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Astron. Astrophys. 352, 355-362 (1999)

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4. Intrinsically elongated sources

In the method as described so far, the average galaxy [FORMULA] is analyzed. Very accurate shear measurements require [FORMULA] to be the average of a large number of galaxies ([FORMULA] for a 1-[FORMULA] shear accuracy of 0.01), otherwise intrinsic ellipticity scatter will dominate the measurement. However, constructing [FORMULA] is only possible if the shear and the PSF the same for all galaxies that are summed. Because of spatial variations of PSF and shear, this is usually not so.

We have therefore tested the algorithm in `galaxy-by-galaxy' mode, fitting individual galaxies as PSF-smeared, intrinsically circular, sheared sources. The resulting shear estimates are then each dominated by the intrinsic galaxy shape, as in KSB; the question is how well the average of such individually PSF-corrected shear estimates can represent the actual shear without bias. Note that galaxies are not generally well-described as constant-ellipticity sources, and hence there is no guarantee that, even in principle, the shear estimates will average to the correct value.

We ran our tests on various double-gaussian model galaxies, of differing axis ratios. To simulate typical galaxies, we included a round, central `bulge' component, and an outer `disk' of axis ratio between 0.1 and 1. (Simulations with different bulge axis ratios yielded essentially the same results.) These were placed at all orientations, smeared with various kinds of elliptical PSF, and analysed with the algorithm described above. The best-fit [FORMULA] values thus derived for each galaxy were then averaged to give an estimate of the shear.

As may be seen in Fig. 9, the new algorithm performs very well, essentially correcting all PSF anisotropy signal in the measured shear. By comparison, the slightly biased answer returned by the KSB algorithm is apparent as before. Residual systematics of the new method are at the level of a few tenths of a percent.

[FIGURE] Fig. 9. The derived shear values from the algorithm applied to individual elongated `disk+bulge' galaxy images, after smearing with an elongated PSF. Each ring of points represents a galaxy seen at many orientations; different rings correspond to different galaxy flattening. Left: the raw [FORMULA] polarizations measured with the standard KSB method, without correction for the PSF. Centre: the result of applying the KSB prescription for PSF anisotropy and circularization correction. The small bias seen before remains. Right: the result of the new algorithm on the same galaxies. In the latter case, the correct average shear estimate (zero) is recovered even though individual galaxies are not correctly described as intrinsically constant-ellipticity sources. The three rows refer to the three kinds of PSF ellipticity profile considered in Figs. 5-7: constant with radius (top), outward-increasing (middle), and outward-decreasing (bottom).

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© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999