Magneticum Hydrodynamical Simulation

• Magneticum Hydrodynamical Simulation is a state-of-the-art simulation suite that models structure formation using gravity, gas dynamics, and AGN feedback in a self-consistent framework.
• It employs a multibox strategy with varying resolutions to capture scales from galaxy clusters to individual galaxies using advanced SPH techniques.
• The simulation generates synthetic observables such as SZ maps and X-ray profiles, enabling detailed comparisons with real astronomical surveys.

Searching arXiv for Magneticum Pathfinder and related papers to ground the article in the cited literature. Magneticum, usually referred to in the literature as the Magneticum Pathfinder hydrodynamical cosmological simulation suite, is a family of state-of-the-art large-volume and high-resolution simulations designed to model structure formation with gravity, gas dynamics, radiative processes, star formation, chemical enrichment, black-hole growth, and AGN feedback in a self-consistent framework. Within the cited literature, it is characterized as the simulation suite that self-consistently covers the largest range in box volumes and resolutions, and as the only cosmological simulation suite tuned on the hot gas content of galaxy clusters rather than on the stellar mass function (Dolag et al., 1 Apr 2025). Across its different realizations, Magneticum has been used to study thermal and kinetic Sunyaev–Zeldovich observables, X-ray emission and stacking systematics, cluster pressure profiles and hydrostatic bias, cluster substructure assembly, satellite planes, galaxy shapes, intra-cluster light, and tidal shells and streams (Dolag et al., 2015).

1. Simulation suite, cosmology, and dynamic range

Magneticum adopts a flat WMAP-7 cosmology in the core suite description, with $\Omega_m=0.272$, $\Omega_\Lambda=0.728$, $\Omega_b=0.0456$, $h=0.704$, $n_s=0.963$, and $\sigma_8=0.809$ (Dolag et al., 1 Apr 2025). Initial conditions are generated with N-GenIC on a regular grid using the Eisenstein & Hu transfer function and the Zel’dovich approximation, and the same random seed and phases are used at different resolutions to enable cross-resolution matching (Dolag et al., 1 Apr 2025). This design allows the suite to span galaxy-cluster scales down to galaxy scales while preserving controlled comparisons across boxes.

A central feature of the suite is its multibox layout. The largest volumes are intended for rare, high-mass systems and light-cone work, while the smaller ultra-high-resolution runs target internal galaxy structure and satellite populations. The main boxes explicitly summarized in the literature are as follows (Dolag et al., 1 Apr 2025).

Run	Comoving side length	Particle load / characteristic mass scale
Box0 (mr)	$2688\,h^{-1}\,\mathrm{Mpc}$	$2\times 4536^3$; $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$, $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$
Box2 (hr)	$\Omega_\Lambda=0.728$0	$\Omega_\Lambda=0.728$1; $\Omega_\Lambda=0.728$2, $\Omega_\Lambda=0.728$3
Box4 (uhr)	$\Omega_\Lambda=0.728$4	$\Omega_\Lambda=0.728$5; $\Omega_\Lambda=0.728$6, $\Omega_\Lambda=0.728$7
Box5 (xhr)	$\Omega_\Lambda=0.728$8	$\Omega_\Lambda=0.728$9; $\Omega_b=0.0456$0, $\Omega_b=0.0456$1

The suite also includes specialized variants. Box2b and Box3 share the Box2/Box4 resolution pattern but are truncated to $\Omega_b=0.0456$2 and $\Omega_b=0.0456$3, respectively (Dolag et al., 1 Apr 2025). Individual studies draw on different realizations: for example, thermal-history tomography uses the very large Box0 volume, cluster substructure work uses Box2b/hr, satellite-plane and galaxy-shape studies use Box4/uhr, and intra-cluster-light analysis uses Box2/hr (Young et al., 2021, Kimmig et al., 2022, Förster et al., 2022, Valenzuela et al., 2024, Kimmig et al., 26 Mar 2025).

