🔭 astrophysics

Euclid: Exploring observational systematics in cluster cosmology -- a comprehensive analysis of cluster counts and clustering

This study utilizes 1,000 Euclid-like simulations to demonstrate that combining galaxy cluster counts with clustering significantly enhances cosmological constraints (by over 300% in figure of merit) while quantifying how systematic effects like photometric redshift uncertainties and redshift-space distortions impact parameter estimates and covariance modeling.

Original authors: A. Fumagalli, M. Costanzi, T. Castro, A. Saro, S. Borgani, M. Romanello, F. Marulli, E. Tsaprazi, P. Monaco, B. Altieri, A. Amara, L. Amendola, S. Andreon, N. Auricchio, C. Baccigalupi, M. Baldi, A. BA. Fumagalli, M. Costanzi, T. Castro, A. Saro, S. Borgani, M. Romanello, F. Marulli, E. Tsaprazi, P. Monaco, B. Altieri, A. Amara, L. Amendola, S. Andreon, N. Auricchio, C. Baccigalupi, M. Baldi, A. Balestra, S. Bardelli, A. Biviano, E. Branchini, M. Brescia, S. Camera, G. Cañas-Herrera, V. Capobianco, C. Carbone, J. Carretero, S. Casas, M. Castellano, G. Castignani, S. Cavuoti, K. C. Chambers, A. Cimatti, C. Colodro-Conde, G. Congedo, L. Conversi, Y. Copin, F. Courbin, H. M. Courtois, A. Da Silva, H. Degaudenzi, S. de la Torre, G. De Lucia, A. M. Di Giorgio, H. Dole, M. Douspis, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, S. Escoffier, M. Farina, R. Farinelli, F. Faustini, S. Ferriol, F. Finelli, P. Fosalba, N. Fourmanoit, M. Frailis, E. Franceschi, M. Fumana, S. Galeotta, K. George, B. Gillis, C. Giocoli, J. Gracia-Carpio, A. Grazian, F. Grupp, L. Guzzo, S. V. H. Haugan, W. Holmes, F. Hormuth, A. Hornstrup, K. Jahnke, M. Jhabvala, B. Joachimi, E. Keihänen, S. Kermiche, A. Kiessling, B. Kubik, M. Kümmel, M. Kunz, H. Kurki-Suonio, A. M. C. Le Brun, S. Ligori, P. B. Lilje, V. Lindholm, I. Lloro, G. Mainetti, D. Maino, E. Maiorano, O. Mansutti, O. Marggraf, M. Martinelli, N. Martinet, R. J. Massey, E. Medinaceli, S. Mei, Y. Mellier, M. Meneghetti, E. Merlin, G. Meylan, J. J. Mohr, A. Mora, M. Moresco, L. Moscardini, E. Munari, R. Nakajima, C. Neissner, S. -M. Niemi, C. Padilla, S. Paltani, F. Pasian, K. Pedersen, V. Pettorino, S. Pires, G. Polenta, M. Poncet, L. A. Popa, L. Pozzetti, F. Raison, R. Rebolo, A. Renzi, J. Rhodes, G. Riccio, E. Romelli, M. Roncarelli, C. Rosset, R. Saglia, Z. Sakr, A. G. Sánchez, D. Sapone, B. Sartoris, P. Schneider, T. Schrabback, A. Secroun, E. Sefusatti, G. Seidel, M. Seiffert, S. Serrano, P. Simon, C. Sirignano, G. Sirri, A. Spurio Mancini, L. Stanco, J. Steinwagner, P. Tallada-Crespí, D. Tavagnacco, A. N. Taylor, I. Tereno, N. Tessore, S. Toft, R. Toledo-Moreo, F. Torradeflot, I. Tutusaus, L. Valenziano, J. Valiviita, T. Vassallo, G. Verdoes Kleijn, A. Veropalumbo, Y. Wang, J. Weller, G. Zamorani, F. M. Zerbi, E. Zucca, C. Burigana, L. Gabarra, M. Maturi, C. Porciani, V. Scottez, M. Sereno, M. Viel

