to constrain the N-body retrieval (i.e. search space) which significantly reduces the number of simulations needed to find a solution.

![](ttv_prior.png)

Match your Lomb-Scargle periodicity to this chart to determine the mass and period of a potential outer planet. A digitized version of this plot is coming soon... Occasionally, the O-C perturbation will experience an additional periodicity with only a single perturber, it is suspected to be due to precession of the inner planet's orbit. For now, just worry about the 1st order solution when matching to your observations.
The example code has recently been refactored from [Nbody-AI](https://github.com/pearsonkyle/Nbody-ai) and is still in development. Some retrievals not work entirely... please be paitent and report any issues to our slack.

![](grid_500_150.png)
If you make use of this code please cite:

The example code is still in development and may not work entirely... please be paitent and report any issues to our slack.
https://ui.adsabs.harvard.edu/abs/2019AJ....158..243P/abstract

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