MultiDark Planck2 Simulation

• MultiDark Planck2 (MDPL2) is a dark-matter-only simulation using Planck cosmology parameters and 3840³ particles in a (1 Gpc/h)³ volume, providing a uniform dark matter backbone for astrophysical studies.
• It employs advanced halo identification methods like Rockstar and Consistent Trees to generate reliable halo catalogues, merger trees, and orbital histories for galaxy formation modeling.
• The simulation supports diverse applications including semi-analytic galaxy models, survey-scale clustering analyses, and synthetic sky generation with high accuracy.

Searching arXiv for relevant MultiDark Planck2 papers and context. The MultiDark Planck2 simulation, commonly abbreviated MDPL2, is a dark-matter-only cosmological $N$-body simulation in the MultiDark suite that provides a Planck-cosmology backbone for halo catalogues, merger trees, mock galaxy catalogues, cluster light-cones, and multi-probe synthetic skies. In the MultiDark-Galaxies release it is described as one of the Planck cosmology MultiDark simulations, with a volume of $(1\,\mathrm{Gpc}/h)^3$, a particle mass resolution of $m_p=1.51\times10^9\,M_\odot/h$, and halo and subhalo structure extracted with Rockstar and Consistent Trees (Knebe et al., 2017). Across subsequent work, MDPL2 serves as a common dark-matter environment for semi-analytic galaxy-formation models, observational association tests, cluster-sample evolution studies, and coherent sky simulations spanning CMB and large-scale-structure observables (Omori, 2022).

1. Definition and numerical realization

MDPL2 stands for the MultiDark Planck2 simulation and is identified as one of the MultiDark suite of large dark-matter-only simulations run in a flat $\Lambda$CDM Planck cosmology (Knebe et al., 2017). The cosmological parameters stated for MDPL2 are

$$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$

with closely related Planck-consistent parameter listings also appearing in later MDPL2-based applications (Knebe et al., 2017).

The simulation follows the evolution of $3840^3$ dark-matter particles in a cubic box of side length $1475.6\,\mathrm{Mpc}/h$, corresponding to $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$, with particle mass resolution

$m_p = 1.51\times 10^9\,M_\odot/h.$

The force resolution is stated as $13\,\mathrm{kpc}/h$ at high redshift to $(1\,\mathrm{Gpc}/h)^3$0 at low redshift, and the simulation is stored in 126 snapshots from $(1\,\mathrm{Gpc}/h)^3$1 to $(1\,\mathrm{Gpc}/h)^3$2 (Knebe et al., 2017). A later multi-component sky simulation using MDPL2 describes it as a dark-matter-only $(1\,\mathrm{Gpc}/h)^3$3-body simulation with box size $(1\,\mathrm{Gpc}/h)^3$4 Gpc, $(1\,\mathrm{Gpc}/h)^3$5 particles, particle mass resolution $(1\,\mathrm{Gpc}/h)^3$6, initial redshift 120, and 130 snapshots (Omori, 2022). This suggests that different downstream works emphasize different bookkeeping details of the stored outputs while treating the underlying simulation as the same common Planck-era structure-formation realization.

The broader MultiDark-Planck program places MDPL2 in a family of Planck-parameter simulations spanning multiple dynamic ranges. In the earlier MultiDark-Planck overview, the $(1\,\mathrm{Gpc}/h)^3$7 MultiDark-Planck run is listed with $(1\,\mathrm{Gpc}/h)^3$8 particles and particle mass $(1\,\mathrm{Gpc}/h)^3$9, alongside smaller and larger companion boxes (Rodriguez-Puebla et al., 2016). The halo-shape calibration work likewise includes the $m_p=1.51\times10^9\,M_\odot/h$0 Planck box with $m_p=1.51\times10^9\,M_\odot/h$1 particles, $m_p=1.51\times10^9\,M_\odot/h$2, and $m_p=1.51\times10^9\,M_\odot/h$3 softening as part of a homogeneous MultiDark Planck dataset (Vega-Ferrero et al., 2016).

2. Halo catalogues, merger trees, and derived structure

A central function of MDPL2 is to provide halo catalogues and merger histories suitable for halo-based modeling. In the MultiDark-Galaxies release, the halo catalogues are built with Rockstar and the merger trees with Consistent Trees (Knebe et al., 2017). The same toolchain appears in later MDPL2 applications, including machine-assisted baryonic assignment, cluster-rank evolution studies, and synthetic-sky generation (Jo et al., 2019).

