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The eROSITA Final Equatorial-Depth Survey (eFEDS): X-ray stacking analysis of Subaru's optically selected clusters spanning low richness regime

This paper presents an X-ray stacking analysis of 997 optically selected galaxy clusters from the Subaru HSC survey using eFEDS data, revealing scaling relations between luminosity, richness, and mass that extend into lower-mass regimes while highlighting systematic differences between X-ray detected and undetected systems.

Original authors: N. T. Nguyen-Dang, N. Ota, N. Okabe, M. Oguri, I. Mitsuishi, T. H. Reiprich, F. Pacaud, E. Bulbul, J. S. Sanders, M. Brüggen, A. Liu, Y. Tsujita, I. Chiu, V. Ghirardini, S. Grandis, M. Klein, K. Migka

Published 2026-04-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: N. T. Nguyen-Dang, N. Ota, N. Okabe, M. Oguri, I. Mitsuishi, T. H. Reiprich, F. Pacaud, E. Bulbul, J. S. Sanders, M. Brüggen, A. Liu, Y. Tsujita, I. Chiu, V. Ghirardini, S. Grandis, M. Klein, K. Migkas, H. Miyatake, S. Miyazaki, M. E. Ramos-Ceja

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, bustling city. In this city, galaxy clusters are the massive downtown districts, packed with thousands of galaxies (the buildings), swirling clouds of super-hot gas (the atmosphere), and invisible dark matter (the foundation holding it all together).

For a long time, astronomers have tried to map this city, but they've been using different flashlights. Some use X-ray flashlights to see the hot gas, while others use optical flashlights to see the galaxies themselves. The problem? These flashlights don't always shine on the same buildings. The X-ray flashlight tends to find the big, shiny, well-organized skyscrapers, while the optical flashlight finds everything, including the small, messy, or dimly lit neighborhoods that the X-ray light misses.

This paper is like a new, super-powered survey that tries to combine both flashlights to get a complete picture of the city. Here is the story of what they found:

1. The Mission: A Bigger, Better Map

The researchers used two massive tools:

eROSITA: A space telescope that scans the sky in X-rays (seeing the hot gas).
Subaru HSC: A giant camera on a mountain in Hawaii that takes deep optical photos (seeing the galaxies).

They focused on a specific patch of sky called eFEDS. In their previous work, they only looked at the "VIPs"—the 43 richest, most massive clusters. In this new study, they cast a much wider net, looking at 997 clusters, including many smaller, "lower-class" ones that were previously ignored. It's like going from studying only the penthouses to studying the entire city block, including the apartments and row houses.

2. The Method: The "Stacking" Trick

Here's the tricky part: Most of these 997 clusters are too faint to be seen individually in X-rays. It's like trying to hear a whisper in a noisy room; you can't hear one person, but if you have 100 people whispering the same thing at once, you can hear the collective sound.

The astronomers used a technique called stacking. They grouped clusters together based on how many galaxies they had (richness) and how far away they were (redshift). Then, they superimposed their X-ray data on top of each other. This amplified the faint signals, allowing them to measure the average properties of these "invisible" clusters.

3. The Big Discoveries

A. The "Richness" vs. "Mass" Connection

Astronomers want to know: If I count the number of galaxies in a cluster (richness), how heavy is the whole cluster (mass)?

The Finding: They found a very reliable rule. The more galaxies you see, the heavier the cluster is.
The Analogy: It's like judging the weight of a suitcase by counting the number of clothes inside. Even if the clothes are different colors, the count is a pretty good guess at the total weight. This rule held true even for the faint, X-ray invisible clusters.

B. The "Luminosity" vs. "Mass" Surprise

This is where it gets interesting. They looked at how bright the hot gas is (luminosity) compared to the mass.

The Finding: The relationship wasn't a straight line. For the clusters that were bright in X-rays, the gas got brighter very quickly as the cluster got heavier. But for the clusters that were faint in X-rays, the gas didn't get as bright as expected.
The Analogy: Imagine two types of campfires.
- Type A (X-ray Detected): These are roaring bonfires. As you add more wood (mass), the fire gets explosively bright.
- Type B (X-ray Undetected): These are smoldering embers. Even if you add a lot of wood, they stay dim and smoky.
- The Conclusion: The optical survey found a whole bunch of these "smoldering ember" clusters that the X-ray survey missed. This means the universe is full of galaxy clusters that are massive but just don't like to glow brightly in X-rays.

