Enhancing Thermal Sunyaev-Zel'dovich Analyses with Digital Twins of the Local Universe

TL;DR

This work investigates how the thermal Sunyaev-Zel'dovich (tSZ) signal can validate and augment Bayesian forward-model constrained simulations of the local Universe. By employing two generations of digital twins, CB2 and CBM, built from the BORG framework, the authors develop a halo-centric framework that pairs tSZ measurements, radial stacking, halo associations, and scaling-relations fitting to Planck Compton-$y$ maps and eROSITA X-ray masses, while accounting for uncertainties in halo masses from the posterior. The results show that CBM offers improved angular fidelity and mass calibration, with $Y_{500c}^{tSZ}$–$M$ scaling closer to the self-similar expectation $m=5/3$ and masses more consistent with weak-lensing-calibrated X-ray masses, compared with CB2. The study demonstrates that digital twins are a powerful tool to extract additional information from tSZ data, validate assumptions in standard analyses, and potentially enable integrated field-level modeling of large-scale structure and CMB secondary anisotropies, including future Bayesian-evidence comparisons and joint likelihoods with tSZ/X-ray data.

Abstract

The thermal Sunyaev-Zel'dovich (tSZ) effect provides a powerful probe of the thermal pressure of ionised gas in galaxy clusters and the cosmic web; constrained simulations reconstruct the mass and velocity fields of the local Universe. We explore how these two may be mutually informative: the tSZ signal provides a benchmark for assessing the fidelity of constrained simulations, and constrained simulations contribute information on the positions, total masses and density profiles of cosmic web structures for use in tSZ studies. We focus on cluster predictions in the Bayesian Origin Reconstruction from Galaxies (BORG) paradigm, introducing CSiBORG-Manticore, a new state-of-the-art suite of digital twins -- data-constrained posterior simulations whose initial conditions are inferred via Bayesian forward modelling. We develop a framework for scoring constrained simulations on their ability to match measured Compton-$y$ maps from Planck for cluster cutouts, and use it to demonstrate improvement from previous BORG reconstructions. We further validate halo masses against weak-lensing-calibrated X-ray masses from eROSITA. We also show how high-fidelity digital twins offer a practical route to extracting additional information from tSZ data through a novel calibration of the mass-observable relation, and provide a complementary framework to purely statistical analyses of Compton-$y$ maps. This paves the way for integrating the large-scale structure information inherent in constrained simulations into the study of CMB secondary anisotropies.

Figures (8)

• Figure 1: Distribution of $p_{\rm tSZ}$ for selected clusters from \ref{['tab:named_clusters']} across realisations in CB2 and CBM. For each cluster, $p_{\rm tSZ}$ is the fraction of random sky positions that yield an equal or higher tSZ signal than the observed cluster position; low values indicate that the simulated halo lies at the observed tSZ hotspot, indicative of a well-reconstructed cluster. The horizontal dashed line marks $p_{\rm tSZ} = 0.05$. We also show $p_{\rm tSZ}$ values for SLOW clusters HernandezMartinez2024_SLOW, computed using the same procedure with their simulated halo positions.
• Figure 2: Compton-$y$ map cutouts centred on selected clusters. White dots mark the positions of CBM halo realisations, the green dot indicates the reported cluster centre from the optical catalogue, and the red dot marks the local peak of the tSZ map. For Shapley (A3558), the cyan dot marks the position of Shapley (A3562), which lies within the field of view.
• Figure 3: Stacked 1D radial tSZ profiles for haloes ranked by mass. Profiles are measured at normalised angular separations $\theta / (2\theta_{500{\rm c}})$ and stacked within cumulative mass bins: top 10, top 50, and top 100 most massive haloes per realisation, then combined across all realisations. Halo masses $M_{200{\rm c}}$ are in units of $h^{-1}\,M_\odot$. Solid lines show the mean stacked profile for CB2 and CBM, with shaded bands indicating the $1\sigma$ uncertainty from bootstrap resampling. The grey band shows the random expectation from stacking at random sky positions. Both simulations show a clear signal above random in the top 10 and top 50 bins, with CBM marginally stronger in the top 10. The signal weakens in the top 100 bin, approaching the random baseline.
• Figure 4: Comparison of Planck tSZ masses and eROSITA X-ray masses for matched clusters; error bars show $1\sigma$ uncertainties. The dashed line shows the one-to-one relation. The Planck masses are systematically lower by ${\sim} 0.14~\mathrm{dex}$ (${\sim}30\%$), consistent with the known hydrostatic mass bias Sereno_2017.
• Figure 5: Planck cluster scaling relations. Top row: integrated Compton parameter $Y_{500{\rm c}}^{\rm tSZ}$ versus BORG halo mass for which we show the expected self-similar slope of $5/3$ as a red dashed line. Bottom row: Planck-calibrated mass $M_{500{\rm c}}^{\rm tSZ}$ versus BORG halo mass, the one-to-one relation is shown as a red dashed line.