In the MultiDark-Planck framework, halo properties are commonly quoted using virial or overdensity-based definitions, and the public Rockstar/Consistent-Trees products provide quantities such as $m_p=1.51\times10^9\,M_\odot/h$4, $m_p=1.51\times10^9\,M_\odot/h$5, $m_p=1.51\times10^9\,M_\odot/h$6, $m_p=1.51\times10^9\,M_\odot/h$7, $m_p=1.51\times10^9\,M_\odot/h$8, and $m_p=1.51\times10^9\,M_\odot/h$9 (Rodriguez-Puebla et al., 2016). The halo-demographics paper emphasizes the use of the virial overdensity definition

$\Lambda$0

with $\Lambda$1 following the Bryan & Norman expression (Rodriguez-Puebla et al., 2016). In the halo-shape analysis, distinct halos are required to have more than 3000 particles within $\Lambda$2, and relaxed systems are selected through the Klypin et al. criteria

$\Lambda$3

(Vega-Ferrero et al., 2016).

Several studies exploit these halo products differently. The group-finding test at $\Lambda$4 uses Rockstar halo positions, velocities, host-satellite relations, virial masses, and virial radii as simulation truth for observational association experiments (Caso et al., 2019). The rank-evolution study follows each halo’s main branch via the most massive progenitor, again using Rockstar identification and ConsistentTrees merger trees (Onions et al., 26 Aug 2025). A plausible implication is that MDPL2’s long-standing utility arises not only from its volume and mass resolution, but from the consistency of its public halo and tree products across independent research programs.

3. Common dark-matter backbone for galaxy-formation modelling

A defining use of MDPL2 is as a shared dark-matter backbone for semi-analytic galaxy catalogues. The MultiDark-Galaxies release applies three independent semi-analytic models to the same MDPL2 merger trees: GALACTICUS, SAG, and SAGE, yielding the public catalogues MDPL2-Galacticus, MDPL2-Sag, and MDPL2-Sage (Knebe et al., 2017). Because all three models are run on the same underlying merger trees, differences among the catalogues are attributable to galaxy-formation prescriptions and calibrations rather than to differences in the dark-matter realization (Knebe et al., 2017).

The released catalogues contain positions, velocities, stellar and cold gas masses, hot gas, black hole mass, star formation rates, metallicities, halo quantities, and for some models luminosities or magnitudes, and are made public through CosmoSim with DOI-linked entries (Knebe et al., 2017). The paper compares the models against observational constraints on the stellar mass function, star formation rate function, cold gas fractions, metallicities, and galaxy clustering, and reports differentiated performance: SAGE gives the closest match to the observed stellar mass function, GALACTICUS is particularly strong in the star formation rate function and cosmic star-formation history, and SAG is strongest in gas fractions and metallicity relations (Knebe et al., 2017).

MDPL2 is also the shared structure-formation stage for a study of $\Lambda$5 emitters at $\Lambda$6, again using SAG, SAGE, and Galacticus on the same MDPL2 merger-tree backbone (Favole et al., 2019). In that work the common MDPL2 environment enables a controlled comparison of how post-processed $\Lambda$7 luminosities, luminosity functions, halo occupation distributions, and clustering depend on both the SAM and the line-assignment method (Favole et al., 2019). The main technical conclusion is that average star formation rates can serve as an acceptable proxy for instantaneous rates over much of the emitter population, while large-scale clustering above $\Lambda$8 is robust to the exact $\Lambda$9 estimator (Favole et al., 2019).

A distinct extension of the same backbone logic appears in the Machine-assisted Semi-Simulation Model (MSSM), where a machine trained on IllustrisTNG is applied directly to the public MDPL2 halo catalogue to assign gas mass, stellar mass, central black hole mass, star formation rate, metallicity, and photometric magnitudes to roughly $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$0 halos in the $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$1 volume (Jo et al., 2019). This use of MDPL2 is not a semi-analytic model in the usual sense, but it preserves the same underlying idea: the dark-matter-only halo catalogue acts as a transferable substrate for baryonic modeling (Jo et al., 2019).

4. Clustering, orphan treatment, and survey-scale catalogue construction

The MDPL2-based galaxy catalogues are explicitly designed for survey-scale clustering analyses. In the MultiDark-Galaxies study, galaxies are selected at fixed number density using stellar mass, cold gas mass, and star formation rate, with three cuts:

• $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$2,
• $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$3,
• $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$4.

