Towards emulating cosmic shear data: Revisiting the calibration of the shear measurements for the Kilo-Degree Survey

TL;DR

This study develops and validates a realistic image-simulation workflow to calibrate weak-lensing shear in KiDS by embedding COSMOS-based galaxy morphologies, realistic correlations, and photometric redshifts into the KV-450 pipeline. The authors derive a rigorous bias framework, demonstrate that tomographic bin calibration must reflect redshift-dependent population shifts, and show that per-bin multiplicative biases can be controlled to within ~0.02 when redshift information is included. They also quantify selection and additive biases, perform extensive sensitivity tests, and confirm that multi-band (photo-$z$) information is crucial for robust tomographic calibration. The work provides practical guidance for future Stage IV surveys, highlighting the limitations of redshift-agnostic simulations and underscoring the value of forward modeling with realistic, multi-band inputs to achieve precise cosmic-shear inferences.

Abstract

Exploiting the full statistical power of future cosmic shear surveys will necessitate improvements to the accuracy with which the gravitational lensing signal is measured. We present a framework for calibrating shear with image simulations that demonstrates the importance of including realistic correlations between galaxy morphology, size and more importantly, photometric redshifts. This realism is essential so that selection and shape measurement biases can be calibrated accurately for a tomographic cosmic shear analysis. We emulate Kilo-Degree Survey (KiDS) observations of the COSMOS field using morphological information from {\it Hubble} Space Telescope imaging, faithfully reproducing the measured galaxy properties from KiDS observations of the same field. We calibrate our shear measurements from lensfit, and find through a range of sensitivity tests that lensfit is robust and unbiased within the allowed 2 per cent tolerance of our study. Our results show that the calibration has to be performed by selecting the tomographic samples in the simulations, consistent with the actual cosmic shear analysis, because the joint distributions of galaxy properties are found to vary with redshift. Ignoring this redshift variation could result in misestimating the shear bias by an amount that exceeds the allowed tolerance. To improve the calibration for future cosmic shear analyses, it will be essential to also correctly account for the measurement of photometric redshifts, which requires simulating multi-band observations.

Figures (17)

• Figure 1: Left: Cutout from the co-add of the COSMOS field observed with VST in the $r$-band as a part of KiDS. Right: The corresponding region, but now simulated under similar seeing conditions with morphological parameters of the galaxies taken from the HST COSMOS catalogue described in \ref{['sec:imsim']}, simulated using the setup described in \ref{['sec:sim_setup']}. The images are 1200 pixels, roughly equivalent to $4\farcm{28}$, on the side and are rendered in ds9 with zscale colour scale. We do not simulate the bright saturated stars that can be seen in the VST image, and choose to place additional stars at random locations. The position angles of the galaxies, as measured by GalFit are noisy, which can be seen from the differences between the galaxy orientations in the left and right panels. The solid green circles indicate some examples of regions with distinctive patterns on the sky involving close pairs of galaxies, which we are able to replicate fairly well. The broken circles in yellow and cyan respectively highlight some objects that are not included in our simulations or not present in the original data.
• Figure 2: Distribution of input magnitudes for all the galaxies (black) and the distributions when the galaxies are divided into the tomographic bins based on their 'true' redshifts. The analytic magnitude distribution used in FC17 is given in yellow for reference. The region enclosed by the vertical lines denotes the range in the output magnitude for which shapes are measured.
• Figure 3: Fraction of the objects in the HST catalogue that are missing, or excluded from the simulations plotted against the Subaru $r^+$-band magnitude.
• Figure 4: Left panel: Distribution of axis ratios of galaxies determined by GalFit from ACS imaging of COSMOS. Right panel: Distribution of half-light radii of galaxies determined by GalFit from ACS imaging of COSMOS. Not all galaxies in the HST catalogue were detected in KiDS, but this does not appear to affect the ellipticity distributions significantly. Faint galaxies ($m_{r}>25$) that are also smaller in size are preferentially detected in KiDS, but no such trend is found among the bright galaxies ($m_{r}\le 25$)
• Figure 5: Average Sérsic $n$ value as a function of ellipticity for galaxies with $20<F814W<24.5$ in COSMOS Griffith2012 and the UDF Coe2006. The solid line indicates the average $n$ as a function of $\epsilon$ used in the image simulations (for galaxies with $20<m_r<25$), whereas the dashed lines is for the case we scramble the ellipticities to resemble the FC17 results more closely.