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Transit Fitting

By  Charlie Sharzer. Charlie  is an undergraduate at Yale working on model fitting the PH planet candidates to estimate their radii and periods

Hey everyone!  For the last month and a half I have been playing around with a program called LCME (Light Curves Made Easy) written by our own Matt Giguere modeling the Planet Hunters planet candidates.  The program creates a graphical user interface that can be used to evaluate the same light curves you see when looking for transits.  All I have to do is enter the ID# of a promising star, and it displays the curve in a graph.  I click around for a few minutes, marking where I think the transits are on the graph, and the program is able to estimate the location and duration of all potential transits.  It then uses this information to get what we really want: an estimate for the radius and period of the planet candidate.

On the technical side of things, once I point out the parts of the graph with dips in the light curve, I can ask the program to trace a curve mirroring the data using a box-least-squares fit.  The box version of the least-squares method, not unlike finding a standard deviation, attempts to minimize the error between the components of each point’s position vector and a linear (or nonlinear) trendline that fits the data.  Most significantly, it can “predict” the further locations of dips in the light curve that I don’t personally highlight.

If the data is confusing or the least squares fit gives a worse estimate than my own (as was the case last week when I was examining a multiple planet system) I can phase-fold the data to get a more accurate reading.  This stacks the mini-image of each period of transit on top of each other and finds the mean values to create a totally new array that is (hopefully!) more accurate.  I can also use the Levenberg-Marquadt algorithm to minimize the sum of the squares of the deviations of all points from the least-squares-fitted curve, or make a lomb-scargle periodogram to, if the light is broken down into frequencies, find the time at which sample frequencies are mutually orthogonal.

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