Astron. Astrophys. 363, 401-414 (2000)

Appendix A: Alternative shear analysis

In the second analysis of the data, we followed the procedure used by Hoekstra et al. (1998). The anisotropic part of the PSF is removed on an object-by-object basis by correcting each object's ellipticity via

where starred quantities refer to parameters measured for stellar images. In this analysis, we calculated the stellar ellipticities and polarizability employing a matched radius for the Gaussian weight function as for the object in question. We fit a second order polynomial to account for spatial variations in the PSF.

We next determine the shear from the anisotropy-corrected galaxy polarizations. Both the (now effectively isotropic) PSF, and the circular weight function, tend to make objects rounder. These effects may be corrected for using the `pre-seeing shear polarizability'

introduced by Luppino & Kaiser (1997), where the * subscript again refers to quantities determined from the objects classified as stars.

Operationally, to determine , we split the faint galaxy catalogs into six bins based on size , with spacing pixels. We reject galaxies with very large, small, or negative values of , and (the off-diagonal terms typically being very small). The rationale for this cut is that the calculation of the shear and smear polarizabilities for these objects failed, typically either because the objects themselves were very faint and near the detection threshold, or due to the presence of very nearby object contaminating the aperture over which the calculations were performed.

In each bin, we calculate the median galaxy polarizabilities, and , and reanalyze the stellar catalog, resetting the value of the stellar to the bin size, and analyzing with a Gaussian with scale and an aperture three times this radius.

We finally estimate the shear for each object using

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
helpdesk.link@springer.de