[Paper Review] Determining the Baryon Impact on the Matter Power Spectrum with Galaxy Clusters

S. Grandis, Giovanni Aricò+2 more|arXiv (Cornell University)|Sep 6, 2023

High-Energy Particle Collisions Research4 citations

TL;DR

This study uses empirical constraints from galaxy cluster gas and stellar mass fractions, along with high-resolution X-ray electron density profiles, to calibrate semi-analytical baryon correction models (BCM) and predict matter power spectrum suppression with sub-percent precision. It finds 4.2–4.9% suppression at k=1 h Mpc⁻¹ and 18.4–17.9% at k=3 h Mpc⁻¹, with baryonic feedback contributing less than 1% suppression at k<0.37 h Mpc⁻¹, challenging its role in resolving the S8 tension.

ABSTRACT

The redistribution of baryonic matter in massive halos through processes like active galactic nuclei feedback and star formation leads to a suppression of the matter power spectrum on small scales. This redistribution can be measured empirically via the gas and stellar mass fractions in galaxy clusters, and leaves imprints on their electron density profiles. We constrain two semi-analytical baryon correction models with a compilation of recent Bayesian population studies of galaxy groups and clusters sampling a mass range above $\sim 3 imes 10^{13}$ $M_\odot$, and with cluster gas density profiles derived from deep, high-resolution X-ray observations. We are able to fit all the considered observational data, but highlight some anomalies in the observations. The constraints allow us to place precise, physically informed priors on the matter power spectrum suppression. At a scale of $k=1 h$ Mpc$^{-1}$ we find a suppression of $0.042^{+0.012}_{-0.014}$ ($0.049^{+0.016}_{-0.012}$), while at $k=3h$ Mpc$^{-1}$ we find $0.184^{+0.026}_{-0.031}$ ($0.179^{+0.018}_{-0.020}$), depending on the model used. In our fiducial setting, we also predict at 97.5 percent credibility, that at scales $k&lt;0.37h$ Mpc$^{-1}$ baryon feedback impacts the matter power less than $1\%$. This puts into question if baryon feedback is the driving factor for the discrepancy between cosmic shear and primary CMB results. We independently confirm results on this suppression from small-scale cosmic shear studies, while we exclude some hydro-dynamical simulations with too strong and too weak baryonic feedback. Our empirical prediction of the power spectrum suppression shows that studies of galaxy groups and clusters will be instrumental in unlocking the cosmological constraining power of future cosmic shear experiments like extit{Euclid} and Rubin-LSST, and invites further investigation of the baryon correction models.

Motivation & Objective

• To empirically constrain baryon feedback effects on the matter power spectrum using observational data from galaxy clusters.
• To reduce theoretical uncertainties in weak lensing and cosmic shear experiments by calibrating baryon correction models (BCMs) with multi-wavelength cluster observations.
• To test whether baryonic feedback can resolve the S8 tension between cosmic shear and primary CMB measurements.
• To validate and exclude hydrodynamical simulations based on their feedback strength relative to empirical constraints.
• To provide precise, physically informed priors on matter power spectrum suppression for future cosmological surveys like Euclid and Rubin-LSST.

Proposed method

• The study employs two semi-analytical baryon correction models (bacco and S19) that model the redistribution of baryons in halos via feedback and star formation.
• It uses Bayesian inference to constrain model parameters using a compilation of weak lensing-informed galaxy group and cluster mass fraction measurements above 3×10¹³ M☉.
• High-resolution X-ray observations of electron density profiles (e.g., from Ghirardini et al. 2019) are incorporated to further constrain the models.
• The models predict the non-linear matter power spectrum suppression by applying baryonic feedback effects to gravity-only N-body simulations.
• Posterior predictive checks are used to assess model consistency with data, and anomalies in observations are identified and addressed.
• The results are compared with hydrodynamical simulations (e.g., OWLS) and small-scale cosmic shear constraints to validate and exclude inconsistent models.

Figure 1: Approximate mass distributions of the galaxy cluster and group samples used. These distributions are not used in our inference and are presented for visualisation purposes only. Our compilation of studies samples the mass range $M_{500\text{c}}\gtrapprox 3\times 10^{13}$ $M_{\odot}$ . Sour

Experimental results

Research questions

• RQ1 To what extent does baryonic feedback suppress the matter power spectrum on small scales, as constrained by empirical cluster data?
• RQ2 Can the baryon correction models (bacco and S19) simultaneously fit gas and stellar mass fractions and electron density profiles in galaxy clusters?
• RQ3 Is baryonic feedback sufficient to explain the S8 tension between cosmic shear and primary CMB measurements?
• RQ4 How do the empirical constraints compare with predictions from hydrodynamical simulations with varying feedback strengths?
• RQ5 What level of matter power spectrum suppression can be expected at k=1 h Mpc⁻¹ and k=3 h Mpc⁻¹ with high credibility?

Key findings

• At k=1 h Mpc⁻¹, the matter power spectrum suppression is constrained to 0.042⁺⁰.⁰¹²₋₀.⁰¹⁴ (bacco model) and 0.049⁺⁰.⁰¹⁶₋₀.⁰¹² (S19 model).
• At k=3 h Mpc⁻¹, the suppression is 0.184⁺⁰.⁰²⁶₋₀.⁰³¹ (bacco) and 0.179⁺⁰.⁰¹⁸₋₀.⁰²⁰ (S19), showing good agreement between models.
• At 97.5% credibility, baryonic feedback contributes less than 1% suppression at scales k<0.37 h Mpc⁻¹, indicating minimal impact on large scales.
• The empirical constraints exclude hydrodynamical simulations with either too strong or too weak baryonic feedback, with OWLS simulations showing closest agreement.
• The predicted suppression levels are consistent with small-scale cosmic shear studies, confirming their empirical validity.
• Baryonic feedback is unlikely to resolve the S8 tension, as the required suppression is too small to account for the observed discrepancy.

Figure 2: Top: Prediction for the gas (magenta) and stellar (orange) mass fraction together with the fitted data points from the cluster analyses considered. We show the 1 sigma region as filled and represent also the 2 sigma region with faded lines. Bottom: Prediction for the mass slope of the gas