Atmospheric Dispersion Effects in Weak Lensing Measurements

Abstract

ABSTRACTThe wavelength dependence of atmospheric refraction causes elongation of finite-bandwidth images along the elevation vector, which produces spurious signals in weak gravitational lensing shear measurements unless this atmospheric dispersion is calibrated and removed to high precision. Because astrometric solutions and point spread function (PSF) characteristics are typically calibrated from stellar images, differences between the reference stars’ spectra and the galaxies’ spectra will leave residual errors in both the astrometric positions () and in the second moment (width) of the wavelength-averaged PSF (ΔV) for galaxies. We estimate the level of ΔV that will induce spurious weak lensing signals in PSF-corrected galaxy shapes that exceed the statistical errors of the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST) cosmic-shear experiments. We also estimate the signals that will produce unacceptable spurious distortions after stacking of exposures taken at different air masses and hour angles. Using standard galaxy and stellar spectral templates we calculate the resultant errors in the griz bands and find that atmospheric dispersion shear systematics, left uncorrected, are up to 6 and 2 times larger in g and r bands, respectively, than the thresholds at which they become significant contributors to the DES error budget, but can be safely ignored in i and z bands. For the stricter LSST requirements, the factors are about 30, 10, and 3 in g, r, and i bands, respectively. These shear systematic errors scale with observed zenith angle z as 〈 tan2 z〉, for which we take a nominal value of unity—simulations of DES and LSST suggest 0.6–1.0. We find that a simple correction linear in galaxy color is accurate enough to reduce dispersion shear systematics to insignificant levels in the r band for DES and i band for LSST, but still as much 5× above the threshold of significance for LSST r-band observations. More complex approaches to correction of the atmospheric dispersion signal will likely be able to reduce the systematic cosmic shear errors below statistical errors for LSST r band. But g-band dispersion effects remain large enough that it seems likely that induced systematics will dominate the statistical errors of both surveys, and cosmic-shear measurements should rely on the redder bands.