Calibrating baryonic effects for Stage-IV cosmic shear: which observables, depths, and systematic controls suffice to recover unbiased cosmological constraints

Uncertainty in baryonic feedback — the redistribution of gas by cooling, star formation, and AGN activity that suppresses the non-linear matter power spectrum by ~10% on small scales — is a leading systematic for Stage-IV weak-lensing surveys such as LSST. Wayland, Alonso & Zennaro (2025) showed by forecast that combining LSST-like cosmic shear with X-ray cluster gas fractions and stacked kinetic Sunyaev-Zel'dovich (kSZ) measurements can calibrate the dominant baryon-correction-model (BCM) parameters and reduce the degradation of the $S_8$ error from a factor 1.9 to ~1.1, but under deliberately idealized assumptions. They identified six unresolved gaps: the BCM's simplifying assumptions (mass-independent, non-evolving parameters); optimistic kSZ modelling (no 2-halo term, satellites, miscentering, or velocity-reconstruction errors); unpropagated X-ray selection and hydrostatic-mass systematics; two parameters ($\log_{10}\theta_{\rm inn}$, $\log_{10}M_1$) that neither X-ray nor kSZ data constrain and that leave residual degradation of $n_s$ and $S_8$; the unexplored alternative of higher-order weak-lensing statistics; and the unquantified bias (as opposed to precision loss) from baryonic mis-modelling. This problem asks for an observationally sufficient and robust calibration strategy for baryonic effects in Stage-IV weak-lensing cosmology: the combination of external gas probes and/or internal higher-order statistics, with stated depth and systematic-control requirements, that calibrates all feedback parameters relevant to cosmological inference and bounds the associated accuracy budget. Follow-up work through 2026 (FRB tomography, real-data multiwavelength baryonification, improved kSZ estimators, LSST forecasts) has advanced pieces of this program but left the core — especially the $\theta_{\rm inn}$/$M_1$ gap and the bias-under-misspecification question — open.

Background

Weak gravitational lensing, or cosmic shear, is the coherent distortion of the shapes of distant galaxies by the gravitational field of intervening large-scale structure; its two-point statistics (angular shear power spectra $C_\ell$ in tomographic redshift bins) are a primary probe of dark matter and dark energy. Stage-IV surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will measure these spectra to multipoles $\ell_{\max}\sim 2000$. On these small, non-linear scales the total matter power spectrum is modified by baryonic feedback: gas cooling, star formation, and feedback from active galactic nuclei (AGN) move baryons out of haloes, suppressing the matter power spectrum by of order 10% for wavenumbers $0.1\lesssim k\lesssim 10\,h\,{\rm Mpc}^{-1}$ (van Daalen et al. 2011). Uncertainty in this suppression is now among the dominant systematics of weak-lensing cosmology.

A standard data-driven treatment is the baryon correction model (BCM; Schneider & Teyssier 2015), also called baryonification: matter in gravity-only simulations is displaced to follow parametric gas and stellar halo profiles, so the impact of feedback on the matter power spectrum is encoded in a handful of physically interpretable halo parameters. In the implementation emulated by Baccoemu (Aricò et al. 2021), the model has seven free parameters: $\log_{10}M_{\rm c}$ (the halo mass below which bound gas is depleted), $\log_{10}\eta$ (the radial extent of gas ejected by AGN), the bound-gas profile shape parameters $\log_{10}\beta$, $\log_{10}\theta_{\rm inn}$, $\log_{10}\theta_{\rm out}$, and $\log_{10}M_{\rm inn}$, and the stellar parameter $\log_{10}M_1$. Marginalizing over these parameters in a shear analysis absorbs the feedback uncertainty at the cost of degraded cosmological constraints.

External tracers of halo gas can calibrate these parameters. X-ray observations of galaxy clusters yield gas mass fractions, which probe the bound hot gas ($M_{\rm c}$); the kinetic Sunyaev-Zel'dovich effect (kSZ) — a Doppler shift of cosmic microwave background (CMB) photons scattered off electrons moving with the halo bulk velocity — traces the electron density profile in stacked measurements; the thermal Sunyaev-Zel'dovich effect (tSZ) traces electron pressure; and fast radio bursts (FRBs) provide dispersion measures (frequency-dependent arrival-time delays proportional to the column of ionised electrons) that probe the diffuse electron distribution. Galaxy–galaxy lensing can characterize the halo samples used.