2. Numerical method and baryonic physics

The suite is based on P-Gadget3-XXL or closely related GADGET-3/P-GADGET3 implementations with modern SPH improvements (Dolag et al., 1 Apr 2025). In the suite-level description, the hydrodynamics includes time-dependent low-viscosity with a Balsara switch, artificial conductivity for better fluid mixing, a Wendland $\Omega_b=0.0456$4 kernel with 295 neighbors, and isotropic conduction at $\Omega_b=0.0456$5 of the Spitzer value (Dolag et al., 1 Apr 2025). In cluster-focused analyses, this framework is also described as entropy-conserving SPH with a sixth-order Wendland kernel and low-viscosity treatment to track turbulence, or as an improved SPH implementation featuring higher-order kernels and entropy-mixing corrections (Gupta et al., 2016, Young et al., 2021). In the magnetohydrodynamical eROSITA-stacking study, the code is further described as an SPH-based version of P-GADGET3 augmented by a ten-order switching kernel, time-dependent viscosity, artificial conductivity, and an ideal MHD solver (Popesso et al., 2024).

Radiative processes are treated with element-by-element cooling for 11 species using CLOUDY tables, together with a uniform UV/X-ray background following Wiersma et al. and Haardt & Madau (Dolag et al., 1 Apr 2025). Star formation follows the Springel & Hernquist two-phase ISM model with a threshold density and a star-formation timescale $\Omega_b=0.0456$6 Gyr, and each gas particle can spawn up to four star particles (Dolag et al., 1 Apr 2025). The stellar population model uses a Chabrier IMF with metallicity-dependent lifetimes, instantaneous SNII recycling in star-forming gas, continuous enrichment from SNIa and AGB stars, and galactic winds with $\Omega_b=0.0456$7 km s$\Omega_b=0.0456$8 (Dolag et al., 1 Apr 2025).

Black-hole growth and AGN feedback are integral to the suite. In the fiducial model, halos with $\Omega_b=0.0456$9 receive seeds of $h=0.704$0, accretion follows a Bondi–Hoyle prescription with $h=0.704$1 capped at $h=0.704$2, radiative efficiency is $h=0.704$3, and the coupled feedback efficiency is $h=0.704$4 in quasar mode, increasing by a factor of four in radio mode when $h=0.704$5 (Dolag et al., 1 Apr 2025). An advanced model separates hot and cold gas accretion with $h=0.704$6 K and smooths the quasar–radio transition, yielding more rapid early black-hole growth and improved high-$h=0.704$7 quenching (Dolag et al., 1 Apr 2025). This numerical architecture underlies the suite’s cluster thermodynamics, galaxy morphology, and feedback-driven environmental effects.

3. Calibration strategy and multiscale predictive scope

The defining calibration choice of Magneticum is that all free parameters are tuned to reproduce the hot gas content of massive clusters at $h=0.704$8, specifically gas mass fractions, pressure profiles, and X-ray observables, with no explicit tuning to the stellar mass function or galaxy stellar properties at $h=0.704$9 (Dolag et al., 1 Apr 2025). This design choice is central to how the suite is positioned in the literature: it tests whether a hot-gas-calibrated baryonic model can also recover galaxy-scale observables and their redshift evolution.

In the synthetic overview of the suite, 28 scaling relations are analyzed from $n_s=0.963$0 to $n_s=0.963$1, spanning halo mass functions, stellar and gas mass functions, cosmic star-formation-rate density, stellar-to-halo-mass ratios, baryon conversion efficiencies, gas-mass fractions, temperature–mass relations, SZ $n_s=0.963$2–mass scaling, X-ray luminosity–mass relations, Fe-metallicity–mass trends, the star-formation main sequence, the Kennicutt–Schmidt relation, color–mass bimodality, stellar age–mass and metallicity–mass relations, specific angular momentum–mass scaling, mass–size evolution, the Fundamental Plane, the $n_s=0.963$3–$n_s=0.963$4 plane, and black-hole–galaxy relations including Magorrian and $n_s=0.963$5–$n_s=0.963$6 (Dolag et al., 1 Apr 2025). The summary explicitly states that Magneticum matches a remarkable number of observed relations from $n_s=0.963$7 to $n_s=0.963$8, including 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 (Dolag et al., 1 Apr 2025).

The same suite-level synthesis also records the principal tensions. At the low-mass end there is overcooling and an overshoot of the stellar mass function for $n_s=0.963$9 at $\sigma_8=0.809$0; at high mass there is a stellar-mass overshoot at $\sigma_8=0.809$1, especially relevant for BCGs; and galaxy velocity dispersions are systematically underpredicted by about 20% (Dolag et al., 1 Apr 2025). The article-level implication is methodological rather than rhetorical: reproducing one tight scaling relation is not, by itself, evidence for correct feedback physics, whereas the scatter and joint evolution across many relations provide a more discriminating test (Dolag et al., 1 Apr 2025).

