Baryonic assembly bias in X-ray-selected galaxy groups and clusters: insights from the Magneticum simulation

Abstract: Galaxy groups and clusters trace the large-scale matter distribution, with their clustering usually interpreted mainly as a function of halo mass. Yet, at fixed mass, their baryonic properties retain information about halo growth, gas accretion, and feedback. The intrinsic scatter in X-ray luminosity and gas fraction suggests that X-ray-selected systems may not be a random subset of the halo population. If these observables correlate with halo assembly, they may trace secondary variations in halo bias. We test this using the Magneticum hydrodynamical simulation, measuring the clustering of systems selected by X-ray luminosity and gas fraction at fixed halo mass. We construct mass-matched subsamples by ranking halos in percentiles of X-ray luminosity and derive the linear halo-matter bias from the halo-matter cross-power spectrum. X-ray-bright halos are more strongly clustered than X-ray-faint halos at fixed mass. For the 84th-16th percentile split, we find $Δb_{\rm lin}=0.17\pm0.03$, corresponding to a $\sim17\%$ enhancement relative to the X-ray-faint sample. A 67th-33rd split gives a consistent signal, with $Δb_{\rm lin}=0.12\pm0.02$ and a $\sim12\%$ enhancement. The effect is strongest at group scales and negligible for cluster-size halos. Gas fraction shows an even stronger clustering dependence, with relative enhancements of $\sim39\%$ and $\sim26\%$ for the two percentile splits. This signal is present from $z\simeq2$, whereas X-ray luminosity becomes significant only at $z\simeq0.3$, once the gas thermodynamic state is more closely coupled to baryon retention. Matching halos by both mass and formation time reduces the large-scale bias difference to below $2σ$, indicating that formation time captures much of the signal. These results show that, in Magneticum, X-ray luminosity traces a baryonic manifestation of halo assembly bias beyond mass.

• The paper reveals that X-ray-bright groups and gas-rich halos exhibit up to 17–39% higher large-scale bias compared to their fainter counterparts.
• It employs the Magneticum hydrodynamical simulation with detailed X-ray luminosity and gas fraction modeling to assess assembly bias at group scales.
• The study finds that differences in halo formation times and baryon retention, influenced by AGN feedback, largely drive the observed clustering variations.

Baryonic Assembly Bias in X-ray-selected Groups and Clusters: Magneticum Simulation Insights

Introduction

The study addresses the secondary dependence of large-scale clustering (assembly bias) in galaxy groups and clusters on baryonic properties—specifically X-ray luminosity and gas fraction—at fixed halo mass, utilizing the Magneticum cosmological hydrodynamical simulations. The central motivation is to understand how non-gravitational physics, such as AGN feedback and gas accretion history, imprint on observable scaling relations and clustering, and thereby test the validity of using X-ray-selected samples for cosmological inference.

Simulation Framework and Methodology

Magneticum employs advanced SPH including metallicity-dependent cooling, chemical enrichment, and AGN feedback. The primary analysis uses the 352 $h^{-1}$ cMpc "Box2/hr" volume, resolving down to $10^{12.5}\,M_\odot$, and considers the X-ray luminosity and gas fraction of halos within $R_{200}$. X-ray luminosities are computed via the PHOX pipeline using rest-frame $0.5-2.0$ keV emission from gas, with detailed modelling of element abundances and foreground absorption.

Halo samples are percentile-split in narrow bins of $M_{200}$ based on $L_X$ or $f_{\rm gas}$, yielding mass-matched "X-ray-bright" and "X-ray-faint," as well as "gas-rich" and "gas-poor" samples. Clustering is quantified by the large-scale, scale-independent halo bias $b_{\rm lin}$ estimated from the halo-matter cross-power spectrum, with internal uncertainties from jackknife resampling. Additional splits by formation time ($z_{50}$) are used to assess physical causality.

Clustering Dependence on X-ray Luminosity

Strong assembly bias is detected in the clustering of X-ray-selected halos. For the 84th--16th percentile split, X-ray-bright groups feature a $\Delta b_{\rm lin}=0.17\pm0.03$ higher bias—$10^{12.5}\,M_\odot$017% enhancement over faint systems, at $10^{12.5}\,M_\odot$1 significance. This effect is robust to subtler percentile thresholds.

Figure 1: Scale-dependent bias for the full halo sample (black), and for X-ray-bright (orange) and X-ray-faint (blue) subsamples. A consistent, significant enhancement of bias is evident for X-ray-bright groups.

At fixed $10^{12.5}\,M_\odot$2, the differential clustering is most pronounced in the $10^{12.5}\,M_\odot$3 ("group") regime, with effects of order 10--30%. For more massive cluster halos, the effect becomes negligible. The enhanced bias of X-ray-bright systems persists across the full range of linear scales, indicating a genuine large-scale environmental signature. Comparison with standard halo bias calibrations [tinker_large-scale_2010] shows that X-ray-bright systems follow the baseline, while faint systems are systematically underbiased.

Figure 2: Mean halo bias as a function of $10^{12.5}\,M_\odot$4, with X-ray-bright (orange) and faint (blue) halos revealing strong divergence at group masses.

Clustering Dependence on Gas Fraction

An even stronger assembly bias manifests when splitting by gas fraction. Gas-rich halos display a $10^{12.5}\,M_\odot$539% higher large-scale bias ($10^{12.5}\,M_\odot$6 at 84th--16th percentile), with high statistical significance ($10^{12.5}\,M_\odot$7). This enhancement dominates at group scales, implying that baryon retention—more so than thermodynamic state—directly correlates with large-scale environment.

Figure 2: (Panel b) shows the clustering separation for gas fraction-selected samples, illustrating the stronger signal versus the X-ray-luminosity split.

