Simulating the Local Web (SLOW)

Updated 27 July 2025

Simulating the Local Web (SLOW) is a constraint-driven simulation series that integrates advanced hydrodynamics and galaxy formation physics to replicate observed cosmic structure.
It uses peculiar velocity data and Wiener Filter reconstruction to generate initial conditions that accurately mimic local density and velocity fields.
The framework validates ICM thermodynamic properties and scaling relations by directly comparing simulation outputs with X-ray, SZ, and synchrotron observations of galaxy clusters.

Simulating the LOcal Web (SLOW) refers to a series of high-resolution, constraint-driven simulations of the local universe that aim to faithfully reproduce both the large-scale structure and the detailed baryonic properties—especially of galaxy clusters—in the cosmic neighborhood. Using peculiar velocity and redshift survey data to constrain initial conditions, SLOW integrates state-of-the-art hydrodynamics, galaxy-formation physics, and cosmic-ray processes to model the evolution and present-day state of the local cosmic web. The project extends to direct comparisons with observed intracluster medium (ICM) thermodynamics, large-scale X-ray and SZ observations, synchrotron emission, and the statistical peculiarities of the local large-scale structure.

1. Simulation Methodology and Physical Modeling

SLOW employs constrained initial conditions derived primarily from peculiar velocities measured in the CosmicFlows-2 catalogue (Dolag et al., 2023, Hernández-Martínez et al., 2 Feb 2024, Hernández-Martínez et al., 21 Jul 2025). Peculiar velocities, which trace the gravitational field, enable the construction of a three-dimensional cosmic displacement field via Wiener Filter reconstruction. These fields are used, with reverse Zel'dovich approximation, to “backtrack” observed galaxies and clusters to their primordial configuration, ensuring that the simulated universe closely matches the local density and velocity field at $z=0$ .

Hydrodynamics are handled by a modern variant of the GADGET code (notably OpenGadget3) using a TreePM and Smoothed Particle Hydrodynamics (SPH) architecture. The code includes comprehensive baryonic physics: radiative cooling, star formation, supernova and black hole feedback, chemical enrichment, and, in certain runs, explicit cosmic ray (CR) models coupled to magnetohydrodynamics (MHD) for the simulation of non-thermal processes (Böss et al., 2023). The inclusion of galaxy formation physics is key to predicting observable ICM diagnostics (X-ray luminosity, temperature, Compton- $y$ ) in direct comparison with observations (Hernández-Martínez et al., 2 Feb 2024).

Cluster-scale objects form self-consistently and are identified via FoF and spherical overdensity algorithms. Their time-dependent mass assembly, thermodynamic, and radiative properties can be tracked in detail.

2. Anomalies and Large-Scale Structure in the Local Universe

SLOW simulations robustly reproduce several prominent features of the local universe formerly considered anomalous (Dolag et al., 2023). Specifically, within a $\sim$ 100 Mpc region, observations indicate both a $\sim$ 50% under-density of galaxy clusters and a significant $\sim$ 1.5 $\sigma$ over-density of massive clusters, as measured via X-ray or mass-limited samples. The SLOW simulation generates both features simultaneously, with the joint probability of both arising in a random patch of a large cosmological volume measured at only 0.28% (44 out of 15,635 patches in the Magneticum reference box), corresponding to the local volume being a %%%%6 $\sim$ 7%%%% outlier.

Mock galaxy catalogues derived from SLOW also recover the observed twofold over-density at $\sim$ 16 Mpc and $15\%$ under-density at $\sim$ 40 Mpc. This demonstrates the necessity of constrained simulations when testing cosmological models in environments like the observed local universe (Dolag et al., 2023).

3. Thermodynamic Properties of Local Galaxy Clusters

SLOW provides extensive three-dimensional profiles for ICM thermodynamic variables, enabling detailed comparison with both X-ray deprojected data and Sunyaev–Zel'dovich (SZ) observations (Hernández-Martínez et al., 21 Jul 2025). The key quantities are:

Pressure: $P_e = n_e k_B T$ (electron pressure).
Temperature profiles: Typically peaking at intermediate radii and declining outward.
Entropy: $S = k_B T n_e^{-2/3}$ , sensitive to non-gravitational processes and departures from self-similarity.
Electron density: Radial profiles tracing gas concentration, particularly central excess in cool-core systems.

Simulated pressure and temperature profiles for clusters such as Perseus, Coma, and A85 generally match observed trends over most radii, with discrepancies emerging at small radii (core regions), likely due to limitations in AGN feedback prescriptions and numerical resolution.

