Mass and selection biases of galaxy clusters: a multi-probe approach

Galaxy clusters are fascinating astrophysical objects with a great interest for cosmological applications.

The recipe: Baryons, detectable at different wavelengths, represent only small amount in the mass budget (12% in the diffuse IntraCluster Medium, ICM, and 3% confined in galaxies), while Dark Matter, DM, is the dominant ingredient (85%) but unfortunately only traceable through its gravitational impact. 

Up to now, clusters have been mostly selected by their minority component: directly through the emission from galaxies or the hot ICM, or through the scattering of the Cosmic Microwave Background (CMB) on the ICM (Sunayev-Zeldovich, SZ, effect). These selection criteria are convenient, have provided us with large samples at various redshifts and have helped us establish many of the cluster properties. However, the samples are biased and the amplitude of the bias is yet to be determined. 

Furthermore, knowledge of the cluster mass is needed for both cosmological and astrophysical studies, but mass cannot be directly observed and needs to be derived from the collected photons. 

Our understanding of galaxy cluster physics, and our ability to use clusters to constrain cosmological parameters, are limited by mass and selection biases of the studied samples. 

Given the critical role played by the mass and selection biases, in this project we (Unit 1) exploit the only sample available so far that contains a sizable fraction of low surface brightness clusters missed in X-ray- and SZ-selected surveys. We aim at better determining the role of the selection bias (against low surface brightness clusters) in scaling relations of cosmological and astrophysical interest with the assistance of our data and hydrodynamic simulations; and we (Unit 2) investigate the amount of mass bias by using multi-probe approaches based on high-resolution and high-sensitivity observations with the support of state-of-the-art hydrodynamical simulations.

With this project, we can address, uniquely and for the first time, the mass bias of a sample non-ICM biased and the impact of the ICM selection on the mass bias by comparing ICM-biased and ICM-unbiased samples. We hope to overcome the limitation of literature studies that address mass bias and selection effects independently.

Research Unit 1 - Projects related on Mass inference and possible biases

• Almost all the research activities related to the PRIN 2022 project were carried out within the framework of the following collaborations: 

The300, hydrodynamical simulation

NIKA2, observations of 38 clusters at mm-waves (Large Program Sunayev-Zeldovich)

CHEX-MATE, observations of 118 clusters with XMM-Newton satellite at X-ray, and 

EURA NOVA, data science company.

• Cluster mass inference could be impacted by cluster dynamical state. Studying the most efficient morphological indicators, or a combination of them, to infer the dynamical state with survey-quality data and with hydrodynamical simulations is mandatory, see Cialone G., M. De Petris, et al. MNRAS (2018), De Luca F., M. De Petris, et al. MNRAS (2021), Zhang B. et al. + M. De Petris, MNRAS (2022). We proposed a novel and promising approach to modeling cluster morphology using Zernike polynomials (ZPs). This parameter, already validated on SZ maps generated from synthetic clusters in The300, see Capalbo V., M. De Petris, et al. MNRAS (2021), was recently extended to images with different angular resolutions and wavelengths, and subsequently to real data, to infer the dynamical state. More specifically in:

  1. 1. 1. Planck nearby clusters (109 clusters at z<0.1), Capalbo V., M. De Petris, et al. A&A (2025);

        2. NIKA2 Large Program Sunyaev Zeldovich dataset (35 clusters at 0.5<z<0.9 observed at 150 & 260 GHz), Pappalardo E. et al. + M. De Petris. (to be submitted to A&A in 2026 together with the first NIKA2 LPSZ results papers);

        3. CHEX-MATE sample (118 clusters  observed by XMM-Newton), Ferragamo A., A. Benincasa, M. De Petris, et al. (under revision CHEX-MATE collaboration, to be submitted to A&A (2026));

        4. optical images (galaxy number density maps), Ferragamo A. et al. + M. De Petris (on-going analysis).

Other different metrics can be used to classify cluster dynamical state: a possibility has been the recent use of two different statistical approaches –Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection (UMAP), as we explored in Haggar R., F. De Luca, M. De Petris et al. MNRAS (2024).

• Inference of a minimally biased total mass by applying Machine Learning techniques. This activity is based on a strong/old collaboration with the Universidad Autonoma de Madrid (G. Yepes, W. Cui, D. de Andres and collabs) and EURA NOVA, a company working on big data. We started by inferring the total mass of Planck clusters, i.e., without any mass bias, by training a CNN on The300 Compton-y maps and then applying it to real Planck maps, see de Andres D. et al. + M. De Petris, Nature Astronomy (2022). We then explored the reconstruction of unbiased 3D total (and gas) mass radial profiles starting from mock Compton-y maps, see Ferragamo A. et al. + M. De Petris, MNRAS (2023). Within the PRIN 2022, we carried out the following activities: 

  1. 1. 1. Generating observations of galaxy clusters from Dark-Matter-only simulations by Deep Learning, Caro A. et al. + M. De Petris, RASti (2025);

        2. Reconstruction of total mass radial profiles of NIKA2 Twin Samples by ML model, Ferragamo A., G. Baris, M. De Petris et al. (in preparation);

        3. How much unbiased Planck clusters masses, inferred by CNN model, could impact cosmological parameters? Wicker R., M. De Petris, et al. (on-going analysis).

