Thursday, June 17, 2010

PDFs, CDFs, and two new clusters





I have added two new clusters to my list, NGC 1664 and NGC 6940, with an assortment of stars in each. I found a cluster that is potentially quite usable, but no one else had an age estimate, so I will work with that after constructing my CMD fitting procedure.

Even though I will fit the masses properly after I have derived my own properties for the clusters, I wrote the program to compute the probability distribution function (PDF) and cumulative distribution function (CDF) for a star given an isochrone. It involves calculating the probability of a given location in the star's Gaussian distribution on the isochrone. For each part of the isochrone, I break it into a certain distance away in the sigma v direction (vertical) and sigma b direction (slope 1) from the star. Each distance is then divided by the respective standard deviations and I take the square root of the sum of the squares. This is the (data - fit)/sigma that goes into the Gaussian equation.
The CDF is merely the integral of the PDF. The PDF is normalized.

The hardest part of this process is actually tracking down the original source of the UBV values to arrive at the error of U and V. Some of the sources are old or have moved around, making it either difficult or impossible to find, so I only managed to compute this for two stars.

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