Are 1-D techniques better than 2-D at fitting low surface brightness regions or irregular galaxies?
• Low surface brightness sensitivity comparison: It has been argued by some that 1-D fitting techniques are more sensitive to low signal-to-noise (S/N) or low surface brightness wings of galaxies than 2-D techniques. Their reasoning goes that if each point being fitted is derived from averaging over an annulus, the averaged points have higher S/N relative to fitting over 2-D pixels directly. However, this is actually not the case if, in Chi2 fitting, the weight of each data point used in a fit comes from Poisson uncertainty, sigma, at that point. Whether you first average over N pixels with similar mean values to obtain smaller set of points for fitting, or you fit all the points without averaging, the effective weights are the same, and scale like: sigma / sqrt(N). This is a natural consequence of Poisson statistics. To be a little more specific, Chi2, or least-squares fitting is a technique that is derived by maximizing the probability of a fit, i.e. a model, to data points. A model
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