Kepler mission exoplanet transit data analysis using fractal imaging

摘要

The Kepler mission is designed to survey a fist-sized patch of the sky within the Milky Way galaxy for thediscovery of exoplanets, with emphasis on near Earth-size exoplanets in or near the habitable zone. The Keplerspace telescope would detect the brightness fluctuation of a host star and extract periodic dimming in thelightcurve caused by exoplanets that cross in front of their host star. The photometric data of a host star could beinterpreted as an image where fractal imaging would be applicable. Fractal analysis could elucidate theincomplete data limitation posed by the data integration window. The fractal dimension difference between thelower and upper halves of the image could be used to identify anomalies associated with transits and stellaractivity as the buried signals are expected to be in the lower half of such an image. Using an image fractaldimension resolution of 0.04 and defining the whole image fractal dimension as the Chi-square expected value ofthe fractal dimension, a p-value can be computed and used to establish a numerical threshold for decisionmaking that may be useful in further studies of lightcurves of stars with candidate exoplanets. Similar fractaldimension difference approaches would be applicable to the study of photometric time series data via theHiguchi method. The correlated randomness of the brightness data series could be used to support inferencesbased on image fractal dimension differences. Fractal compression techniques could be used to transform alightcurve image, resulting in a new image with a new fractal dimension value, but this method has been foundto be ineffective for images with high information capacity. The three studied criteria could be used together tofurther constrain the Kepler list of candidate lightcurves of stars with possible exoplanets that may be plannedfor ground-based telescope confirmation.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.