FLAMINGO: Baryonic effects on the weak lensing scattering transform

Abstract: The scattering transform is a wavelet-based statistic capable of capturing non-Gaussian features in weak lensing (WL) convergence maps and has been proven to tighten cosmological parameter constraints by accessing information beyond two-point functions. However, its application in cosmological inference requires a clear understanding of its sensitivity to astrophysical systematics, the most significant of which are baryonic effects. These processes substantially modify the matter distribution on small to intermediate scales ($k\gtrsim 0.1\,h\,\mathrm{Mpc}^{-1}$), leaving scale-dependent imprints on the WL convergence field. We systematically examine the impact of baryonic feedback on scattering coefficients using full-sky WL convergence maps with Stage IV survey characteristics, generated from the FLAMINGO simulation suite. These simulations include a broad range of feedback models, calibrated to match the observed cluster gas fraction and galaxy stellar mass function, including systematically shifted variations, and incorporating either thermal or jet-mode AGN feedback. We characterise baryonic effects using a baryonic transfer function defined as the ratio of hydrodynamical to dark-matter-only scattering coefficients. While the coefficients themselves are sensitive to both cosmology and feedback, the transfer function remains largely insensitive to cosmology and shows a strong response to feedback, with suppression reaching up to $10\%$ on scales of $k\gtrsim 0.1\,h\,\mathrm{Mpc}^{-1}$. We also demonstrate that shape noise significantly diminishes the sensitivity of the scattering coefficients to baryonic effects, reducing the suppression from $\sim 2 - 10 \;\%$ to $\sim 1\;\%$, even with 1.5 arcmin Gaussian smoothing. This highlights the need for noise mitigation strategies and high-resolution data in future WL surveys.

• The paper presents a simulation-based baryonic transfer function that corrects weak lensing scattering coefficients against AGN and star formation feedback.
• It reveals a scale-dependent suppression of up to 8% in ST coefficients due to baryonic effects, while the response remains largely independent of cosmology.
• The study underscores the need for high-resolution data and effective noise mitigation to discriminate feedback models and ensure unbiased parameter inference.

Baryonic Modulation of the Weak Lensing Scattering Transform: Insights from the FLAMINGO Suite

Introduction and Theoretical Background

The inference of cosmological parameters from weak lensing (WL) surveys on small non-linear scales is fundamentally limited by baryonic physics, prominently feedback from AGN and star formation processes, which redistribute matter on $k \gtrsim 0.1\,h\,\mathrm{Mpc}^{-1}$ scales. While two-point statistics (e.g., power spectrum) are well-studied in this context, non-Gaussian and higher-order WL statistics have become critical for extracting additional cosmological information in Stage IV survey analyses. The wavelet-based scattering transform (ST) is emerging as a leading candidate for these non-Gaussian summaries, offering stable, interpretable, and multi-scale coefficients that complement standard measurements [2020MNRAS.499.5902C; 2021MNRAS.507.1012C].

This work provides a detailed, simulation-based evaluation of baryonic impacts on WL scattering coefficients, using suite-scale hydrodynamical and dark matter only (DMO) realizations from the FLAMINGO simulations, with particular emphasis on defining and validating a baryonic transfer function for ST coefficients. Such transfer functions are essential in marginalizing baryonic uncertainties and enabling robust cosmological inference at scale.

FLAMINGO Simulation Suite and Convergence Map Generation

FLAMINGO provides large-volume, multi-resolution cosmological hydrodynamics built on SWIFT and SPHENIX [2024MNRAS.530.2378S; 2022MNRAS.511.2367B], with both DMO and baryonic runs matched from $z=31$ initial conditions (including variations in AGN feedback – thermal and jet modes – and calibration to SMF and cluster gas fractions). The key characteristic is its machine-learning-based calibration of subgrid feedback to reproduce observed cluster and galaxy properties [2023MNRAS.526.6103K]. For WL, full-sky convergence ($\kappa$) maps are constructed via backward ray tracing, partitioned into 3183 nearly non-overlapping $3.6\times3.6\,\rm deg^2$ sky patches using a Fibonacci lattice for isotropic sampling.

