The Copernicus Complexio: a high-resolution view of the small-scale Universe
Open accessAbstract
We introduce Copernicus Complexio (coco), a high-resolution cosmological N-body simulation of structure formation in the ΛCDM model. coco follows an approximately spherical region of radius ∼17.4 h−1 Mpc embedded in a much larger periodic cube that is followed at lower resolution. The high-resolution volume has a particle mass of 1.135 × 105 h−1 M⊙ (60 times higher than the Millennium-II simulation). coco gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms ∼60 haloes of galactic size, each resolved with about 10 million particles. We confirm the power-law character of the subhalo mass function, |$\overline{N}(>\mu )\propto \mu ^{-s}$|, down to a reduced subhalo mass Msub/M200 ≡ μ = 10−6, with a best-fitting power-law index, s = 0.94, for hosts of mass 〈M200〉 = 1012 h−1 M⊙. The concentration–mass relation of coco haloes deviates from a single power law for masses M200 < afew × 108 h−1 M⊙, where it flattens, in agreement with results by Sanchez-Conde et al. The host mass invariance of the reduced maximum circular velocity function of subhaloes, ν ≡ Vmax/V200, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalized radial distribution of subhaloes is approximately universal (i.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual haloes. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts.
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The high concentration inferred by such studies is in tension with theoretical expectations from cosmological simulations, which predict a mean concentration of ∼9 and a 68 percentile range of ∼[7,12].
“that is in tension with theoretical expectations based on cosmological simulations, which predict a mean concentration of ∼ 9 and a 68 percentile range of ∼ [7 , 12]”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Hellwing et al. 2016
Section 3.2 reports median halo concentrations from the COCO and COLOR cosmological simulations, and the Figure 5 caption describes their 16th–84th percentile scatter. The passages do not give a mean concentration of ∼9 or a range of ∼[7,12], nor do they establish tension with the high concentration inferred by the citing studies. Page numbers were not available in our copy. (LLM, conf=0.79)
Experimental — accuracy not yet measuredThe ML concentration is equal to the median concentration of ∼1×10^12 M⊙ haloes.
“The ML value for the concentration is, in fact, equal to the median concentration of ∼ 1 × 10 12 M ⊙ haloes (e.g. Neto et al. 2007; Hellwing et al. 2016)”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Hellwing et al. 2016
Section 3.2 reports median halo concentration as a function of mass, including around 10^12 h^-1 M⊙. It does not identify a maximum-likelihood (ML) concentration or establish that an ML value equals that median; the paper also expresses the mass in h^-1 M⊙ rather than M⊙. (LLM, conf=0.78)
Experimental — accuracy not yet measured
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Percentages, sums and reported differences re-computed from the paper’s own numbers.
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THE NEW HORIZON RUN COSMOLOGICAL N-BODY SIMULATIONS
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The Milky Way system in Λ cold dark matter cosmological simulations
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Self-citationBoylan-Kolchin, M. (2014) · Nature · doi:10.1038/509170a · Cited by 2 · see citing works
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Cosmological simulations of galaxy formation
Vogelsberger, M., Marinacci, F., Torrey, P., & Puchwein, E. (2019) · Nature Reviews Physics · doi:10.1038/s42254-019-0127-2 · Cited by 365 · see citing works
The mass–concentration–redshift relation of cold and warm dark matter haloes
Ludlow, A. D., Bose, S., Angulo, R. E., Wang, L., Hellwing, W. A., Navarro, J. F., Cole, S., & Frenk, C. S. (2016) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw1046 · Cited by 341 · see citing works
Self-citationThe milky way total mass profile as inferred from Gaia DR2
Cautun, M., Benítez-Llambay, A., Deason, A. J., Frenk, C. S., Fattahi, A., Gómez, F. A., Grand, R. J. J., Oman, K. A., Navarro, J. F., & Simpson, C. M. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa1017 · Cited by 332 · see citing works
“E-mail: cautun@strw.leidenuniv.nl host halo mass (e.g. Purcell & Zentner 2012; Wang et al. 2012; Cautun et al. 2014a; Hellwing et al. 2016) while the radial mass profile plays a key role in determining the orbits of satellite galaxies and tidal streams (e.g. Barber et al. 2014; Monachesi et al.…”
BackgroundMethodInfluentialSelf-citationThe Milky Way total mass profile as inferred from Gaia DR2
Cautun, M., Benitez-Llambay, A., Deason, A. J., Frenk, C. S., Fattahi, A., Gómez, F. A., Grand, R. J. J., Oman, K. A., Navarro, J. F., & Simpson, C. M. (2019) · arXiv · doi:10.48550/arxiv.1911.04557 · Cited by 335
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Self-citationAn Accurate Physical Model for Halo Concentrations
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Tacchella, S., Bose, S., Conroy, C., Eisenstein, D., & Johnson, B. (2018) · Astrophysical Journal · doi:10.3847/1538-4357/aae8e0 · Cited by 159 · see citing works
Self-citationQuenching and ram pressure stripping of simulated Milky Way satellite galaxies
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The mass of the Milky Way from satellite dynamics
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Self-citationDark Matter Haloes and Subhaloes
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Self-citationThe Copernicus Complexio: statistical properties of warm dark matter haloes
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Self-citationThe total satellite population of the Milky Way
