Using a Novel Hybrid Algorithm for Two-Dimensional Model of Brightness Profiles in Elliptical and Spiral Galaxy Images
Juan Carlos Gómez, Olac Fuentes · ASPC · 2006
J. C. Gomez, O. FuentesComputer Science Department, INAOE, Tonantzintla, Puebla, Mexico,72000Abstract. In this work we present a novel two-dimensional fitting al-gorithm to model brightness profiles of spatially well resolved ellipticaland spiral galaxies from an image. The algorithm is based on EvolutionStrategies (ES), an optimization technique that has been used in otherastronomical problems with good results (Gomez et al.2004), and LocallyWeighted Linear Regression (LWLR). The problem can be seen as an op-timization problem because we need to minimize the difference betweenthe observational image and the model we produce.For the fitting we used two models: the de Vaucoleurs profile and anexponential disk. The model is constructed with generalized ellipses thatfit brightness profile of the image following the equations given by thetwo models used. In the end, we have an artificial image that representsthe light distribution in the real image. Results presented here show thatES+LWR is a well suited method to work with two-dimensional fittingin spiral and elliptical galaxy images.1. IntroductionGalaxies span a wide range of morphology and luminosity, and a very useful wayto quantify them is to fit their light distribution. Fitting profiles for galaxies inone dimension is frequently done because it suffices for some applications andis easy to implement (Karttunen 1996), but many studies now resort to two-dimensional fitting, because many well-resolved nearby galaxies are often poorlyfitted by standard one-dimensional models. We illustrate the two-dimensionalmodeling of galaxy images with 5 examples, which include elliptical and spiralgalaxies displaying various levels of complexities.In this work we propose a new hybrid algorithm for fitting brightness profilesin two dimensions. The algorithm is called ES+LWLR, a combination betweenEvolution Strategies (ES) (Rechenberg 1973), and Locally Weighted Linear Re-gression (LWLR) (Atkenson et al. 1997), an instance based learning algorithm.This algorithm intends to take advantage of the knowledge generated by ES ineach iteration by using it with LWLR to approximate a new better solution.Therestofthepaperisstructuredasfollows: inSection2abriefdescriptionoftheory of brightness profiles and a description of the problem are presented, thealgorithm is shown in Section 3, results are presented in Section 4 and Section5 includes conclusions and future work.232