4. Light-cones, synthetic observables, and survey forward modelling

A major strength of Magneticum is its systematic construction of light-cones and mock observables. For SZ work, the Compton-$\sigma_8=0.809$2 field is defined as

$\sigma_8=0.809$3

and is computed by depositing SPH particle pressure onto a mesh, stacking simulation snapshots in comoving coordinates, and summing $\sigma_8=0.809$4 along the line of sight (Young et al., 2021). Earlier SZ-map production used stacked snapshots in redshift shells with random rotations and translations and the SMAC pipeline to generate HEALPix maps with $\sigma_8=0.809$5, producing full-sky tSZ/kSZ maps to $\sigma_8=0.809$6 and a deep $\sigma_8=0.809$7 realization to $\sigma_8=0.809$8 (Dolag et al., 2015). Cluster-centered light cones for SZE-scaling work use 27 snapshots to $\sigma_8=0.809$9, a $2688\,h^{-1}\,\mathrm{Mpc}$0 field of view, $2688\,h^{-1}\,\mathrm{Mpc}$1 pixels, and a dynamic $2688\,h^{-1}\,\mathrm{Mpc}$2-range of $2688\,h^{-1}\,\mathrm{Mpc}$3 to $2688\,h^{-1}\,\mathrm{Mpc}$4 (Gupta et al., 2016).

The same forward-modelling philosophy is used in X-ray analyses. In the eROSITA stacking study, a $2688\,h^{-1}\,\mathrm{Mpc}$5 deg$2688\,h^{-1}\,\mathrm{Mpc}$6 light cone to $2688\,h^{-1}\,\mathrm{Mpc}$7 is carved from Box2/hr, and each gas, BH, and star particle is treated as an X-ray emitter (Popesso et al., 2024). PHOX generates photon lists for IGM, AGN, and XRB emission, and these are fed to SIXTE with eROSITA RMF, ARF, background, and PSF to simulate eRASS:4-depth observations processed by the eSASS pipeline (Popesso et al., 2024). A matched optical catalog with $2688\,h^{-1}\,\mathrm{Mpc}$8, 95% completeness, random redshift errors of $2688\,h^{-1}\,\mathrm{Mpc}$9 km s$2\times 4536^3$0, and 5% catastrophic failures is then analyzed with the R11, Y05, and T17 group finders, enabling an end-to-end test of observational systematics (Popesso et al., 2024).

The suite-level synthesis also emphasizes public-facing infrastructure. The web portal at https://c2papcosmosim.lrz.de/ provides PHOX, SMAC, SimCut, a cluster conversion solver, and ClusterInspect, alongside interactive visualizations and downloadable flat-cone catalogs, light-cone FITS products, and cluster catalogs; subsets of simulation outputs are available at www.magneticum.org/Data, while full snapshots are available upon request (Dolag et al., 1 Apr 2025).

5. Cluster thermodynamics, SZ/X-ray observables, and dynamical state

Magneticum has been particularly influential in cluster and group thermodynamics. In the thermal and kinetic SZ analysis, the unsmoothed deep-light-cone one-point PDF of $2\times 4536^3$1 has a high-$2\times 4536^3$2 tail following a power law $2\times 4536^3$3, the simulated tSZ power spectrum agrees with Planck up to $2\times 4536^3$4 after rescaling with $2\times 4536^3$5, and the mean fluctuating Compton $2\times 4536^3$6 is $2\times 4536^3$7 for $2\times 4536^3$8 and $2\times 4536^3$9, with roughly half of the signal coming from halos below $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$0 and diffuse gas (Dolag et al., 2015). The same study notes that the kSZ spectrum is broadly consistent with previous post-reionization calculations, while large scales $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$1 remain underconverged because of finite box size (Dolag et al., 2015).

For galaxy clusters, Magneticum has been used to calibrate pressure profiles and SZE scatter with a sample of about 50,000 systems with $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$2 out to $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$3 (Gupta et al., 2016). That work finds a generalized NFW pressure profile with best-fit parameters $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$4, $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$5, $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$6, $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$7, $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$8, $m_{\rm DM}\approx1.3\times10^{10}\,h^{-1}M_\odot$9, and $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$0, thereby quantifying modest departures from self-similarity (Gupta et al., 2016). At $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$1, the thermal pressure is only about 80% of the pressure required for hydrostatic equilibrium, implying a $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$2 hydrostatic mass underestimate even in idealized analyses, while the scatter in $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$3 rises from $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$4 for spherical measurements to $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$5 in the full light cone because of correlated and uncorrelated line-of-sight structure (Gupta et al., 2016).

