DES Y3 results: Blending shear and redshift biases in image simulations

As the statistical power of galaxy weak lensing reaches percent level precision, large, realistic and robust simulations are required to calibrate observational systematics, especially given the increased importance of object blending as survey depths increase. To capture the coupled effects of blending in both shear and photometric redshift calibration, we define the effective redshift distribution for lensing, $n_{\gamma}(z)$, and describe how to estimate it using image simulations. We use an extensive suite of tailored image simulations to characterize the performance of the shear estimation pipeline applied to the Dark Energy Survey (DES) Year 3 dataset. We describe the multi-band, multi-epoch simulations, and demonstrate their high level of realism through comparisons to the real DES data. We isolate the effects that generate shear calibration biases by running variations on our fiducial simulation, and find that blending-related effects are the dominant contribution to the mean multiplicative bias of approximately $-2\%$. By generating simulations with input shear signals that vary with redshift, we calibrate biases in our estimation of the effective redshfit distribution, and demonstrate the importance of this approach when blending is present. We provide corrected effective redshift distributions that incorporate statistical and systematic uncertainties, ready for use in DES Year 3 weak lensing analyses.