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The Perils of Exoplanet Radial Velocity Fitting.
Philip Cowperthwaite AY193 Final Project Presentation May 6th 2015


A Primer On RV Curves

Source: ESO


Plenty of Data
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A collection of ~850 RV curves for stars with confirmed planets from the Caltech Exoplanet Archive (http://exoplanetarchive.ipac.caltech.edu/) Data contains date of observations, spectroscopically determined radial velocity, and errors. (e.g., data is pre-reduced)

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The Model and The Method
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The Keplerian Model (Hou et al. 2011)

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Numerical Methods:
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MCMC sampling of parameter space using M-H algorithm. Solve for mean/true anomaly using root-finding from Brent (1973).

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Gaussian Likelihood Function

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Parameter space strongly degenerate. How to deal with # of planets?

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Turns Out This is Tricky...
Sometimes it works ok.... ... but usually not so much.


So, what's going wrong?
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General data quality issues:
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No standardization in data from the archive. Planet not always RV confirmed?

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Determination of priors/initial conditions.
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Strong degeneracies in orbital parameters.

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Poor likelihood function. Unaccounted for physics in the model.
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e.g., Stellar variability is also sinusoidal...


What Could We Do Better?
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More sophisticated samplers -- Simple M-H method is not sufficient.
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Ensemble samplers (Goodman & Weare 2010) Affine-Invariant Samplers (Hou et al. 2011) "Fusion MCMC" Methods (Gregory et al. 2011) Diffusive Nested Sampling (Brewer et al. 2011)

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Better determination of priors - numerically optimize likelihood function first. In general, automation of RV fitting will require more data standardization and sophisticated statistics.

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