The simulation has also been used to test SZ tomography of the cosmic thermal history. The key quantity is the Compton-$m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$6-weighted halo bias,

$m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$7

which can be compared directly to a simulation estimator derived from the $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$8 limit of the density–pressure cross-spectrum (Young et al., 2021). Up to $m_{\rm gas}\approx2.6\times10^9\,h^{-1}M_\odot$9, the halo-model prediction and simulation measurement agree to better than 1%, corresponding to a rescaling factor $\Omega_\Lambda=0.728$00, and the tomographically recovered density-weighted mean temperature matches the true Magneticum value to within $\Omega_\Lambda=0.728$01, with $\Omega_\Lambda=0.728$02 (Young et al., 2021). At $\Omega_\Lambda=0.728$03, however, $\Omega_\Lambda=0.728$04 falls below $\Omega_\Lambda=0.728$05 by tens of percent, suggesting either feedback or heating outside virialized halos or an early-time breakdown of halo-model assumptions (Young et al., 2021).

Cluster dynamical assembly has been examined from several complementary angles. In the Abell 2744 analogue study, a projection-based “cylinder” mass estimator shows that projected substructure mass fractions are typically $\Omega_\Lambda=0.728$06–$\Omega_\Lambda=0.728$07 larger than bound subhalo fractions, mainly because of main-halo residuals and projection effects (Kimmig et al., 2022). Using Box2b/hr, one simulated cluster reproduces eight substructures comparable to the observational threshold used for Abell 2744, and its history involves a recent major merger plus at least six massive minor merger events since $\Omega_\Lambda=0.728$08, with high projected substructure fractions tracing merger activity within the last $\Omega_\Lambda=0.728$09 Gyr (Kimmig et al., 2022). In a different diagnostic, the intra-cluster-light study finds that the fraction $\Omega_\Lambda=0.728$10 is the best tracer of the formation redshift $\Omega_\Lambda=0.728$11 among the tested dynamical indicators, with Pearson $\Omega_\Lambda=0.728$12 in Magneticum and a best-fit relation $\Omega_\Lambda=0.728$13; undisturbed clusters increase $\Omega_\Lambda=0.728$14 by about $\Omega_\Lambda=0.728$15–$\Omega_\Lambda=0.728$16 per Gyr (Kimmig et al., 26 Mar 2025).

6. Galaxy morphology, satellite structures, and stellar debris

At galaxy scales, Magneticum has been used to relate internal morphology to accretion history and environment. In the satellite-plane analysis based on Box4/uhr, the “Momentum in Thinnest Plane” method identifies the thinnest plane containing a given fraction of satellites and then measures the mass-weighted in-plane momentum fraction

$\Omega_\Lambda=0.728$17

When at least 50% of satellites are required, nearly all halos, including $\Omega_\Lambda=0.728$18 of $\Omega_\Lambda=0.728$19 systems, host a plane with $\Omega_\Lambda=0.728$20, and 75% of such planes have $\Omega_\Lambda=0.728$21 (Förster et al., 2022). Milky-Way-mass halos show $\Omega_\Lambda=0.728$22 in about 86% of cases, there is no discernible correlation with central-galaxy morphology as quantified by the $\Omega_\Lambda=0.728$23-value, and the plane normal preferentially aligns with the host-galaxy minor axis (Förster et al., 2022).

The internal 3D structure of galaxies and halos has been studied with inertia-tensor shape measurements in Box4 (Valenzuela et al., 2024). For 690 main subhalos with $\Omega_\Lambda=0.728$24, $\Omega_\Lambda=0.728$25 kpc, and $\Omega_\Lambda=0.728$26, stellar and dark-matter axis ratios are tightly correlated at $\Omega_\Lambda=0.728$27, with $\Omega_\Lambda=0.728$28 and $\Omega_\Lambda=0.728$29, implying that the inner halo follows the baryonic potential (Valenzuela et al., 2024). By contrast, the total dark-matter halo is uncorrelated with the inner shape and instead tracks the large-scale anisotropy of gas inflow; ellipticals are more spherical and more prolate than disks, fast rotators are flatter, and at fixed stellar mass the more extended ellipticals have larger triaxialities (Valenzuela et al., 2024). The same study argues that stellar shape, stellar mass, and inclination together can be used as a proxy for the in-situ fraction of stars (Valenzuela et al., 2024).

