Mathematics – Logic
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aas...211.1317k&link_type=abstract
American Astronomical Society, AAS Meeting #211, #13.17; Bulletin of the American Astronomical Society, Vol. 39, p.757
Mathematics
Logic
Scientific paper
In this study, we investigate the use of features in the Fourier Bessel power spectra to aid in the classification of galaxies. Let I(r,θ) represent a galaxy image function in polar coordinates. The image function may be represented as a two-dimensional Fourier-Bessel series. The coefficients in the expansion, An,i and Bn,i , multiply the radial Bessel functions of order n, Jn(αn,i r/R) and the polar functions cos(nθ) and sin(nθ), respectively. The coefficients are known as the Fourier-Bessel Transform (FBT) of I(r,θ). The parameter αn,i is the ith root of the Bessel function of the first kind of order n, Jn(x), and R is the radius to the edge of the galaxy image. We have computed the coefficients An,i and Bn,i for a number of representative galaxy images of each morphological classification type to generate representative FBT specta. Spectra are presented as 3D plots of the modulus of An,i and Bn,i versus the root number, i, and the order, n. Radial structure (such as spiral arms) are manifest in the spectra as peaks in amplitude at certain values of i, whereas, azimuthal variations are seen as amplitude peaks at particular values of n. We also investigate the possibility of automatically classifying galaxies by minimizing the Euclidean distance of the galaxy's FBT spectrum to typical spectra of each morphological type. This research has been funded by an internal grant from the Andrews University Office of Scholarly Research.
Kutzner Mickey
Riess Jeff
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