C. The Shape of the Gas

They also looked at the shape of the gas clouds.

The Finding: The bright clusters had gas packed tightly in the center (like a dense crowd in a stadium). The faint clusters had gas spread out loosely (like people scattered in a park).
The Analogy: The bright clusters are like a packed concert where everyone is huddled near the stage. The faint clusters are like a festival where people are spread out across the whole field. The "messy" clusters are harder to spot with an X-ray flashlight because the light is too spread out.

4. Why This Matters

Before this study, we thought we knew most of the galaxy clusters because we found the bright ones. This paper tells us we were missing a huge chunk of the population.

The "Hidden" Population: About 80% of the clusters they found in the optical photos didn't show up in the X-ray catalog. They are real, massive structures, but they are "X-ray faint."
The Lesson: If you only use an X-ray flashlight, you only see the "perfect" clusters. If you use an optical flashlight, you see the whole city, including the messy, evolving, and faint neighborhoods.

Summary

This paper is a victory for teamwork. By combining the deep optical eyes of the Subaru telescope with the X-ray vision of eROSITA, astronomers realized that the universe is more diverse than we thought. There are many galaxy clusters that are massive but "quiet" in X-rays.

The Takeaway: To understand the true history of the universe, we can't just look at the shiny, perfect objects. We have to look at the faint, messy, and hidden ones too, because they tell a different, equally important story about how the cosmic city grows and changes.

1. Problem Statement

Galaxy clusters are critical tracers of cosmic structure and cosmology, but different selection methods (optical, weak lensing, X-ray) introduce systematic biases.

Selection Bias: X-ray flux-limited surveys tend to favor massive, relaxed clusters with cool cores, often missing lower-mass or dynamically disturbed systems. Conversely, optically selected clusters (based on red-sequence galaxy overdensities) capture a broader mass range but may suffer from projection effects and include systems with irregular X-ray morphologies.
Knowledge Gap: There is a need to understand the systematic differences in X-ray properties between optically selected clusters that have X-ray counterparts and those that do not. Furthermore, scaling relations (Luminosity-Mass and Richness-Mass) for optically selected clusters in the low-mass and low-luminosity regimes remain poorly constrained compared to X-ray-selected samples.
Objective: This study aims to investigate the scaling relations ( $L-M$ and $N-M$ ) and radial X-ray profiles of a large sample of optically selected clusters using data from the eROSITA Final Equatorial-Depth Survey (eFEDS) and the Subaru Hyper Suprime-Cam (HSC).

2. Methodology

The study employs a multi-wavelength approach combining deep optical imaging with X-ray stacking techniques.

Sample Selection:
- Optical: 997 galaxy clusters from the CAMIRA catalog (Subaru HSC) located within the eFEDS field.
- Parameters: Richness ( $N$ ) range of $15 < N < 114$ and redshift $0.10 < z < 1.34$ .
- X-ray Counterparts: Only 171 clusters (17%) were individually detected in the eFEDS X-ray catalog. The remaining 826 were treated as "undetected."
- Matching: Counterparts were identified by searching for spatially extended X-ray sources within the characteristic radius $R_{500}$ with redshift consistency ( $|\Delta z| < 0.02$ ).
X-ray Analysis (Stacking):
- Luminosity: Due to low photon statistics for individual clusters, the authors performed a stacking analysis. Clusters were grouped into 32 bins based on richness and redshift.
- Luminosity Calculation: Bolometric luminosity ($0.01-30$ keV) was derived from observed count rates ($0.5-2.0$ keV) using an APEC plasma model and conversion factors, rather than individual spectral fitting.
- Surface Brightness: Radial profiles were stacked for detected and undetected subsamples separately. Profiles were modeled using a 1D $\beta$ -model convolved with the eROSITA Point Spread Function (PSF).
Mass Calibration:
- Weak Lensing (WL): Cluster masses ( $M_{500}$ ) were estimated using the HSC-Y3 shape catalog.
- Modeling: Shear profiles were fitted with a spherical Navarro-Frenk-White (NFW) profile. The analysis explicitly accounted for miscentering (offset between the optical center and the true halo center) using a probabilistic model.
Scaling Relation Analysis:
- Framework: A hierarchical Bayesian regression framework (HiBRECS) was used to fit power-law relations between Mass ( $M$ ), Luminosity ( $L$ ), and Richness ( $N$ ).
- Evolution: The model tested for redshift evolution beyond the standard self-similar expectation ( $E(z)$ corrections) by allowing evolution parameters ( $c, d$ ) to vary.
- Subgroups: Relations were fitted separately for the full sample, X-ray detected clusters, and X-ray undetected clusters.