The ICM entropy and density in cores are less accurately reproduced; for example, central entropy is sometimes overestimated and density underestimated in simulated cool-core (CC) clusters—this highlights the need for refinement in subgrid physics and increased resolution for inner regions (Hernández-Martínez et al., 21 Jul 2025).

4. Cluster Assembly Histories and Core Classification

A core result of SLOW is the demonstrated linkage between cluster formation history and present-day ICM core state (Hernández-Martínez et al., 21 Jul 2025):

Strong cool-core (SCC) clusters assemble the bulk of their mass early (higher redshift), leading to quiescent cores that retain dense cooling gas.
Non-cool-core (NCC) clusters experience extended or late-time mergers, disrupting central densities and resulting in flatter entropy and density profiles.
Weak cool-core (WCC) clusters are intermediate, undergoing partial core disruption reflected in their mass assembly histories.

These trends are recovered statistically by mapping the redshifts at which clusters accumulate 50\%, 75\%, and 90\% of their final mass, compared directly to observed SCC/WCC/NCC classifications.

5. Evaluation Against Observational Surveys

SLOW achieves robust one-to-one cross-identification of $\gtrsim$ 45 individual clusters directly corresponding to observed systems from datasets such as the Planck SZ, CLASSIX, and Tully group catalogs (Hernández-Martínez et al., 2 Feb 2024, Hernández-Martínez et al., 21 Jul 2025). The simulation-based mass predictions fall within the uncertainties of available X-ray, SZ, and dynamical mass estimates for the majority of clusters, allowing a statistical inference of hydrostatic mass bias. For the SLOW cross-identified sample, the hydrostatic mass bias is $(1-b)\approx 0.87$ , directly quantifying that observed masses underestimate true simulated masses by approximately 13\%.

Scaling relations between X-ray luminosity, SZ signal, temperature, and cluster mass derived from the simulation are in excellent agreement with those derived from observations, further validating the approach (Hernández-Martínez et al., 2 Feb 2024).

6. Non-Thermal Emission from the Local Cosmic Web

Extending beyond thermal gas, SLOW incorporates on-the-fly cosmic ray electron and proton evolution within a constrained MHD setting (Böss et al., 2023). CR electrons are injected at shocks (identified by Mach number and obliquity constraints) according to diffusive shock acceleration models, and their evolution—including radiative losses and adiabatic effects—is integrated within each hydrodynamic resolution element.

Synchrotron emission is computed by integrating over the local CR electron spectrum and instantaneous magnetic field:

$j_\nu(t) = \left(\sqrt{3}\frac{e^3}{m_e^2 c^3}\right) B(t) \sum_i \int_{p_i}^{p_{i+1}} d\hat{p}~ 4\pi\hat{p}^2 f(\hat{p}, t) K(x)$

where $K(x)$ is the first synchrotron function, with $x$ defined using the local field and electron momentum. Several magnetic field scaling models are considered, including plasma- $\beta$ , turbulent pressure scalings, and density-based dynamo/flux-freezing.

The predicted surface brightness for filaments at 144 MHz (LOFAR) is $S_\nu\sim 0.01-1~\mu$ Jy beam $^{-1}$ depending on model assumptions. Spectral indices in filaments are $\alpha\sim-1.0$ to $-1.5$ . Stacking strategies could bring such signals within reach of existing facilities, though direct detection remains challenging (Böss et al., 2023).

Higher-resolution zoom-ins (e.g., Coma) show increased CR injection and nonthermal emission, emphasizing the importance of numerical detail in low-density regions.

While SLOW represents a substantial advance in reproducing the observable features and detailed physics of the local web and cluster population, several limitations remain:

Subgrid modeling of AGN feedback, radiative cooling, and star formation in cluster cores show residual inconsistencies, especially in central entropy and density (over- and underestimations, respectively).
Enhanced resolution, as demonstrated by the CR3072 $^3$ high-resolution runs, can ameliorate deficiencies in inner profiles, suggesting that ongoing increases in computational detail will yield tangible improvements.
The explicit connection between assembly history and core state enables future studies of cluster evolution, irreversible core transformations, and environmental dependence.

SLOW’s constraint-driven approach offers a direct pathway to interpret emergent cosmic variance, calibrate mass proxies, and explore unique features of the nearby universe that are not adequately represented in random cosmological volumes. The combination of detailed baryonic physics, CR modeling, and robust statistical analysis sets a new standard for simulating and interpreting the cosmic web within the local universe.