Wavelength Dependent PSFs and their impact on Weak Lensing Measurements

TL;DR

This paper investigates how the wavelength dependence of the PSF affects weak lensing measurements, models this chromaticity, and demonstrates that it can be corrected to meet LSST survey accuracy requirements.

Contribution

It provides a detailed measurement and modeling of PSF chromaticity in the HSC survey and shows that the wavelength dependence can be accurately inferred and corrected for LSST-like weak lensing surveys.

Findings

PSF chromaticity is at 1-2% in g, r, i-bands and 0.1-0.2% in z, y-bands.

The wavelength dependence follows a power law with b between -0.2 and -0.5.

Correcting for PSF chromaticity is feasible with current models and data for LSST-like surveys.

Abstract

We measure and model the wavelength dependence of the PSF in the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey. We find that PSF chromaticity is present in that redder stars appear smaller than bluer stars in the $g, r,$ and $i$-bands at the 1-2 per cent level and in the $z$ and $y$-bands at the 0.1-0.2 per cent level. From the color dependence of the PSF, we fit a model between the monochromatic PSF trace radius, $R$, and wavelength of the form $R(\lambda)\propto \lambda^{b}$. We find values of $b$ between -0.2 and -0.5, depending on the epoch and filter. This is consistent with the expectations of a turbulent atmosphere with an outer scale length of $\sim 10-100$ m, indicating that the atmosphere is dominating the chromaticity. We find evidence in the best seeing data that the optical system and detector also contribute some wavelength dependence. Meyers and Burchat (2015) showed that $b$ must be measured to an accuracy of $\sim 0.02$ not to dominate the systematic error budget of the Large Synoptic Survey Telescope (LSST) weak lensing (WL) survey. Using simple image simulations, we find that $b$ can be inferred with this accuracy in the $r$ and $i$-bands for all positions in the LSST field of view, assuming a stellar density of 1 star arcmin$^{-2}$ and that the optical PSF can be accurately modeled. Therefore, it is possible to correct for most, if not all, of the bias that the wavelength-dependent PSF will introduce into an LSST-like WL survey.