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Astron. Astrophys. 364, 26-42 (2000)

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4. Fitting the surface brightness distributions

A model brightness distribution has been fitted to each object, using a modified version of the code described in Moriondo et al. (1998). Such a code was originally implemented to analyze the brightness distribution of nearby spiral galaxies by fitting to the data a bi-dimensional two-component model (disk+bulge), convolved with a gaussian PSF.

4.1. The point spread function

The main changes introduced to make the fitting code suitable for the WFPC2 and NICMOS data concern the convolution of the model galaxy with the PSF, which is not axisimmetric and subject to significant changes from one point to another in the field. In other words, the gaussian approximation is no longer accurate enough, and the PSF needs to be represented by a full bi-dimensional image. The model PSF were computed using the TinyTim code (Krist & Hook 1997, http://www.stsci.edu/ftp/software/tinytim/ ). Such a theoretical PSFs proved to be accurate within about 15%, when compared with observed stars and considering the average residuals in the inner 5 [FORMULA] 5 pixels. The accuracy achieved by TinyTim is not worse than what could be obtained using stars in the field; this is mainly due to the variation of the PSF shape across the field of view (differences up to 20%, even in the central pixels, are easily observed), coupled to the fact that it is usually difficult for WFPC2 images - almost impossible for the NICMOS ones - to find a star in the neighbourhood of each object. A further advantage offered by TinyTim is the possibilty of computing an oversampled PSF, which greatly improves the accuracy of the model convolution. This is particularly true in the case of WFPC2 data, where the image scale undersamples the PSF: a few tests have shown that in this case a good convolution of the model can be obtained only if it is performed on a finer grid. The convolved model is then rebinned to the proper scale and compared to the data. In the case of the HDFS, since the reduced frames have been resampled by DRIZZLE, we have chosen to use a PSF derived directly from the stars in the field.

The convolution is performed as the inverse Fourier transform of the product of the direct transforms of the model and the PSF, using a Fast Fourier Transform algorithm.

4.2. The model

Because we want to identify elliptical galaxies, and given the small size of the sample objects, we have considered only one-component models with constant apparent ellipticity (i.e. no bulge+disk galaxies). The radial trend adopted for the model brightness distribution in every fit is a generalized exponential (Sersic 1982): [FORMULA], including the case of an exponential distribution ([FORMULA]) and of a de Vaucouleurs one ([FORMULA]). The parameters of each fit are the effective radius [FORMULA] and the effective surface brightness [FORMULA] of the distribution, as well as its center coordinates; the apparent ellipticity and position angle are held fixed since they can be determined more reliably from the ellipse fitting routine. The "shape index" n is also fixed, in every fit, to an integer value ranging from 1 to 6, due to the fact that, at the low signal-to-noise ratio ([FORMULA]) typical of our data, the fitting routine is not able to obtain a reliable estimate for both n and the other parameters at the same time. The best value of the shape index n for each galaxy is determined instead a posteriori, by choosing the least [FORMULA] resulting from the different fits. The accuracy of the final best-fit parameters, including n, has been assesed using a large set of simulated galaxies, and will be discussed in the next section.

The fits are performed inside a circular region centered on the galaxy; its radius is chosen, using the radial brightness profile, as the one at [FORMULA] for the ellipse-averaged intensity. The background level is estimated on blank sky regions close to the source; its uncertainty turns out to be dominated, in most cases, by fluctuations on scales of order 10 pixels or more, due to a non-perfect image flattening.

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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