• Impact of filaments on cluster properties, such as mass and bias. How much the filamentary structures around clusters are correlated with their properties? 

  1. 1. 1. Cluster connectivity, estimated by gas density field, is recostructured in The300 regions with the filament finder DisPerSE and realted to their mass, Santoni S., M. De Petris et al. A&A (2024).

        2. The peculiar case of short filaments, i.e. bridges, has been studied on ACT maps and The300 mock images, see G. Isopi, et al. + M. De Petris, submitted to JCAP (2025).

        3. Impact of line of sight projection on filament reconstruction, an example using tSZ maps, Santoni S., M. De Petris et al. (in preparation).

        4. Mapping intracluster gas filaments in the X-ray maps of CHEX-MATE, Santoni S., I. Bartalucci, M. De Petris, et al. (on-going analysis).

• To better understand the thermodynamics and spatial distribution of the ICM in clusters, and thus potentially obtain more accurate cluster mass estimates, we take advantage of the high angular resolution and sensitivity of NIKA2 tSZ observations. We had the opportunity to contribute to and lead several projects together with the NIKA2 LPSZ team. Some results have already been published, while others are still pending and will be submitted together with the main first NIKA2 LPSZ results papers, with submission to A&A planned for early 2026. In the following the main analyses related to the PRIN activity.

  1. 1. 1. The mapping of the ICM and the inference of the dynamical state of ACT-CL J0240.0+0116 using a multi-wavelength approach are reported in Paliwal A., M. De Petris, A. Ferragamo, et al. A&A (2025).

        2. The capability of double band, high resolution observations to blindly detect clusters in the NIKA2 survey, see D. Chérouvrier, et al. + M. De Petris, A&A (2025) 

        3. All the NIKA2 maps of 35 clusters (C. Hanser (a), et al. + M. De Petris), the impact of these massive objects on background sources (F.X. Desert, et al. + M. De Petris), their ICM properties radial profiles (C. Hanser (b), et al. + M. De Petris), the SZ observable-Mass scaling law (A. Moyer-Anin, et al. + M. De Petris), the study of the gas turbulence (R. Adam, et al. + M. De Petris), (NIKA2 LPSZ Results papers to be submitted all together to A&A in 2026).

        4. The capability to map shocks in the disturbed cluster PSZ2G091.83+26.11 and their impact on mass estimates is reported in Artis E., et al. + M. De Petris, (to be submitted to A&A).

        5. The comparison of gas pressure profiles in the NIKA2 redshift range (0.5-0.9) reconstructed from NIKA2 Twin Sample mock images at 150 GHz provided by The300 simulation: comparison with catalog profiles and available models in literature, Paliwal A., M. De Petris, et al., (on-going analysis).

• The Sparsity in clusters, a common parameter based on the ratio of spherical halo masses estimated at two radii enclosing different overdensities, is useful to infer constraints on cosmological model parameters. However, it is important to account for the impact of possible mass biases, such as the hydrostatic mass bias, see Corasaniti P.S. et al. + M. De Petris, A&A (2025).

• For very distant objects, where X-ray spectrometers are starved of photons, it is difficult to obtain an accurate map of the temperature of the gas in the clusters. This could affect the estimate of the hydrostatic mass. The combination of SZ and X-ray intensity observations allows to reconstruct such kind of maps.

  1. 1. 1. We have validated a model to recover mass-weighted temperature maps using simulated SZ and X-ray images of The300 clusters affected by observational impacts of NIKA2 and XMM-Newton instruments. Wicker R., M. De Petris, et al., (submitted to A&A (2025)). 

        2. The application on real NIKA2 LPSZ with XMM-Newton maps is on going, see Wicker R., M. De Petris, et al., (on-going analysis). 

• Thanks to the XMM-Newton observations from the CHEX-MATE project, it has been possible to investigate ICM profiles in a large sample of clusters, including both nearby low- to intermediate-mass systems and massive distant ones, see M. Muñoz-Echeverría, et al. + M. De Petris (submitted to A&A (2025)) and R. Seppi, et al. + M. De Petris (submitted to A&A (2025)).

• Finally, the baryon content in galaxy clusters is investigated using The300 simulations dataset to assess the  possible impact of sample selection on the derived cosmological parameters. The evolution of baryons and, more specifically, the hot gas is reported in E. Rasia, et al. + M. De Petris, A&A (2025). With almost the same dataset, we studied the peculiar population of clusters with low gas content: their envirnment and impact on Y-M scaling law, F. Guidi, M. De Petris, et al. (on-going analysis).