Figure 1: Example uniform sky patching via Fibonacci lattice for spatially distributed scattering statistics.

The construction exploits a Euclid-motivated source $n(z)$ and ensures DMO/HYDRO maps share cosmic variance via identical random seeds and observer positions, isolating baryonic effects.

Scattering Transform Formalism: Implementation for Weak Lensing

The 2D ST is implemented to second-order, with Morlet wavelet filters at 8 dyadic scales and $L$ orientations [see also 2021arXiv211201288C]. For isotropic analyses, orientation averaging and $j_1<j_2$ selection reduce redundancy, yielding a compact, physically interpretable vector of coefficients. $\mathcal{S}_1^{j_1}$ capture scale-dependent amplitude of $\kappa$ fluctuations; $\mathcal{S}_2^{j_1,j_2}$ encode cross-scale clustering. Discrete convolution and spatial averaging over each map patch produce robust, low-variance descriptors.

Results: Baryonic Impact and Transfer Function Characterization

Sensitivity of Scattering Coefficients to Cosmology and Baryonic Physics

The coefficient amplitudes scale as power laws in $S_8 \equiv \sigma_8\sqrt{\Omega_m/0.3}$, with slopes in $[1.0,1.6]$ for first-order coefficients, similar in both DMO and hydro runs. The $S_8$-sensitivity is essentially scale-independent, delivering a direction of degeneracy in parameter inference.

Figure 2: $S_8$-scaling and amplitude variation of scattering coefficients over cosmological runs.

Baryonic feedback drives a scale-dependent suppression in ST coefficients, strongest at $j=1\,{\rm to}\,3$ (small/intermediate scales), with amplitude reductions up to $\sim 8\%$ across physically plausible feedback shifts. Notably, this magnitude is comparable to cosmological coefficient shifts between Planck and LS8 cosmologies.

Figure 3: ST coefficient suppression/enhancement for different baryonic feedbacks on the same cosmological background.

Constructing the Baryonic Transfer Function

A key contribution is the map-level baryonic transfer function $$\mathcal{T} = \overline{\mathcal{S}^{\rm HYDRO}}/\overline{\mathcal{S}^{\rm DMO}}$$ evaluated per coefficient and averaged over sky patches. The distribution of transfer function values is close to Gaussian across patches and is insensitive to cosmology—mean shifts $<0.3\%$ across all cosmological runs—while being strongly feedback-dependent (up to $4\%$ mean shifts for feedback strength variations). Variance is $\sim0.3$–$0.4\%$ of the mean.

Figure 4: Patch-wise PDF of transfer function components for both cosmology and feedback variations (at $j_1=1, j_2=2$).

These statistics demonstrate that $\mathcal{T}$ is a physically stable, predictive object for baryonic corrections.

Figure 5: Full set of transfer functions $\mathcal{T}_2^{j_1,j_2}$ for all cosmological settings (upper), showing near-overlap; ratios to fiducial highlighted in the lower panel.

For all models, the shape of $\mathcal{T}$ exhibits the expected "spoon-like" features—i.e., maximum suppression peaks at small/intermediate scales and flattens on large scales ($j_1\geq 5$).

Figure 6: Transfer functions for various hydrodynamical feedback models with fixed cosmology; amplitude and scale-dependence notably exceed those seen in cosmology-only changes.

AGN Feedback Modalities and the Importance of High Resolution

Thermal AGN feedback produces severe, scale-localized suppression ($\sim 4$–$9\%$), while kinetic jet-mode feedback shifts suppression to larger scales (less small-scale suppression, stronger on larger scales). Extreme feedback settings (e.g., jet+low gas fraction and extreme kinetic) become indistinguishable above a resolution threshold, emphasizing the requirement for high-resolution observational data to unambiguously differentiate astrophysical feedback scenarios.