Redshift Evolution of the Signal

The gas-fraction-dependent clustering enhancement is established by $10^{12.5}\,M_\odot$8 and remains stable to $10^{12.5}\,M_\odot$9, indicating an early and persistent link between baryon retention and environment. In contrast, the $R_{200}$0-dependent assembly bias emerges appreciably only at $R_{200}$1, reflecting the delayed coupling of thermodynamic state with halo assembly history.

Figure 3: Significance of large-scale bias as a function of redshift. Clustering difference by gas fraction is persistent, whereas X-ray luminosity-dependent bias rises sharply at late epochs.

These findings imply that while baryonic assembly bias is set early via gas accretion, X-ray luminosity becomes a reliable tracer only after halos reach a mature thermodynamic state.

Role of Formation Time

When simultaneously matching halos by both mass and formation time, the large-scale bias differences in $R_{200}$2 and $R_{200}$3 sub-samples drop below $R_{200}$4. This demonstrates that in Magneticum, assembly bias in X-ray and gas properties can largely be attributed to differences in halo formation epoch, with residuals at small (nonlinear) scales possibly due to variations in recent accretion, concentration, or feedback efficiency.

Figure 4: Scale-dependent bias for samples split by mass and formation time, showing substantial suppression of the assembly bias signal.

Physical Interpretation

The secondary clustering dependence of X-ray luminosity and gas content on large-scale environment arises from the co-evolution of baryon retention, AGN feedback, and assembly history. At high $R_{200}$5, rapid accretion renders $R_{200}$6 sensitive to environment, but $R_{200}$7 remains a poor proxy until the ICM becomes both sufficiently hot and dense. At low $R_{200}$8, AGN feedback and reduced infall tightly couple $R_{200}$9 to assembly history.

Group-scale halos are most sensitive to these processes—AGN feedback efficiently expels gas, making $0.5-2.0$0 and $0.5-2.0$1 strongly environment-dependent, in contrast to more massive clusters where deeper potentials moderate baryonic effects and subgrid physics become less differentiating [dolag_encyclopedia_2025, marini_impact_2025].

Observational and Cosmological Implications

These results have several practical and theoretical implications:

• Observational selection effects: X-ray flux-limited samples may be biased toward high-$0.5-2.0$2, late-forming, more strongly clustered groups. This introduces environment-dependent selection functions that must be modeled to avoid biases in cosmological analyses of X-ray samples [popesso_hot_2024, seppi_modelling_2025].
• Mass–observable relation modelling: The scatter and secondary trends of the $0.5-2.0$3–$0.5-2.0$4 relation encode significant physical information about feedback and assembly, and their covariance with clustering must be included in forward models for next-generation cluster surveys [lau_x-raying_2025, comparat_full-sky_2020].
• Assembly bias as a probe of baryonic physics: Contradictory predictions among major simulation suites (e.g., Magneticum vs. Flamingo/Hyenas on the sign of the $0.5-2.0$5–assembly trend [costello_flamingo_2025, cui_hyenas_2024]) mean that measurements of assembly bias with X-ray and tSZ-selected samples can constrain subgrid feedback implementations in hydrodynamical simulations.
• Suppression of matter power spectrum: The coupled effect of baryon-environment interplay shapes the matter power spectrum at nonlinear scales, imposing requirements for precision lensing cosmology [van_daalen_effects_2011, grandis_determining_2024].
• Future constraints: Deeper wide-field X-ray and SZ samples, combined with improved mass calibration from weak lensing (Euclid, LSST, DESI, SPT/ACT), will enable measurements of galaxy group and cluster assembly bias at high precision [grandis_srgerosita_2024, schrabback_euclid_2025].

  Figure 5: Dependence of the clustering signal on large-scale cut in $0.5-2.0$6 demonstrates the robustness and scale-dependence of the detected baryonic assembly bias.

Conclusion

The Magneticum simulation demonstrates that baryonic assembly bias, manifested primarily through gas content, and secondarily through X-ray luminosity, is a significant feature of group-scale halos. This secondary dependence of clustering is driven by differences in assembly history, as encoded in formation time, and modulated by AGN feedback and gas accretion efficiency. The enhanced bias is most significant for groups, persists over cosmic time for gas fraction, and emerges late for X-ray luminosity. These findings must be quantitatively integrated into survey modeling and cosmological analyses of X-ray and tSZ-selected group and cluster samples. Future simulation–observation synergy, using robust forward-modelled selection functions, will be paramount for precision cosmology using the large-scale structure traced by baryonic properties.

• Marini et al., "Baryonic assembly bias in X-ray-selected galaxy groups and clusters: insights from the Magneticum simulation," (2607.03746)
• Tinker et al., "The Large-scale Bias of Dark Matter Halos," [tinker_large-scale_2010]
• Dolag et al., "Encyclopedia Magneticum," [dolag_encyclopedia_2025]
• Marini et al., "The impact of assembly history on the X-ray detectability of halos," [marini_impact_2025]
• Costello et al., "FLAMINGO: Tracing the co-evolution of hot gas and black holes," [costello_flamingo_2025]
• Cui et al., "Hyenas: the assembly and evolution of galaxy groups," [cui_hyenas_2024]
• Grandis et al., "The SRG/eROSITA All-Sky Survey: Dark Energy Survey year 3 weak gravitational lensing," [grandis_srgerosita_2024]
• Popesso et al., "The hot gas mass fraction in halos. From Milky Way-like groups to massive clusters," [popesso_hot_2024]
• Van Daalen et al., "The effects of galaxy formation on the matter power spectrum," [van_daalen_effects_2011]

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This essay provides a technical overview, highlights quantitative results and claims, and contextualizes the work within simulation and cosmological survey applications, with figures integrated at key points for clarity.