Research Unit 1

Publications funded by PRIN 2022   

1. V. Capalbo, M. De Petris, A. Ferragamo, et al. "Inference of morphology and dynamical state of nearby Planck-SZ galaxy clusters with Zernike polynomials" A&A, 698, A201 (2025),  https://doi.org/10.1051/0004-6361/202452649

2. A. Caro, D. de Andres, W. Cui, et al + M. De Petris, "Deep learning generated obser v ations of galaxy clusters from dark-matter-only simulations ", RAS Techniques and Instruments, Volume 4, (2025), rzaf007, https://doi.org/10.1093/rasti/rzaf007

3. D. Chérouvrier, et al. + M. De Petris, "NIKA2 Cosmological Legacy Survey - Blind detection of galaxy clusters in the COSMOS field via the SZ effect", A&A, 700, A30 (2025), https://doi.org/10.1051/0004-6361/202554450

4. P.S. Corasaniti, et al. + M. De Petris, "The impact of baryons on the sparsity of simulated galaxy clusters from The Three Hundred Project: Astrophysical and cosmological implications", A&A, 697, A33 (2025) https://doi.org/10.1051/0004-6361/202553914

5. R. Haggar, F. De Luca, M. De Petris, et al. "Reconsidering the dynamical states of galaxy clusters using PCA and UMAP" MNRAS, 532, 1, (2024),  https://doi.org/10.1093/mnras/stae1566 

6. A. Paliwal, M. De Petris, A. Ferragamo, et al. "Exploiting the high-resolution NIKA2 data to study the intracluster medium and dynamical state of ACT-CL J0240.0+0116" A&A, 698, A2 (2025),  https://doi.org/10.1051/0004-6361/202452597

7. E. Rasia, et al. + M. De Petris, "The Three Hundred Project: Modeling baryon and hot-gas fraction evolution in simulated clusters", A&A, 702, A182 (2025), https://doi.org/10.1051/0004-6361/202554283

8. S. Santoni, M. De Petris, G. Yepes, et al. "The Three Hundred project: Estimating the dependence of gas f ilaments on the mass of galaxy clusters " A&A, 692, A44 (2024), https://doi.org/10.1051/0004-6361/202450895 

in preparation or under review 

1. R. Adam, et al. + M. De Petris, "NIKA2 LPSZ Results XI: Turbulence in the intracluster medium as seen through Sunyaev-Zel’dovich fluctuations", to be submitted to A&A (2026)

2. E. Artis, et al. + M. De Petris, "NIKA2 LPSZ: High resolution study of the complex massive and high redshift cluster PSZ2G091.83+26.11", to be submitted to A&A (2026)

3. F.X. Desert, et al. + M. De Petris, "NIKA2 LPSZ Results II: Point-source population across clusters of galaxies Evidence for a gravitational lensing effect", to be submitted to A&A (2026)

4. A. Ferragamo, A. Benincasa, M. De Petris, et al "CHEX-MATE: Classification of galaxy clusters dynamical state with Zernike Polynomials on X-ray images" under revision CHEX-MATE collaboration, to be submitted to A&A (2026)

5. A. Ferragamo, G. Baris, M. De Petris, et al. "NIKA2 LPSZ Results XV. Mass estimates from tSZ using Machine Learning model" in preparation (2026)

6. C. Hanser (a), L. Perotto, et al + M. De Petris, "NIKA2 LPSZ Results I. High-angular resolution maps of the galaxy cluster sample of the Sunyaev-Zeldovich NIKA2 Large Programme", to be submitted to A&A (2026)

7. C. Hanser (b), I. Bartalucci, et al + M. De Petris, "NIKA2 LPSZ Results III. Thermodynamic profiles of a sample of high-redshift clusters from high angular resolution SZ and X-ray synergy", to be submitted to A&A (2026)

8. G. Isopi, et al. + M. De Petris, "The Atacama Cosmology Telescope: A census of bridges between galaxy clusters", submitted to JCAP (2025).

9. A. Moyer-Anin, F. Kéruzoré, et al. + M. De Petris, "NIKA2 LPSZ Results V. The scaling relation between SZ observables and the hydrostatic equilibrium masses", to be submitted to A&A (2026)

10. M. Muñoz-Echeverría, et al. + M. De Petris, "CHEX-MATE: towards a consistent universal pressure profile and  cluster mass reconstruction", submitted to A&A (2025)

11. E. Pappalardo, A. Ferragamo, et al. + M. De Petris "NIKA2 LPSZ Results VII: Clusters dynamical state inference by Zernike polynomials on high-angular resolution tSZ images", to be submitted to A&A (2026)

12. S. Santoni, M. De Petris, et al. "The Three Hundred project: Cosmic Web extraction from 2D gas and Compton-y maps of clusters outskirts", in preparation (2026)

13. S. Santoni, I. Bartalucci, M. De Petris, et al. "Study of gas filamentary structures within CHEX-MATE galaxy clusters", in preparation (2026)

14. R. Seppi, et al. + M. De Petris, "CHEX-MATE: Are we getting cluster thermodynamics right?", submitted to A&A (2025)

15. R. Wicker, M. De Petris, et al., "Galaxy cluster temperature maps from joint X-ray and tSZ maps with The Three Hundred hydrodynamical simulations", submitted to A&A (2025)