Low-surface-brightness tidal debris has likewise been quantified in Magneticum. In Box4-uhr, visual classification at $\Omega_\Lambda=0.728$30 yields 24 shell-hosting and 66 stream-hosting systems among galaxies with $\Omega_\Lambda=0.728$31, using LSST-like $\Omega_\Lambda=0.728$32-band mock images with $\Omega_\Lambda=0.728$33 mag arcsec$\Omega_\Lambda=0.728$34 (Stoiber et al., 29 Sep 2025). Shells peak at radii of about 20 kpc, streams at about 27 kpc, shells have median angular extents around $\Omega_\Lambda=0.728$35 versus $\Omega_\Lambda=0.728$36 for streams, and both feature classes show localized depressions in stellar velocity dispersion relative to their surroundings in about 95% of shells and 80% of streams (Stoiber et al., 29 Sep 2025). By tracing star particles through merger trees, the study identifies 26 shell progenitors and 40 stream progenitors; shells are associated with progenitors of $\Omega_\Lambda=0.728$37, streams with $\Omega_\Lambda=0.728$38, and the visible debris mass is on average about 20% of progenitor mass (Stoiber et al., 29 Sep 2025). The work also introduces a class of in-situ star-forming streams distinguished by very young ages $\Omega_\Lambda=0.728$39 and the absence of an external progenitor (Stoiber et al., 29 Sep 2025).

7. Systematic uncertainties, known caveats, and interpretive limits

The Magneticum literature repeatedly emphasizes that predictive success depends on matching the analysis pipeline to the observation. In the eROSITA stacking study, AGN and XRBs dominate the X-ray surface-brightness profiles of low-mass halos, while the halo-mass proxy is identified as the primary source of systematic error (Popesso et al., 2024). The intrinsic $\Omega_\Lambda=0.728$40–$\Omega_\Lambda=0.728$41 relation for $\Omega_\Lambda=0.728$42 has slope $\Omega_\Lambda=0.728$43, but stacked relations based on optical priors are flatter by 5–15%, with $\Omega_\Lambda=0.728$44, $\Omega_\Lambda=0.728$45, and $\Omega_\Lambda=0.728$46; below $\Omega_\Lambda=0.728$47, mass-proxy mixing can overestimate the stacked surface brightness by up to a factor of two (Popesso et al., 2024). Above that mass, however, the recovery is unbiased to better than 10%, and the recovered $\Omega_\Lambda=0.728$48–$\Omega_\Lambda=0.728$49 relation matches the intrinsic one to within 10% over $\Omega_\Lambda=0.728$50–$\Omega_\Lambda=0.728$51 (Popesso et al., 2024).

Other limitations are physical rather than purely observational. The SZ tomographic reconstruction is robust only up to $\Omega_\Lambda=0.728$52, after which non-virial pressure or halo-model failure becomes important (Young et al., 2021). The kSZ spectrum remains underconverged on the largest angular scales because of finite box size (Dolag et al., 2015). In the intra-cluster-light analysis, Magneticum shows the highest absolute $\Omega_\Lambda=0.728$53 among the compared simulations, a difference attributed to lower particle resolution in Box2/hr and potentially more efficient stripping physics in its SPH implementation, even though the slope of the $\Omega_\Lambda=0.728$54–$\Omega_\Lambda=0.728$55 relation and the shredding rate agree across all four simulation suites (Kimmig et al., 26 Mar 2025). At the suite level, the persistent low-mass overcooling, high-mass stellar overshoot, and systematically low velocity dispersions define the main outstanding tensions (Dolag et al., 1 Apr 2025).

Taken together, these caveats delimit the epistemic status of Magneticum’s results. The suite is not a single monolithic realization but a coordinated hierarchy of boxes, resolutions, and forward models. Its strongest domain is the joint treatment of baryonic thermodynamics, cluster hot gas, and multiwavelength observables across scales, while its known discrepancies identify where feedback, satellite disruption, and galaxy internal dynamics remain open modelling problems (Dolag et al., 1 Apr 2025).