The contribution from small scales on two-point shear analysis: comparison between power spectrum and correlation function

TL;DR

The paper investigates the consistency between real-space $(\xi_±)$ and harmonic-space $(C_\ell^{EE})$ cosmic-shear analyses when extending to smaller scales in HSC-Y3 data. It shows that sharp baryonic and intrinsic-alignment features are smeared by the Hankel transforms, making $C_\ell$ analyses less sensitive to small-scale modeling than $\xi_±$. Using HMCode-2016 and BACCO, the authors demonstrate that a flexible BACCO+TATT model delivers the most consistent cross-space cosmological constraints, with marginal biases in $S_8$ across scale cuts; marginalizing over a single baryonic-physics parameter $M_c$ captures the essential suppression. The results highlight a complementary strategy: leverage harmonic-space robustness for current data while using real-space analyses to discriminate baryonic physics in upcoming surveys. Collectively, the work emphasizes developing joint, space-agnostic models to robustly extract cosmology from small-scale shear information.

Abstract

A known problem in cosmic shear two-point statistics is the apparent inconsistency between analyses performed in harmonic space (power spectrum) and real space (angular correlation). This arises mainly from two factors: first, scale cuts in one space correspond to soft cuts in the other, as the relationship between the two spaces is mediated by Bessel functions. For the same reason, astrophysical effects that are compact in one space may not be in the other, which can lead to biased parameter estimates. In this paper, we argue that these two statistics are complementary: we expect a robust theory to provide consistent constraints regardless of the chosen scale cuts. We present the consequences of pushing our analysis to smaller scales in both spaces, accounting for different models of Intrinsic Alignment and Baryonic Feedback in HSC Y3 data: we find that the harmonic-space analysis is significantly less sensitive to the specific modeling of small-scale physics, with model-choice-driven biases in $S_8$ being 2-3 times smaller than in real space. We show that using a flexible, simulation-based emulator for baryonic feedback (BACCO) in combination with the TATT model for intrinsic alignments provides the most consistent cosmological constraints between the two spaces when pushing to the smallest scales. In contrast, the standard HMCode-2016 model results in a $\sim 1.1σ$ tension between the two statistics. While harmonic space appears more robust for cosmological inference given current model uncertainties, real-space analyses offer a clearer separation of baryonic effects and will play a crucial role in distinguishing between baryonic feedback models in upcoming surveys.

Figures (16)

• Figure 1: The full $\xi_\pm$ data vector (in blue) for the HSC Y3 measurements. The red and green lines are the convolutions of $C_\ell$ to $\xi$ via Eqs. \ref{['eq:xi_plus']}-\ref{['eq:xi_minus']}, computed with the best-fit values from li2023hypersuprimecamyear3 and different multipole intervals. The shaded areas correspond to scales cut away from the official HSC-Y3 analysis.
• Figure 2: (Left) Compact signals in harmonic space (given by $\delta_D(\ell-\ell^\prime)$) as seen in real space. (Right) Interpolation of Doux et al. Doux_2021$k_{\rm max}\longleftrightarrow(\theta^\pm_{\rm min},\ell_{\rm max})$. The upper scatter corresponds to $\theta^-_{\rm min}\longleftrightarrow\ell_{\rm max}$, and the lower scatter corresponds to $\theta^+_{\rm min}\longleftrightarrow\ell_{\rm max}$. For visualization purposes, we also plot the usual Nyquist frequency $\ell=\pi\,/\,\theta$ .
• Figure 3: Impact of baryonic feedback on the dark-matter-only correlation functions. We show the fractional suppression predicted by the HMCode-2016 and BACCO models, each fitted to HSC-Y3 data. The magenta region marks the sensitivity range of the HSC-Y3 measurements.
• Figure 4: Main cosmological results for all scenarios. For comparison, we show Planck 2018 (in red), and the HSC Y3 harmonic- and real-space analyses in the upper panels. Harmonic-space analyses are shown in blue, whereas the real-space analyses are shown in orange. The middle panels correspond to models employing HMCode-2016 for baryonic feedback and nonlinear corrections, while the lower panels use BACCO.
• Figure 5: Left: evolution of $S_8$ constraints for all modeling scenarios. Orange lines correspond to analyses in real space, whereas blue lines correspond to harmonic space. From left to right, we include more data points in the analysis (lower $\theta_{\rm min}$ or higher $\ell_{\rm max}$). For clarity, we show only the $68\%$ confidence interval of BACCO+TATT, our baseline scenario (the other scenarios have uncertainties of comparable magnitude). The red line indicates Planck 2018's best-fit value. Right: evolution of the reduced chi-squared for different models.