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A.C. McDaniel (U.C Santa Cruz)
Ongoing radial velocity surveys have revealed the existence of multiple planet systems such as GJ876. Such systems are proving to be both a great challenge and a great opportunity to those who study them. Traditional independent Keplerian fitting techniques are insufficient to model the strong planet-planet interactions that are present in resonant systems. We analyze the performance of a fully self-consistent method for determining the orbital parameters of a multi-planet system which, while computationally challenging, breaks the M*sin(i) degeneracy of Keplerian fitting. The code is a Levenberg-Marquardt minimization routine which drives a Bulirsch-Stoer integrator. Initial orbital elements are fed to the integrator which produces a radial velocity curve that is compared to the data. The minimization routine attempts to find minima in the Chi-Squared space defined by the set of all possible initial conditions.
The space that must be searched for the correct orbital solution is very complex and is littered with false minima and perhaps more interesting statistically equivalent, but dynamically separate minima. This complexity is due to several factors including the complicated coupling between different orbital elements, the non-zero error in the data, and possible aliasing effects due to the sampling of the data. Given these complications, the multidimensional minimization technique must be given a reasonably good initial guess in order to find an acceptable solution. We describe ways of determining initial guesses for our algorithm that include 1) understanding the shape of the Chi-Squared space and 2) maximizing the amount of information extracted from the Periodogram. As the baseline and accuracy of radial velocity surveys grow more multi-planet systems are sure to be found. As they are, the development of efficient, self-consistent fitting techniques will become increasingly important in understanding the data.
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Bulletin of the American Astronomical Society, 34, #3
© 2002. The American Astronomical Society.