Wayland, Alonso & Zennaro (2025) built mock-data likelihood forecasts for an LSST-like survey ($\ell_{\max}=2000$), simultaneously sampling five cosmological parameters ($\Omega_{\rm m}$, $\sigma_8$, $h$, $n_s$, $\Sigma m_\nu$ — the matter density fraction, the amplitude of matter fluctuations, the Hubble and primordial-spectral-index parameters, and the neutrino mass sum), two intrinsic-alignment parameters (modeling the contamination of shear correlations by physically aligned galaxy shapes), and the seven BCM parameters. They found that marginalizing over baryonic parameters grows the errors on $h$ and $n_s$ by factors of 1.4 and 1.8; that the dominant parameters $\log_{10}M_{\rm c}$ and $\log_{10}\eta$ must be calibrated to $\sigma\lesssim 0.1$ (roughly 10–20%) to avoid significant degradation; that near-term X-ray and kSZ data already meet much of this requirement, with long-term data from $\mathcal{O}(5000)$ clusters and a CMB-S4-like kSZ experiment reducing the error on $S_8 \equiv \sigma_8(\Omega_{\rm m}/0.3)^{1/2}$ (the conventional late-time structure-amplitude combination) by a degradation factor from 1.9 (weak lensing alone) to about 1.1; but that neither probe constrains $\log_{10}\theta_{\rm inn}$ or $\log_{10}M_1$, which drive residual degradation of $n_s$ and $S_8$. Their kSZ modelling omits the 2-halo term (the correlation contribution from gas associated with pairs of haloes rather than a single halo), satellite galaxies, miscentering, correlated velocity–density terms, and velocity-reconstruction uncertainties; their X-ray treatment does not propagate selection functions, hydrostatic-mass bias (the assumption that cluster gas is in equilibrium used to infer masses), or mass–observable scatter and covariance; and the analysis quantifies precision loss, not the bias induced by mis-modelling baryons. Prior work had established the adjacent ingredients: cluster-gas constraints on baryonification (Grandis et al. 2024), baryonic signatures in the matter bispectrum (Foreman et al. 2020; Aricò et al. 2021), and a baryonification extension to tSZ pressure (Aricò & Angulo 2024).

Problem Statement

For a Stage-IV (LSST-like) cosmic-shear analysis that marginalizes over baryonic feedback, determine an observationally sufficient and robust calibration strategy. Specifically, determine whether any combination of external gas observables — stacked kinetic Sunyaev-Zel'dovich profiles, X-ray gas mass fractions and electron-density profiles, X-ray cross-correlations, thermal Sunyaev-Zel'dovich measurements, and fast-radio-burst dispersion measures (a list that does not exclude further probes the solver may introduce) — and/or internal higher-order weak-lensing statistics (bispectrum, peak counts), and at what observational depth (sample sizes, sensitivity, redshift coverage) and level of systematic control, can satisfy all of the following:

1. all feedback parameters that degrade cosmological constraints are calibrated to the required precision — in particular $\log_{10}\theta_{\rm inn}$ and $\log_{10}M_1$, which X-ray gas fractions and stacked kSZ measurements leave unconstrained and which produce residual degradation of the constraints on the scalar spectral index $n_s$ and on $S_8$, and degradation of the constraint on the Hubble parameter $h$ when marginalized over without external calibration (the dominant parameters $\log_{10}M_{\rm c}$ and $\log_{10}\eta$ requiring calibration to $\sigma\lesssim 0.1$, i.e. roughly 10–20%); for any feedback parameter whose target precision is not already established (notably $\log_{10}\theta_{\rm inn}$ and $\log_{10}M_1$), the required precision is itself part of the result and must be derived and stated;
2. the conclusion holds under realistic treatment of kSZ systematics (the 2-halo term, satellite contamination, miscentering, correlated velocity–density terms, and velocity-reconstruction uncertainties) and X-ray systematics (selection functions, hydrostatic-mass bias, mass–observable scatter and covariance), rather than the idealized modelling used in existing forecasts;
3. it is robust to generalizing the baryonic model beyond the seven-parameter BCM, including mass- and redshift-dependent feedback parameters; and
4. the bias (accuracy), not only the precision loss, of cosmological parameters under plausible baryonic mis-modelling is quantified, together with the ability of the external probes themselves to detect and correct such biases.

All four conditions are jointly required for a strategy to count as resolving the task (condition 4 being a required accuracy analysis rather than a further constraint on the probe design). A demonstrated negative result is also an admissible resolution: if no combination of the probes above — or of other observables the solver introduces — satisfies those conditions, showing that no such strategy exists, together with the residual degradation and bias it entails, discharges the task. The common objective uniting these deliverables is that baryonic effects cease to limit the cosmological return of Stage-IV weak-lensing surveys; a demonstration may be at the forecast or data level. The sharpest sub-target within this objective, not a substitute for the four conditions, is the removal of the residual degradation of $n_s$ and $S_8$ attributed to the feedback parameters that existing external X-ray and kSZ data leave unconstrained.

References

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