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Self-citationA unified model for the spatial and mass distribution of subhaloes
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Self-citationSensitivity projections for dark matter searches with the Fermi large area telescope
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Sensitivity projections for dark matter searches with the Fermi large area telescope
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Halo Profiles and the Concentration–Mass Relation for a ΛCDM Universe
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The Cosmic Ballet: spin and shape alignments of haloes in the cosmic web
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Planes of satellite galaxies: when exceptions are the rule
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Substructure and galaxy formation in the Copernicus Complexio warm dark matter simulations
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Self-citationConstraints on the identity of the dark matter from strong gravitational lenses
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Hidden depths in the local Universe: The Stellar Stream Legacy Survey
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Self-citationHalo Substructure Boosts to the Signatures of Dark Matter Annihilation
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The Imprint of Cosmic Reionization on the Luminosity Function of Galaxies
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Symphony: Cosmological Zoom-in Simulation Suites over Four Decades of Host Halo Mass
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Astrophysical tests of modified gravity: Stellar and gaseous rotation curves in dwarf galaxies
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Strong Dark Matter Self-interactions Diversify Halo Populations within and surrounding the Milky Way
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Search for gamma-ray lines towards galaxy clusters with the Fermi-LAT
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Self-citationPredicting the density profiles of the first halos
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Dwarf stellar haloes: a powerful probe of small-scale galaxy formation and the nature of dark matter
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Self-citationMeasuring subhalo mass in redMaPPer clusters with CFHT Stripe 82 Survey
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The aftermath of the Great Collision between our Galaxy and the Large Magellanic Cloud
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symfind : Addressing the Fragility of Subhalo Finders and Revealing the Durability of Subhalos
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The tangential velocity excess of the Milky Way satellites
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Self-citationFirst Results on Dark Matter Substructure from Astrometric Weak Lensing
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On the stability of satellite planes – I. Effects of mass, velocity, halo shape and alignment
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Probing features in the primordial perturbation spectrum with large-scale structure data
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The Missing Satellite Problem Outside of the Local Group. I. Pilot Observation
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The galaxy population in cold and warm dark matter cosmologies
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Self-citationZOMG - III. The effect of halo assembly on the satellite population
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Nusser, A. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/ab792c · Cited by 20 · see citing works
Universality of the halo mass function in modified gravity cosmologies
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Self-citationAnother baryon miracle? Testing solutions to the ‘missing dwarfs’ problem
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Pushing down the low-mass halo concentration frontier with the Lomonosov cosmological simulations
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The survival of globular clusters in a cuspy Fornax
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Self-citationThe abundance of dark matter haloes down to Earth mass
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Self-citationA high-resolution cosmological simulation of a strong gravitational lens
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Self-citationEvolution of subhalo orbits in a smoothly growing host halo potential
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Halo concentrations from extended Press–Schechter merger histories
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Matching the mass function of Milky Way satellites in competing dark matter models
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Extragalactic stellar tidal streams: Observations meet simulation
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Self-citationPahl, A. J., Shapley, A. E., Steidel, C. C., Reddy, N. A., & Chen, Y. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac1767 · Cited by 11 · see citing works
Spatial extension of dark subhalos as seen by Fermi -LAT and the implications for WIMP constraints
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Hütten, M., Combet, C., & Maurin, D. A. (2018) · Desy Publications Database (Deutsches Elektronen-Synchrotron DESY) · Cited by 11 · see citing works
Simulations of the accreted stellar haloes of low-mass field galaxies
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Self-citationDating the Tidal Disruption of Globular Clusters with GAIA Data on Their Stellar Streams