3. Key Contributions

Sample Size and Depth: This is the largest study of its kind for optically selected clusters in the eFEDS field, extending the analysis from a previous small sample of 43 high-richness clusters to 997 clusters, significantly probing the low-mass and low-luminosity regimes.
Systematic Comparison: It provides a rigorous comparison between X-ray detected and undetected optically selected clusters, quantifying how selection effects impact scaling relations.
Mass Calibration: It utilizes a robust weak-lensing mass calibration that includes miscentering corrections, reducing systematic biases in the mass estimates compared to previous studies.
Methodological Advance: The use of hierarchical Bayesian regression allows for the simultaneous handling of measurement errors, intrinsic scatter, and selection effects (specifically the richness threshold).

4. Key Results

A. Scaling Relations ( $L-M$ and $N-M$ )

$L-M$ Relation: The best-fit slope for the full sample is $1.56^{+0.14}_{-0.12}$ . This is slightly steeper than the self-similar prediction ( $4/3 \approx 1.33$ $4/3 \approx 1.33$ ) but consistent with previous CAMIRA studies.
- Subgroup Difference: X-ray detected clusters show a steeper slope ( $1.80^{+0.34}_{-0.26}$ ) compared to undetected clusters ( $1.17^{+0.26}_{-0.21}$ ), though the difference is only marginally significant ( $\sim 2\sigma$ ).
$N-M$ Relation: The slope is $0.766^{+0.070}_{-0.060}$ , broadly agreeing with theoretical expectations and other optical samples.
- Subgroup Consistency: The $N-M$ slope is consistent between detected and undetected subgroups, suggesting optical richness is a robust mass proxy independent of X-ray detectability.
Redshift Evolution: The data do not require additional redshift evolution beyond the standard self-similar scaling ( $E(z)$ corrections). Evolution parameters were found to be consistent with zero, though constraints remain weak due to sample size and binning.

B. Surface Brightness Profiles

Concentration: X-ray detected clusters exhibit higher central surface brightness ( $I_0$ ) and smaller core radii ( $r_c$ ) compared to undetected clusters.
Morphology: Detected clusters have more centrally concentrated X-ray profiles. Undetected clusters show flatter, more extended emission, or are intrinsically fainter.
Implication: The lack of X-ray detection in many optically selected clusters is likely due to intrinsically diffuse intracluster medium (ICM) or low luminosity, rather than just observational limits.

5. Significance and Conclusions

Optical Selection Completeness: Optical surveys (like Subaru HSC) successfully recover a diverse population of galaxy clusters, including X-ray faint and morphologically diffuse systems that are missed by X-ray flux-limited surveys.
Physical Differences: The systematic differences in $L-M$ slopes and surface brightness profiles confirm that optically selected clusters without X-ray counterparts represent a distinct physical population (likely lower mass or more disturbed) compared to their X-ray detected counterparts.
Cosmological Implications: By extending scaling relation analyses to lower masses and luminosities, this work demonstrates the necessity of combining deep X-ray (eROSITA) and optical (HSC) surveys to build a complete picture of cluster evolution and to reduce selection biases in cosmological parameter estimation.
Future Outlook: The results highlight the potential of the full eROSITA all-sky survey (eRASS:4) combined with HSC to provide even tighter constraints on cluster physics and cosmology.