Systematic errors in weak lensing: application to SDSS galaxy-galaxy weak lensing

Weak lensing is emerging as a powerful observational tool to constrain cosmological models, but is at present limited by an incomplete understanding of many sources of systematic error. Many of these errors are multiplicative and depend on the population of background galaxies. We show how the commonly cited geometric test, which is rather insensitive to cosmology, can be used as a ratio test of systematics in the lensing signal at the 1 per cent level. We apply this test to the galaxy-galaxy lensing analysis of the Sloan Digital Sky Survey (SDSS), which at present is the sample with the highest weak lensing signal-to-noise ratio and has the additional advantage of spectroscopic redshifts for lenses. This allows one to perform meaningful geometric tests of systematics for different subsamples of galaxies at different mean redshifts, such as brighter galaxies, fainter galaxies and high-redshift luminous red galaxies, both with and without photometric redshift estimates. We use overlapping objects between SDSS and the DEEP2 and 2df-Sloan LRG and Quasar (2SLAQ) spectroscopic surveys to establish accurate calibration of photometric redshifts and to determine the redshift distributions for SDSS. We use these redshift results to compute the projected surface density contrast Δσ around 259 609 spectroscopic galaxies in the SDSS; by measuring Δσ with different source samples we establish consistency of the results at the 10 per cent level (1σ). We also use the ratio test to constrain shear calibration biases and other systematics in the SDSS survey data to determine the overall galaxy-galaxy weak lensing signal calibration uncertainty. We find no evidence of any inconsistency among many subsamples of the data.