The real-space two-point correlation function is computed with corrfunc using 60 logarithmic bins between $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$5 and $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$6, and projected correlation functions are integrated to

$$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$7

The result is that clustering is broadly similar among the three models, especially for stellar-mass selections, and that the shape of the 2PCF is quite robust, with differences affecting mainly the amplitude and becoming stronger for rarer samples (Knebe et al., 2017).

A recurring issue in these comparisons is the treatment of orphan galaxies, defined as galaxies that have lost their resolved dark-matter host halo because of finite mass resolution or tidal stripping. MDPL2 provides the common environment in which distinct orphan prescriptions can be isolated. In GALACTICUS, orphan galaxies remain after subhalo loss but their orbits are not integrated, and their positions are assigned to the central galaxy of the host halo. In SAG, orphans have full orbit integration with tracked positions and velocities. In SAGE, there are no orphan galaxies; satellite disruption is handled before orphan formation, and disrupted satellites may contribute to intracluster light (Knebe et al., 2017). Despite these model differences, the paper finds that the clustering signal remains comparable, especially for stellar-mass-selected samples (Knebe et al., 2017).

The same large MDPL2 volume is emphasized as being comparable to that probed by major current and upcoming surveys such as eBOSS, DES, J-PAS, DESI, LSST, Euclid, and WFIRST, making it suitable for mock catalogues, clustering predictions, and survey-selection tests (Knebe et al., 2017). This suggests that MDPL2’s practical importance lies in enabling both controlled inter-model comparisons and direct survey-facing statistical analyses within the same cosmological volume.

5. Cluster and intracluster-medium applications

Although the first public MultiDark-Clusters release is built primarily on BigMDPL rather than MDPL2, it is closely connected to the same MultiDark Planck program and illustrates a broader methodological use of MultiDark dark-matter simulations: halo catalogues from a Planck cosmology $$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$8-body run are “painted” with a phenomenological intracluster medium model to construct cluster light-cones, scaling relations, X-ray observables, and eROSITA count-rate predictions (Zandanel et al., 2018). In that work BigMDPL uses the Planck year-1 cosmology

$$\Omega_m = 0.307,\quad \Omega_B = 0.048,\quad \Omega_\Lambda = 0.693,\quad \sigma_8 = 0.823,\quad n_s = 0.96,\quad h = 0.678,$$9

and the halo catalogues are based on Rockstar (Zandanel et al., 2018). While this is not MDPL2 itself, it is explicitly described as the Planck-cosmology branch of the MultiDark cluster-mock program and is therefore part of the same simulation ecosystem.

A still earlier paper develops a phenomenological ICM model on the original MultiDark framework, using a $3840^3$0 ART simulation with a BDM halo catalogue rather than MultiDark Planck2 directly (Zandanel et al., 2013). That work classifies halos by the disturbance parameter $3840^3$1, assigns cool-core and non-cool-core gas-density profiles, and computes $3840^3$2, $3840^3$3, and $3840^3$4 for public mock cluster catalogues (Zandanel et al., 2013). The methodological lineage is relevant because later MultiDark cluster-light-cone work applies closely related halo-based ICM painting strategies to Planck-cosmology MultiDark runs (Zandanel et al., 2018).

A separate MDPL2-specific cluster application studies whether the most massive halos at one epoch remain top-ranked at later times. Using MDPL2, the authors construct a mass-complete sample of the 100 most massive halos in the $3840^3$5 volume and show that by $3840^3$6, only $3840^3$7 of the 100 most massive halos at $3840^3$8 were also in the top 100 at $3840^3$9 (Onions et al., 26 Aug 2025). The study further reports that major mergers and dynamical state are closely connected to rank reshuffling: in the top 30 halos at $1475.6\,\mathrm{Mpc}/h$0, 7 have experienced a major merger since $1475.6\,\mathrm{Mpc}/h$1, whereas in the 70–100 rank bin only 1 object has had such a merger, and around 77% of the clusters are unrelaxed at $1475.6\,\mathrm{Mpc}/h$2 (Onions et al., 26 Aug 2025). The practical conclusion is that fixed-rank or fixed-mass cluster samples are not temporally stable populations, so evolving completeness limits are required for consistent redshift comparisons (Onions et al., 26 Aug 2025).

6. Multi-component skies, halo statistics, and methodological extensions

MDPL2 is not restricted to halo catalogues and galaxy mocks; it also functions as a unified scaffold for correlated sky simulations. In Agora, each probe is implemented in a single coherent lightcone using halo catalogues and or particles from MDPL2 (Omori, 2022). The products include CMB lensing convergence maps, lensed primary CMB $1475.6\,\mathrm{Mpc}/h$3 maps, tSZ and kSZ maps, CIB maps and source catalogues, radio-source maps and catalogues, galaxy overdensity maps, galaxy weak-lensing maps and shape catalogues, intrinsic-alignment maps, and frequency maps for Planck-like and SPT-SZ-like experiments (Omori, 2022).