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Determining satellite infall times using machine learning
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Self-citationAn accurate comprehensive approach to substructure – II. Stripped subhaloes
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The spatial distribution of satellites in galaxy clusters
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Self-citationOman, K. A., Frenk, C. S., Crain, R. A., Lovell, M. R., & Pfeffer, J. (2024) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stae1772 · Cited by 8 · see citing works
Self-citationA Random Walk Model for Dark Matter Halo Concentrations
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Differentiating small-scale subhalo distributions in CDM and WDM models using persistent homology
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Self-citationFluorescent rings in star-free dark matter haloes
Sykes, C., Fumagalli, M., Cooke, R., Theuns, T., & Benítez-Llambay, A. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz1234 · Cited by 7 · see citing works
Wu, J., Chan, T. K., & Moreno, V. J. F. (2025) · Physical review. D/Physical review. D. · doi:10.1103/59fw-974t · Cited by 5 · see citing works
The viability of low-mass subhaloes as targets for gamma-ray dark matter searches
Aguirre-Santaella, A., & Sánchez-Conde, M. Á. (2024) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stae940 · Cited by 4 · see citing works
Caught in the cosmic web: Environmental effects on subhalo abundance and internal density profiles
Hunde, F. M., Newton, O., Hellwing, W. A., Bilicki, M., & Naidoo, K. (2025) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202452246 · Cited by 4 · see citing works
Self-citationGhostly Galaxies: Accretion-dominated Stellar Systems in Low-mass Dark Matter Halos
Wang, C.-W., Cooper, A. P., Bose, S., Frenk, C. S., & Hellwing, W. A. (2023) · The Astrophysical Journal · doi:10.3847/1538-4357/ad011d · Cited by 4 · see citing works
Self-citationNewton, O., Cautun, M., Jenkins, A., Frenk, C. S., & Helly, J. C. (2018) · Proceedings of the International Astronomical Union · doi:10.1017/s1743921318006464 · Cited by 3 · see citing works
Self-citationHalo assembly in cold and warm dark matter during the JWST frontier epoch
Lovell, M. R. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad3415 · Cited by 3 · see citing works
Stellar-mass Measurements in A133 with Magellan/IMACS
Starikova, S., Vikhlinin, A. A., Kravtsov, A. V., Kraft, R., Connor, T., Mulchaey, J. S., & Nagai, D. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/ab7924 · Cited by 3 · see citing works
Demiański, M., & Doroshkevich, А. G. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.07989 · Cited by 3 · see citing works
Constraints on the properties of warm dark matter using the satellite galaxies of the Milky Way
Newton, O., Leo, M., Cautun, M., Jenkins, A. R., Frenk, C. S., Lovell, M. R., Helly, J. C., Benson, A. J., & Cole, S. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/08/062 · Cited by 2 · see citing works
Self-citationOu, X., Necib, L., Wetzel, A. R., Frebel, A., Bailin, J., & Oeur, M. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ae0b63 · Cited by 2 · see citing works
An accurate comprehensive approach to substructure – IV. Dynamical friction
Salvador-Solé, E., Manrique, A., & Rocamora, A. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf2099 · Cited by 1 · see citing works
Impact of baryons on the population of Galactic subhalos and implications for dark matter searches
Porras-Bedmar, S., Sánchez-Conde, M. Á., & Aguirre-Santaella, A. (2026) · Physics of the Dark Universe · doi:10.1016/j.dark.2026.102262 · Cited by 1 · see citing works
Brown, S. T., Fattahi, A., Gutcke, T. A., Ploeckinger, S., Sureda, J., Bose, S., Doppel, J. E., Pakmor, R., & Jenkins, A. R. (2026) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stag439 · Cited by 1 · see citing works
Self-citationThe progenitor galaxies of stellar haloes as ‘failed’ Milky Ways
Bose, S., & Deason, A. J. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad1123 · Cited by 1 · see citing works
Self-citationNewton, O., & Cautun, M. (2018) · Figshare · doi:10.5281/zenodo.1205621 · Cited by 1 · see citing works
Self-citation
- Authors
- Hellwing, W. A., Frenk, C. S., Cautun, M., Bose, S., Helly, J., Jenkins, A., Sawala, T., & Cytowski, M.
- Affiliations
- Durham University (GB)
- Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw (PL)
- ORCID
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 2016-02-08
- Volume
- 457
- Issue
- 4
- Pages
- 3492-3509
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W1780978098
- Cited by
- 107
- References
- 181
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 4 · 2023: 9 · 2022: 8 · 2021: 12 · 2020: 9 · 2019: 11 · 2018: 20 · 2017: 7 · 2016: 13 · 2015: 3
- FWCI
- 8.13
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Monthly Notices of the Royal Astronomical Society (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- Durham Research Online (Durham University) (acceptedVersion)
- Durham Research Online (Durham University) (submittedVersion, cc-by)
- HighWire Press Open Archive (submittedVersion)
- arXiv (Cornell University)
- Funders
- Durham University (ST/K00042X/1, ST/K003267/1, ST/H008519/1)
- Uniwersytet Warszawski
- Science and Technology Facilities Council (ST/I00162X/1, ST/H008519, ST/K00042X/1, ST/L00075X/1, ST/M007006/1, ST/I001573/1, ST/F001166/1, ST/H008519/1, ST/K003267/1, UMO-2012/07/D/ST9/02785)
- European Regional Development Fund
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Keywords
- dark matter halos, subhalo mass function, halo concentration-mass relation, small-scale structure formation
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