The Integrated Sachs-Wolfe (ISW) effect is a large-angle modulation of the cosmic microwave background (CMB), generated when CMB photons traverse evolving potential wells associated with large scale structure (LSS). Recent efforts have been made to reconstruct maps of the ISW signal using information from surveys of galaxies and other LSS tracers, but investigation into how survey systematics affect their reliability has so far been limited. Using simulated ISW and LSS maps, we study the impact of galaxy survey properties and systematic errors on the accuracy of reconstructed ISW signal. We find that systematics that affect the observed distribution of galaxies along the line of sight, such as photo-z and bias-evolution related errors, have a relatively minor impact on reconstruction quality. In contrast, however, we find that direction-dependent calibration errors can be very harmful. Specifically, we find that in order to avoid significant degradation of our reconstruction quality statistics, direction-dependent number density fluctuations due to systematics must be controlled so that their variance is smaller than $10^{-6}$ (which corresponds to a 0.1% calibration). Additionally, we explore the implications of our results for attempts to use reconstructed ISW maps to shed light on the origin of large-angle CMB alignments. We find that there is only a weak correlation between the true and reconstructed angular momentum dispersion, which quantifies alignment, even for reconstructed ISW maps which are fairly accurate overall.
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