The MDPL2 lightcone in Agora is built by tiling the simulation periodically into concentric spherical shells of thickness $1475.6\,\mathrm{Mpc}/h$4 Mpc, projected to HEALPix $1475.6\,\mathrm{Mpc}/h$5, with random rotations every 1 box length to reduce repetition along the line of sight (Omori, 2022). The same shell rotations are applied to both particle density or velocity shells and halo catalogues, preserving cross-component correlations (Omori, 2022). The resulting CMB lensing power spectrum agrees with theory at better than 5% over $1475.6\,\mathrm{Mpc}/h$6, and an idealized multi-probe analysis recovers the input cosmology to within about $1475.6\,\mathrm{Mpc}/h$7 in the $1475.6\,\mathrm{Mpc}/h$8 plane (Omori, 2022).

MDPL2 also underpins methodological tests that are not primarily about mock observables. The group-association study uses the $1475.6\,\mathrm{Mpc}/h$9 Rockstar halo catalogue as ground truth for observational Friends-of-Friends tests and finds that contamination becomes severe for massive halos in dense environments, with projected linking length $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$0 driving performance more strongly than the radial-velocity threshold $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$1 (Caso et al., 2019). For main halos above $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$2, the percolation method yields about 4 times more systems than expected and about 7 times more associated satellites than the simulation truth (Caso et al., 2019). This shows that MDPL2 is also useful as a controlled benchmark for inference systematics.

Finally, later machine-learning work on merger-tree emulation is trained on VSMDPL, the Very Small MultiDark Planck box, rather than MDPL2 proper, but it uses the same MultiDark Planck cosmological framework and the same Rockstar plus Consistent-Trees pipeline (Nguyen et al., 14 Jul 2025). This broader context indicates that the MultiDark Planck family, including MDPL2, increasingly serves as a data source not only for direct analysis but also for surrogate modeling of halo assembly histories.

7. Scientific significance and limitations

The principal significance of MDPL2 is that it combines a survey-scale comoving volume with halo resolution adequate for a wide range of halo-based applications. In the MultiDark-Galaxies release, the $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$3 box and $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$4 particle mass are explicitly presented as sufficient for rare massive systems, large-scale clustering, and survey-scale mock catalogues (Knebe et al., 2017). In the MultiDark Planck demographics program, the corresponding Planck-parameter $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$5 simulation is part of a suite designed to probe galaxy-hosting halos from Milky Way scale to clusters, with halos and subhalos of $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$6 particles described as reliably resolved (Rodriguez-Puebla et al., 2016).

The Planck cosmology adopted by MDPL2 is scientifically important because, relative to WMAP-era cosmologies, the higher matter density yields more massive halos, especially at high redshift. In the Planck-vs-WMAP comparison, there are about 12% more Milky-Way-mass halos at $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$7 and about 25% more at $(1000\,\mathrm{Mpc}/h)^3=(1\,\mathrm{Gpc}/h)^3$8, with the discrepancy increasing strongly toward high redshift (Rodriguez-Puebla et al., 2016). This provides part of the motivation for the MultiDark-Planck program and for subsequent MDPL2-based mock catalogues and observational comparisons.

At the same time, several limitations recur across MDPL2-based studies. Orphan treatment is a major source of model variance in galaxy catalogues (Knebe et al., 2017). Fixed-rank or fixed-mass cluster selections are shown to be unstable over time because of mergers, accretion variability, and stripping (Onions et al., 26 Aug 2025). Group-finding performance degrades strongly in crowded environments even when the underlying halo catalogue is exact (Caso et al., 2019). In the machine-assisted baryonic-assignment approach, transfer from a hydrodynamic simulation to MDPL2 neglects baryonic back-reaction and produces somewhat narrower property distributions than the training target (Jo et al., 2019). In the synthetic-sky context, small calibration factors of at most 5% are applied to some maps to better match observations (Omori, 2022).

Taken together, these results define MDPL2 less as a single-purpose simulation than as an infrastructure layer for Planck-cosmology halo-based cosmology and astrophysics. It is a public, high-volume dark-matter realization with standardized halo catalogues and merger trees, and its most distinctive role is to make otherwise disparate modeling programs directly comparable because they share the same underlying matter distribution (Knebe et al., 2017).