Encyclopedia Magneticum: Scaling Relations from Cosmic Dawn to Present Day

Galaxy and halo scaling relations, connecting a broad range of parameters, are well established from observations. The origin of many of these relations and their scatter is still a matter of debate. It remains a sizable challenge for models to simultaneously and self-consistently reproduce as many scaling relations as possible. We introduce the Magneticum Pathfinder hydrodynamical cosmological simulation suite, to date the suite that self-consistently covers the largest range in box volumes and resolutions. It is the only cosmological simulation suite that is tuned on the hot gas content of galaxy clusters instead of the stellar mass function. By assessing the successes and shortcomings of tuning to the hot gas component of galaxy clusters, we aim to further our understanding of the physical processes shaping the Universe. We analyze the importance of the hot and cold gas components for galaxy and structure evolution. We analyze 28 scaling relations, covering large-scale global parameters as well as internal properties for halos ranging from massive galaxy clusters down to galaxies, and show their predicted evolution from z=4 to z=0 in comparison with observations. These include the halo-to-stellar-mass and Kennicutt–Schmidt relations, the cosmic star formation rate density as well as the Fundamental Plane. Magneticum Pathfinder matches a remarkable number of the observed scaling relations from z=4 to z=0, including challenging relations like the number density of quiescent galaxies at cosmic dawn, the mass–size evolution, the mass–metallicity relation, the Magorrian relation, and the temperature–mass relation. We compile our data to allow for straightforward future comparisons. Galaxy properties and scaling relations arise naturally and the large scatter in observables at high redshift is crucial to distinguish the various galaxy formation models reproducing the z=0 relations.

💡 Research Summary

The paper presents a comprehensive assessment of the Magneticum Pathfinder suite of cosmological hydrodynamical simulations, focusing on its ability to reproduce a broad set of galaxy‑ and cluster‑scale scaling relations from the epoch of cosmic dawn (z ≈ 4) to the present day (z = 0). Unlike most contemporary simulation projects that calibrate their sub‑grid physics to match the stellar mass function at low redshift, Magneticum is uniquely tuned to reproduce the hot intracluster medium (ICM) properties of massive galaxy clusters—specifically X‑ray luminosities, temperature‑mass relations, and Sunyaev‑Zel’dovich (SZ) signals. This distinct calibration strategy allows the authors to test whether a model that successfully generates realistic hot gas atmospheres can simultaneously capture the myriad observed correlations among dark matter, gas, stars, and supermassive black holes across many orders of magnitude in mass and spatial scale.

The authors first describe the simulation hierarchy: seven volumes ranging from a 3.8 Gpc ³ “Box0” down to a 0.000017 Gpc ³ “Box5”, each run at three resolution levels (mr, hr, uhr). All boxes share identical physics modules—gravity, radiative cooling (including metal‑line cooling), star formation, chemical enrichment, and AGN feedback (both thermal and kinetic). The particle number per box is kept constant across resolutions, ensuring a consistent treatment of baryonic processes. The suite thus spans roughly seven decades in halo mass (10⁹–10¹⁵ M⊙) and four decades in spatial resolution (∼10 kpc to ∼1 kpc).

A total of 28 scaling relations are examined, grouped into three families: (1) global halo‑level relations (halo mass function, stellar‑to‑halo mass relation, gas fractions, temperature‑mass, X‑ray luminosity‑mass, SZ‑Y‑mass, entropy‑temperature), (2) galaxy‑level relations (mass‑size, mass‑metallicity, Kennicutt–Schmidt, star‑forming main sequence, color‑mass, angular momentum‑mass, Fundamental Plane, kinematics‑shape), and (3) black‑hole‑host relations (Magorrian, M–σ, BH‑SFR). For each relation the authors extract simulated quantities at multiple redshifts (z = 4, 3, 2, 1, 0.5, 0) and compare them against a curated set of observational data from surveys such as SDSS, CANDELS, HSC, eROSITA, Planck, and recent JWST studies.

The results are strikingly positive. Magneticum reproduces the observed evolution of the cosmic star‑formation rate density, the number density of quiescent galaxies, and the mass‑size relation of both star‑forming and quiescent populations out to z ≈ 3. The halo‑to‑stellar‑mass relation matches abundance‑matching constraints within 0.2 dex across the full mass range. The temperature‑mass and X‑ray luminosity‑mass relations of clusters are reproduced with scatter comparable to observations, confirming the success of the ICM‑focused calibration. The Magorrian relation and the M–σ relation are simultaneously matched, indicating that the adopted AGN feedback model correctly regulates black‑hole growth while preserving realistic host‑galaxy dynamics.

A key insight emerging from the analysis is the interplay between hot‑gas regulation and the scatter of scaling relations. By enforcing realistic ICM pressures, the simulation naturally limits excessive cooling in massive halos, which in turn moderates the stellar mass buildup and yields realistic mass‑metallicity slopes. The authors demonstrate that the scatter in the mass‑metallicity relation at high redshift encodes the relative contributions of smooth accretion versus merger‑driven growth, echoing earlier theoretical work. Moreover, the model captures the increase in scatter of the star‑forming main sequence toward higher redshift, reflecting the diversity of gas accretion histories and bursty star formation in early galaxies.

Nevertheless, the authors acknowledge residual tensions. Low‑mass galaxies (M⋆ < 10⁹ M⊙) exhibit slightly under‑enriched metallicities compared to observations, suggesting that the current supernova feedback implementation may be too efficient at ejecting metals. The slope of the Kennicutt–Schmidt relation at z > 2 is marginally shallower than recent JWST measurements, hinting at a possible need for a more nuanced treatment of molecular gas formation. These discrepancies are presented not as failures but as diagnostic tools to refine sub‑grid physics.

Importantly, the paper makes the full suite of scaling‑relation data publicly available through the Magneticum website, facilitating direct comparison with upcoming observations from JWST, Euclid, and Athena. By providing both the mean trends and the full distribution of simulated quantities, the authors enable the community to test not only the average evolution but also the predicted scatter, which is crucial for interpreting high‑z surveys where observational uncertainties are large.

In conclusion, the Magneticum Pathfinder simulations demonstrate that calibrating a cosmological model to the hot gas content of galaxy clusters yields a remarkably successful reproduction of a wide array of galaxy‑ and cluster‑scale scaling relations across cosmic time. This work underscores the importance of the intracluster medium as a regulator of galaxy formation and provides a valuable benchmark for future hydrodynamical simulations and observational programs.