Kepler mission exoplanet transit data analysis using fractal imaging

S. Dehipawala; G. Tremberger Jr.; Y. Majid; T. Holden; D. Lieberman; T. Cheung

doi:10.1117/12.930004

15 October 2012 Kepler mission exoplanet transit data analysis using fractal imaging

S. Dehipawala, G. Tremberger Jr., Y. Majid, T. Holden, D. Lieberman, T. Cheung

Proceedings Volume 8500, Image Reconstruction from Incomplete Data VII; 85000T (2012) https://doi.org/10.1117/12.930004
Event: SPIE Optical Engineering + Applications, 2012, San Diego, California, United States

Abstract

The Kepler mission is designed to survey a fist-sized patch of the sky within the Milky Way galaxy for the discovery of exoplanets, with emphasis on near Earth-size exoplanets in or near the habitable zone. The Kepler space telescope would detect the brightness fluctuation of a host star and extract periodic dimming in the lightcurve caused by exoplanets that cross in front of their host star. The photometric data of a host star could be interpreted as an image where fractal imaging would be applicable. Fractal analysis could elucidate the incomplete data limitation posed by the data integration window. The fractal dimension difference between the lower and upper halves of the image could be used to identify anomalies associated with transits and stellar activity as the buried signals are expected to be in the lower half of such an image. Using an image fractal dimension resolution of 0.04 and defining the whole image fractal dimension as the Chi-square expected value of the fractal dimension, a p-value can be computed and used to establish a numerical threshold for decision making that may be useful in further studies of lightcurves of stars with candidate exoplanets. Similar fractal dimension difference approaches would be applicable to the study of photometric time series data via the Higuchi method. The correlated randomness of the brightness data series could be used to support inferences based on image fractal dimension differences. Fractal compression techniques could be used to transform a lightcurve image, resulting in a new image with a new fractal dimension value, but this method has been found to be ineffective for images with high information capacity. The three studied criteria could be used together to further constrain the Kepler list of candidate lightcurves of stars with possible exoplanets that may be planned for ground-based telescope confirmation.

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S. Dehipawala, G. Tremberger Jr., Y. Majid, T. Holden, D. Lieberman, and T. Cheung "Kepler mission exoplanet transit data analysis using fractal imaging", Proc. SPIE 8500, Image Reconstruction from Incomplete Data VII, 85000T (15 October 2012); https://doi.org/10.1117/12.930004

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KEYWORDS

Fractal analysis

Exoplanets

Image compression

Stars

Fourier transforms

Image analysis

Space telescopes

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