Published 2026-05-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: A. Fumagalli, M. Costanzi, T. Castro, A. Saro, S. Borgani, M. Romanello, F. Marulli, E. Tsaprazi, P. Monaco, B. Altieri, A. Amara, L. Amendola, S. Andreon, N. Auricchio, C. Baccigalupi, M. Baldi, A. Balestra, S. Bardelli, A. Biviano, E. Branchini, M. Brescia, S. Camera, G. Cañas-Herrera, V. Capobianco, C. Carbone, J. Carretero, S. Casas, M. Castellano, G. Castignani, S. Cavuoti, K. C. Chambers, A. Cimatti, C. Colodro-Conde, G. Congedo, L. Conversi, Y. Copin, F. Courbin, H. M. Courtois, A. Da Silva, H. Degaudenzi, S. de la Torre, G. De Lucia, A. M. Di Giorgio, H. Dole, M. Douspis, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, S. Escoffier, M. Farina, R. Farinelli, F. Faustini, S. Ferriol, F. Finelli, P. Fosalba, N. Fourmanoit, M. Frailis, E. Franceschi, M. Fumana, S. Galeotta, K. George, B. Gillis, C. Giocoli, J. Gracia-Carpio, A. Grazian, F. Grupp, L. Guzzo, S. V. H. Haugan, W. Holmes, F. Hormuth, A. Hornstrup, K. Jahnke, M. Jhabvala, B. Joachimi, E. Keihänen, S. Kermiche, A. Kiessling, B. Kubik, M. Kümmel, M. Kunz, H. Kurki-Suonio, A. M. C. Le Brun, S. Ligori, P. B. Lilje, V. Lindholm, I. Lloro, G. Mainetti, D. Maino, E. Maiorano, O. Mansutti, O. Marggraf, M. Martinelli, N. Martinet, R. J. Massey, E. Medinaceli, S. Mei, Y. Mellier, M. Meneghetti, E. Merlin, G. Meylan, J. J. Mohr, A. Mora, M. Moresco, L. Moscardini, E. Munari, R. Nakajima, C. Neissner, S. -M. Niemi, C. Padilla, S. Paltani, F. Pasian, K. Pedersen, V. Pettorino, S. Pires, G. Polenta, M. Poncet, L. A. Popa, L. Pozzetti, F. Raison, R. Rebolo, A. Renzi, J. Rhodes, G. Riccio, E. Romelli, M. Roncarelli, C. Rosset, R. Saglia, Z. Sakr, A. G. Sánchez, D. Sapone, B. Sartoris, P. Schneider, T. Schrabback, A. Secroun, E. Sefusatti, G. Seidel, M. Seiffert, S. Serrano, P. Simon, C. Sirignano, G. Sirri, A. Spurio Mancini, L. Stanco, J. Steinwagner, P. Tallada-Crespí, D. Tavagnacco, A. N. Taylor, I. Tereno, N. Tessore, S. Toft, R. Toledo-Moreo, F. Torradeflot, I. Tutusaus, L. Valenziano, J. Valiviita, T. Vassallo, G. Verdoes Kleijn, A. Veropalumbo, Y. Wang, J. Weller, G. Zamorani, F. M. Zerbi, E. Zucca, C. Burigana, L. Gabarra, M. Maturi, C. Porciani, V. Scottez, M. Sereno, M. Viel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, three-dimensional city made of invisible matter, where galaxies are the buildings and massive clusters of galaxies are the skyscrapers. Astronomers want to understand the "blueprint" of this city: how much matter there is, how fast it's growing, and what forces are shaping it.

This paper is like a quality control report for a massive new survey called Euclid, which is a space telescope designed to take a 3D map of these cosmic skyscrapers. The authors are asking: "If we use this new map to figure out the universe's blueprint, what mistakes (systematic errors) could mess up our calculations, and how do we fix them?"

Here is a breakdown of their findings using everyday analogies:

1. Two Ways to Count the Skyscrapers

To understand the city, the astronomers use two different methods:

Method A (The Census): They simply count how many skyscrapers exist at different heights (redshifts) and sizes (richness). This is like counting how many people live in a city to guess the city's total population.
Method B (The Neighborhood Map): They look at how the skyscrapers are arranged relative to each other. Are they clumped together in a downtown district, or spread out in the suburbs? This is like looking at the street layout to understand the city's structure.

