Imaging systematics induced by galaxy sub-sample fluctuation: new systematics at second order

TL;DR

This work identifies a second-order imaging systematic, termed sub-sample systematics, where spatial variations in the redshift distribution $n(z,\textbf{sys})$ and galaxy bias $b(z,\textbf{sys})$ across a survey footprint arise from the varying composition of galaxy sub-samples. It develops a formal framework extending traditional imaging-systematics theory to multiple sub-samples, showing that these effects add a multiplicative-like contribution to the observed two-point statistics that enhances small-scale galaxy clustering while leaving galaxy-galaxy lensing and cosmic shear largely unaffected at first order. Through toy models and analytical expressions, the authors demonstrate how sub-sample systematics can bias cosmological inferences, including degeneracies with neutrino mass and primordial non-Gaussianity, and propose forward modeling with a truth catalog and a Source Injection Emulator as a practical mitigation strategy. The forward-modeling approach enables estimation of spatially varying $n(z,\textbf{sys})$ and $b(z,\textbf{sys})$, providing a route to quantify and correct for sub-sample systematics in upcoming LSST DESC analyses, thereby safeguarding precision cosmology. The results underscore the importance of accounting for second-order imaging systematics in high-precision cosmology programs.

Abstract

Imaging systematics refers to the inhomogeneous distribution of a galaxy sample caused by varying observing conditions and astrophysical foregrounds. Current mitigation methods correct the galaxy density fluctuations caused by imaging systematics assuming that all galaxies in a sample have the same galaxy density fluctuations. Under this assumption, the corrected sample cannot perfectly recover the true correlation function. We name this effect sub-sample systematics. For a galaxy sample, even if its overall sample statistics (redshift distribution n(z), galaxy bias b(z)), are accurately measured, n(z), b(z) can still vary across the observed footprint. It makes the correlation function amplitude of galaxy clustering higher, while correlation functions for galaxy-galaxy lensing and cosmic shear do not have noticeable change. Such a combination could potentially degenerate with physical signals on small angular scales, such as the amplitude of galaxy clustering, the impact of neutrino mass on the matter power spectrum, etc. Sub-sample systematics cannot be corrected using imaging systematics mitigation approaches that rely on the cross-correlation signal between imaging systematics maps and the observed galaxy density field. In this paper, we derive formulated expressions of sub-sample systematics, demonstrating its fundamental difference with other imaging systematics. We also provide several toy models to visualize this effect. Finally, we discuss a potential method to estimate and mitigate sub-sample systematics by forward modeling its behavior using Synthetic Source Injection.

Figures (14)

• Figure 1: Illustration of how sub-sample systematics is formed. A galaxy sample is composed of multiple sub-samples defined by their intrinsic properties like flux, shape, etc. Here we show 3 sub-samples denoted as 1 for blue, 2 for black, and 3 for orange. Looking horizontally, the sub-samples respond differently to the imaging systematics map. The solid black line represents what we can observe: the $n_{\mathrm{gal}}/\bar{n}_{\mathrm{gal}}$ fluctuation as a function of x. With an optimal imaging systematics correction treating the sample as a whole, this line becomes flat with x. However, the variation in sub-samples still exists. Looking vertically in the right figure, we see that the composition of different sub-samples changes with x. Since each sub-sample has a different redshift and galaxy bias distribution, this leads to a varying redshift and galaxy bias distribution across the entire footprint.
• Figure 2: An illustration showing how sub-sample systematics modifies the observed galaxy density field and the two-point statistics. We show a fiducial systematics map with its color gradient representing the change in systematics map value $\textbf{sys}(\Omega)$. The redshift and galaxy bias distribution changes with $\textbf{sys}(\Omega)$. The galaxies at sky positions of similar color are more similar to each other. In this example, we see that the color pairs at $\alpha_1$ are more similar to the galaxy pairs at $\alpha_2$. In Section \ref{['sec:generalized-framework']}, we develop a theoretical framework to describe this phenomenon.
• Figure 3: The angular correlation function of the galaxy sample with sub-sample systematics (orange) versus the clean sample(blue). The orange curve is derived from equation \ref{['equ:generalized-wtheta']}. The blue curve is a clean, homogeneous sample theoretically derived with the overall $b(z), n(z)$ identical to the orange curve.
• Figure 4: Correlation function for the case of Galaxy Galaxy Lensing (1st row) and Cosmic shear (2nd and 3rd row). Orange curves are the observed correlation function with sub-sample systematics and blue curves are the correlation function computed from the $n(z),b(z)$ of the whole sample. No significant difference due to sub-sample systematics is detected for all these cases.
• Figure 5: Blue: A galaxy sample with bias variation, divided by a homogeneous sample. The sample has a neutrino mass of 0.07 eV. Orange: Theoretical correlation function of neutrino mass 0 eV, divided by a curve with the same cosmology but having neutrino mass 0.07 eV.