Impact of Observational Noise and Smoothing

Addition of realistic shape noise rapidly degrades the detectability of baryonic suppression: suppression reduces from 2–10% (ideal) to $\sim$1% and below when noise and smoothing on the order of 1.5 arcmin is added. On the finest scales, ST coefficients become essentially noise-dominated, reducing the discriminating power of the transfer function.

Figure 7: Noise and smoothing-induced flattening of transfer function coefficients, with information on baryonic effects retained only on intermediate scales.

Discussion of Practical and Theoretical Implications

The results deliver several strong statements and actionable insights:

• Transfer function stability: The baryonic suppression factor for ST coefficients is nearly independent of background cosmology for variations covered in FLAMINGO (fiducial to Planck/LS8), but highly sensitive to the thermal and jet feedback implementation and calibration targets. This validates the feasibility of correction factors that are feedback-calibrated but cosmology-agnostic, provided $S_8$ does not depart too drastically.
• Parameter inference: Naïvely neglecting baryonic suppression at $k\gtrsim 0.1\,h\,\mathrm{Mpc}^{-1}$ in ST analyses introduces systematics of a magnitude comparable to cosmological variation in coefficient amplitudes. Transfer function calibration is essential for robust modeling in likelihood-free and simulation-based inference frameworks.
• Noise and angular resolution: With current and near-future survey characteristics (e.g., Euclid), shape noise fundamentally limits the constraining power of non-Gaussian statistics to intermediate and large scales. Smoothing slightly mitigates the discrepancy at the cost of erasing high-resolution features critical for feedback discrimination. As such, survey design must prioritize noise reduction and improved resolution to leverage ST statistics fully.
• Feedback model discrimination: Multiple baryonic feedback prescriptions, even with vastly different energetics and gas redistribution scales, produce degenerate ST coefficient suppression profiles at insufficient resolution/noise. Model choice and physical feedback constraints will increasingly rely on multi-wavelength, multi-tracer data and further development of tomographic, redshift-dependent transfer functions.

Future Directions

The study demonstrates transferability for ST-based cosmological pipelines but also highlights the necessity of extending the transfer function framework to tomographic bins to capture redshift evolution in baryonic processes. Further, synergistic analyses combining WL ST coefficients with cluster observables and tSZ/X-ray probes can break degeneracies in feedback model parameter spaces [2023MNRAS.523.2247S, 2023MNRAS.526.4978S].

Ongoing and near-term simulation and observational campaigns should focus on:

• Expanding baryonic feedback model coverage, especially with jet/cosmic ray-dominated AGN models
• Developing refined noise-mitigation and denoising pipelines for ST applications [2024A&A...681A...1A]
• Integrating ST-based transfer functions into hierarchical Bayesian and simulation-based inference schemes alongside traditional peak count, Minkowski functional, and topological statistics [2025MNRAS.536.2064G].

Conclusion

This work establishes the statistical reproducibility and utility of a baryonic transfer function for the weak lensing scattering transform, showing that ST-based higher-order statistics for WL can incorporate baryonic suppression corrections that are cosmology-independent (to leading order) and feedback-sensitive. The scale-dependence, amplitude, and model variations detailed here set the groundwork for noise-aware, likelihood-free cosmological inference from Stage IV lensing data. The requirements for high-resolution data, careful noise modeling, and targeted baryonic feedback calibration are strongly justified if the scientific community wishes to extract unbiased, high-SNR non-Gaussian information from future surveys.

Figure 8: Visualization of wavelet choices in the 2D scattering transform, illustrating the diversity of directional and spatial characteristics important for signal extraction.

Figure 9: Direct demonstration of the $S_8$ scaling of selected ST coefficients, confirming utility for cosmological parameter constraints.