The Big Discovery: The paper finds that these two methods are like two friends who don't talk to each other. They are independent. Knowing the total count doesn't tell you anything about the arrangement, and vice versa. When you combine them, you get a much clearer picture than using either one alone. In fact, combining them improves the accuracy of the cosmic blueprint by over 300%.

2. The "Blurry Glasses" Problem (Photometric Redshifts)

One of the biggest challenges is knowing exactly how far away a skyscraper is. The telescope uses "photometric redshifts," which are like estimating distance by looking at the color of a building's lights. It's fast, but it's not perfect; the colors can look slightly different than they really are, making the distance estimate "fuzzy."

The Impact: If your glasses are a little blurry, your map of the city gets distorted. The paper shows that if the distance estimates are off by a realistic amount, your final answer about the universe's composition becomes 20–30% less precise. It's like trying to measure the size of a room with a ruler that stretches and shrinks randomly.

3. The "Traffic Jam" Effect (Redshift-Space Distortions)

Galaxies aren't just sitting still; they are moving. Sometimes they move toward us, and sometimes away, due to the gravity of nearby massive clusters. This movement messes up the distance calculation, making clusters look squashed or stretched along the line of sight. This is called Redshift-Space Distortion (RSD).

The Impact: If you ignore this "traffic jam" effect, your map becomes biased. You might think the universe is shaped differently than it actually is. The paper shows that while this effect doesn't ruin the whole picture, ignoring it shifts the results enough to be a serious problem (a "bias"). You have to correct for the traffic to get the right shape of the city.

4. The "Zoom Level" Issue (How Close to Look)

When looking at the arrangement of skyscrapers, how close should you look?

Too far away: If you only look at very large distances (beyond the size of a typical city block), you miss the interesting details. The paper finds that looking at scales smaller than 60 "units" (megaparsecs) actually adds valuable information.
Too close: Looking at scales larger than the "acoustic oscillation" (a specific cosmic rhythm, roughly 130 units) doesn't add much new info. It's like zooming out so far on a map that you just see a blank ocean; you've lost the details of the city.

5. The "Noise" in the Data (Covariance)

In statistics, "covariance" is like understanding how errors in one part of your map might affect errors in another part.

The paper found that the "blurry glasses" (photo-z errors) and the "traffic jams" (RSDs) change the noise in the data.
If you don't account for this changing noise, you might think your measurements are more precise than they really are. It's like thinking your scale is accurate when it's actually vibrating. The authors created a new, better formula to account for this "vibration," ensuring the final results aren't overconfident.

The Bottom Line

The authors built a simulation using 1,000 fake universes to test these ideas. They concluded that:

Combine the methods: Using both the "Census" (counts) and the "Neighborhood Map" (clustering) together is the best way to understand the universe.
Fix the errors: You must correct for the "blurry glasses" and "traffic jams," or your map will be wrong.
Don't ignore the small stuff: Looking at smaller scales (closer distances) gives you more power to solve the mystery of the universe's composition.

In short, this paper provides the instruction manual for how to use the Euclid telescope's data to build the most accurate map of the universe possible, while avoiding the common traps that could lead to a wrong conclusion.

Technical Summary: Euclid: Exploring systematics effects in cluster cosmology

Problem Statement
Galaxy clusters serve as critical cosmological probes for constraining the matter density parameter ( $\Omega_m$ ) and the amplitude of density fluctuations ( $\sigma_8$ ). While traditional analyses rely on cluster number counts, the spatial distribution of clusters (clustering) offers complementary information to break degeneracies in cosmological and mass-observable parameters. However, the upcoming Euclid mission, which aims to map $\sim 10^5$ clusters up to $z=2$ , requires sub-percent accuracy. A major challenge lies in characterizing the impact of observational and modelling systematic effects—specifically photometric redshift (photo- $z$ ) uncertainties and redshift-space distortions (RSDs)—on both cluster counts and clustering statistics, as well as their covariance matrices. Furthermore, the necessity of combining these probes to maximize constraining power requires a rigorous understanding of their cross-correlations and the dependence of covariance matrices on cosmology.

Methodology
The authors utilize a framework based on 1,000 Euclid-like lightcone catalogues generated using the PINOCCHIO code (employing third-order Lagrangian perturbation theory and ellipsoidal collapse). These simulations cover a sky area of 10,313 deg $^2$ and redshifts $z=0$ to $2.5$, containing approximately $10^5$ haloes per catalogue with $M_{vir} \ge 10^{13.5} h^{-1} M_{\odot}$ .

