Validating Digital Twins of the Local Universe with the Thermal Sunyaev-Zel'dovich Signal

Technical Summary: Validating Digital Twins of the Local Universe with the Thermal Sunyaev–Zel'dovich Signal

Problem Statement
The thermal Sunyaev–Zel'dovich (tSZ) effect serves as a premier probe of the thermal pressure of ionised gas in galaxy clusters and the cosmic web. While standard cosmological analyses utilize tSZ data for statistical constraints (e.g., power spectra, cluster counts), these approaches often lack the spatial phase information necessary for object-by-object comparisons. Conversely, constrained simulations of the local Universe aim to reproduce the specific large-scale structure observed in our neighborhood but require robust, independent validation beyond velocity field comparisons. The paper addresses the need to validate these "digital twins"—data-constrained posterior simulations—against the tSZ signal to assess their fidelity in reconstructing the positions, masses, and thermal pressure distributions of local cosmic structures.

Methodology
The authors introduce CSiBORG-Manticore (CBM), a new suite of digital twins representing the state-of-the-art in Bayesian Origin Reconstruction from Galaxies (BORG) reconstructions. These simulations sample the posterior distribution of the local density field (within $\sim155 h^{-1}$ Mpc) inferred from the 2M++ galaxy catalogue, augmented with high-resolution dark matter zoom-ins. The authors compare CBM against the previous generation, CSiBORG (CB2), and the hydrodynamical SLOW simulation (based on CLUES initial conditions).

The validation framework employs three complementary metrics using Planck Compton-$y$ maps (McCarthy and Hill 2024) and eROSITA X-ray cluster catalogues (calibrated with weak lensing):

1. Angular Positioning ($p_{tSZ}$): For specific observed clusters, the authors measure the tSZ signal at the simulated halo positions using aperture photometry. They compute a $p$-value ($p_{tSZ}$) by comparing the signal to a null distribution of random sky positions. Low $p_{tSZ}$ values indicate the simulated halo coincides with an observed tSZ hotspot.
2. Stacked Radial Profiles: To assess mass dependence, the authors stack 1D radial tSZ profiles for haloes ranked by mass (top 10, 50, and 100) across realisations. This tests whether the simulations reproduce the expected trend of increasing tSZ signal with halo mass.
3. Mass Scaling Relations: Using a Bayesian linear regression that marginalises over mass uncertainty, the authors infer scaling relations between BORG halo masses and observed quantities:
   • $Y_{500c}^{tSZ}$ vs. Halo Mass (testing the self-similar slope $m \approx 5/3$).
   • BORG Mass vs. Planck tSZ Mass.
   • BORG Mass vs. Weak-lensing-calibrated eROSITA X-ray Mass.
     Matching is performed using strict criteria ($\Delta\theta < 60'$, $\Delta cz < 300$ km s$^{-1}$) and the Local Universe Model (LUM) matching procedure to associate observed clusters with simulated halo associations.

Key Contributions

• Introduction of CSiBORG-Manticore (CBM): A new suite of 50 posterior samples representing the latest BORG reconstruction (Manticore-Local initial conditions), offering improved initial conditions and galaxy bias modelling compared to previous iterations.
• Novel Validation Framework: Development of a scoring system for constrained simulations based on the tSZ signal, moving beyond velocity field comparisons to directly test the thermal pressure reconstruction of the cosmic web.
• Calibration of Mass-Observable Relations: Demonstration of how high-fidelity digital twins can be used to calibrate mass–observable relations (specifically $Y$–Mass) without relying on external mass proxies, by leveraging the known dark matter distribution from the simulations.

Results

• Positional Accuracy: The majority of selected local clusters (e.g., Coma, Shapley A3558, Perseus) are reproduced with high fidelity in CBM, with $p_{tSZ} < 0.05$ across realisations. CBM significantly outperforms the SLOW simulation; while SLOW yields only two clusters with $p_{tSZ} < 0.05$ (Perseus and Shapley A3558) and large angular offsets ($\sim15^\circ$ for Coma), CBM achieves high significance for most targets with offsets typically $<1^\circ$.
• Per-Cluster Reconstruction: Perseus (A426), a cool-core cluster absent in CB2, is robustly reproduced in CBM ($p_{tSZ} \approx 2.9 \times 10^{-4}$), highlighting improvements in the underlying BORG inference. Conversely, Hercules (A2151) remains poorly reproduced in CBM.
• Mass Scaling:
  • $Y$–Mass Relation: CBM yields a slope of $m = 1.79 \pm 0.28$ for the $Y_{500c}^{tSZ}$–Mass relation, consistent with the self-similar expectation ($5/3$) and closer to the theoretical value than CB2 ($m = 1.43 \pm 0.31$). CBM also exhibits lower intrinsic scatter ($\sigma_{int} = 0.09 \pm 0.07$ dex) compared to CB2.
  • Mass Calibration: When comparing BORG masses to Planck tSZ masses, CBM shows a systematic offset ($c \approx -0.20$ dex), implying BORG masses are $\sim1.6\times$ higher. This is consistent with the known $\sim30\%$ hydrostatic mass bias in Planck tSZ masses.
  • Weak-Lensing Validation: Crucially, when compared to weak-lensing-calibrated eROSITA X-ray masses, CBM shows excellent agreement with the one-to-one relation ($m = 0.84 \pm 0.19$, $c = 0.02 \pm 0.06$, $0.5\sigma$ tension). In contrast, CB2 deviates significantly ($2.1\sigma$ tension). This suggests CBM halo masses more accurately reflect true cluster masses than previous reconstructions.

Significance
The paper claims that the tSZ effect provides a powerful, independent validation observable for constrained simulations, complementary to velocity field tests. The results demonstrate that the latest BORG-based digital twins (CBM) achieve substantially higher positional and mass fidelity than previous generations and alternative velocity-constrained simulations (SLOW).

The authors posit that these high-fidelity digital twins offer a practical route to extracting additional physical information from tSZ data. By anchoring the tSZ signal to a posterior set of large-scale structure realisations, researchers can explicitly model projection effects and line-of-sight contributions that are typically absorbed into nuisance parameters in statistical analyses. The work paves the way for integrating large-scale structure information inherent in constrained simulations into the study of Cosmic Microwave Background (CMB) secondary anisotropies, potentially enabling future joint analyses of CMB primary and secondary signals with large-scale structure in a self-consistent, field-level likelihood framework.