The study employs the following methodological steps:

Theoretical Modelling: The authors model cluster number counts and the 2-point correlation function (2PCF) monopole, incorporating effects from photo- $z$ errors (modeled as Gaussian scatter), RSDs (Kaiser effect), infrared (IR) resummation for BAO damping, and geometric distortions (GD). They also model the weak lensing mean mass as a supporting probe to break degeneracies in scaling relations.
Covariance Analysis: Numerical covariances are computed directly from the 1,000 mocks. These are compared against semi-analytical models (adapted from Fumagalli et al. 2021 and Euclid Collaboration: Fumagalli et al. 2024) to validate the treatment of shot-noise, sample variance, and cross-correlations.
Likelihood Analysis: A Bayesian inference is performed using PolyChord to explore the posterior distributions of $\Omega_m$ , $\sigma_8$ , and four mass-observable relation parameters. The analysis evaluates the Figure of Merit (FoM) and the Index of Inconsistency (IoI) across various probe combinations (counts, clustering, weak lensing) and systematic configurations.
Systematic Testing: The impact of neglecting specific systematics (e.g., RSDs, photo- $z$ errors) in the modelling of both the statistics and their covariance matrices is quantified by comparing results against a "full model" baseline.

Key Contributions and Results

Independence of Probes: The analysis confirms that cluster number counts and cluster clustering are effectively uncorrelated observables. The Pearson correlation coefficient between their log-likelihood residuals is $\rho = -0.011 \pm 0.031$ , consistent with zero. This independence arises because counts measure the mean comoving number density, while clustering measures fluctuations around that mean.
Constraining Power of Combination: Combining cluster clustering with number counts significantly enhances cosmological constraints. The FoM increases by over 300% compared to number counts alone. The combination of all three probes (counts, clustering, and weak lensing mass) yields the tightest and most accurate constraints, with the full-probe analysis being less susceptible to prior-volume effects than two-probe combinations.
Impact of Photo- $z$ Uncertainties: Photometric redshift errors are the dominant systematic effect. An optimistic uncertainty ( $\sigma_{z0} = 0.005$ ) broadens posteriors by less than 10%, whereas a more realistic uncertainty ( $\sigma_{z0} = 0.01$ ) broadens them by 20–30%. Photo- $z$ errors also significantly reduce the sample variance in the number count covariance.
Impact of Secondary Distortions: While RSDs, IR resummation, and geometric distortions have a smaller impact on the FoM (5% for clustering alone, ~10% for the full combination) compared to photo- $z$ errors, neglecting RSDs introduces a significant bias (shift of $\sim 2\sigma$ ) in the $\Omega_m$ – $\sigma_8$ posteriors.
Scale Dependence: Clustering data at scales below $60 h^{-1}$ Mpc provides additional constraining power, whereas scales larger than the acoustic oscillation scale ( $>130 h^{-1}$ Mpc) add negligible information on $\Omega_m$ and $\sigma_8$ .
Covariance Modelling: The study demonstrates that neglecting RSDs and photo- $z$ effects in the number count covariance leads to a 10–20% underestimation of the posterior amplitude. The authors propose an effective power spectrum model (summing monopole and quadrupole terms) that accurately captures the sample covariance without the computational cost of full anisotropic modelling.
Cosmology-Dependent Covariance: Using a cosmology-dependent covariance matrix improves clustering constraints by ~40%. However, when number counts are combined with clustering, this additional gain vanishes, suggesting that number counts already encapsulate the information encoded in the clustering covariance's cosmological dependence.

Significance
The paper establishes a robust framework for the joint analysis of cluster counts and clustering for the Euclid mission. It highlights that while combining these probes drastically improves cosmological constraints, it simultaneously increases sensitivity to systematic effects. The work underscores the necessity of accurately modelling photo- $z$ uncertainties and RSDs not only in the statistics themselves but also within the covariance matrices to avoid biased constraints. By validating that counts and clustering are independent and demonstrating the efficacy of the combined approach, the study provides essential prescriptions for maximizing the scientific return of Euclid cluster cosmology, while cautioning that narrower constraints from combined analyses require even more rigorous systematic control than single-probe analyses.