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arxiv: 2606.09997 · v1 · pith:IVIQTDOVnew · submitted 2026-06-08 · 🌌 astro-ph.CO · astro-ph.GA

A universal model for the accretion rates and formation times of dark matter halos

Ankita Bera , Benedikt Diemer This is my paper

Pith reviewed 2026-06-27 15:32 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords dark matter halosmass accretion rateshalo formation timescosmological simulationsuniversal modelpeak heightpower spectrumΛCDM
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The pith

Mass accretion rates of dark matter halos are described by a universal six-parameter function of peak height, power spectrum slope, and growth rate.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures median mass accretion rates and half-mass formation times of dark matter halos across simulations in ΛCDM and Einstein-de Sitter cosmologies from redshift zero to fourteen. It establishes that these rates increase with mass and redshift yet stay virtually identical whether gas physics is included or not. The central claim is that a single six-parameter function of three variables—the peak height, the effective power spectrum slope, and the effective growth rate—fits the accretion rates across the entire range. A two-parameter model for formation redshifts improves on earlier formulas by anchoring one parameter to a physical value and adding dependence on the power spectrum slope. If this holds, halo growth can be predicted directly from these variables without new simulations for each case.

Core claim

The mass accretion rates of dark matter halos are accurately described by a universal six-parameter function of the peak height ν, the slope of the linear power spectrum n_eff, and the effective linear growth rate α_eff. This description holds for median rates extracted from dark-matter-only and hydrodynamical simulations in ΛCDM and Einstein-de Sitter cosmologies at redshifts from zero to fourteen. A complementary two-parameter fit for half-mass formation redshifts improves on the Lacey and Cole function by fixing one parameter to its physical value and adding a dependence on n_eff.

What carries the argument

A universal six-parameter function of the peak height ν, the slope of the linear power spectrum n_eff, and the effective linear growth rate α_eff that fits the median mass accretion rates.

If this is right

  • Mass accretion rates increase with halo mass and redshift.
  • Mass accretion rates remain virtually identical in hydrodynamical and dark-matter-only simulations.
  • The model is broadly consistent with some existing prescriptions but covers a larger range and achieves higher accuracy at high redshifts and low masses.
  • The fitting functions are implemented in the publicly available Colossus toolkit.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The function could supply accretion histories as inputs to semi-analytic galaxy formation models across a wider set of cosmologies without requiring dedicated simulations.
  • Dependence on the power spectrum slope suggests that variations in the initial conditions might produce measurable differences in the distribution of galaxy properties at fixed mass.
  • Extending the same functional form to simulations that include baryonic feedback or modified gravity would test whether the three-variable dependence survives beyond the dark-matter-dominated cases examined here.

Load-bearing premise

The median mass accretion rates extracted from the specific simulations in ΛCDM and Einstein-de Sitter cosmologies at redshifts zero to fourteen represent the true universal behavior across all cosmologies, masses, and redshifts.

What would settle it

Median mass accretion rates measured in a new simulation using a cosmology outside the tested set, such as one with massive neutrinos or a different dark energy model, that deviate substantially from the six-parameter function's predictions would falsify the claim of universality.

Figures

Figures reproduced from arXiv: 2606.09997 by Ankita Bera, Benedikt Diemer.

Figure 1
Figure 1. Figure 1: The dark matter density field from the L0016-WMAP7 simulation of the Erebos suite, illustrating the mass accretion of a single halo across cosmic time. The large right panel shows a projection through about 10% of the simulation volume (16 h −1Mpc ≈ 23 cMpc) at z = 4; the dashed box marks the region around a massive halo sitting at the intersection of several cosmic-web filaments. The remaining panels show… view at source ↗
Figure 2
Figure 2. Figure 2: Dependence of the median mass accretion rate Γdyn on cosmology and simulation suite. Each panel shows Γdyn as a function of peak height ν200m at multiple redshifts (colors as labeled), with shaded regions indicating 1–σ bootstrap uncertainties. Top left: Comparison of Planck (solid) and WMAP7 (dashed) cosmologies using the Erebos suite. The two cosmologies yield similar results at low redshift but diverge … view at source ↗
Figure 3
Figure 3. Figure 3: Top panel: Comparison of Γdyn for IllustrisTNG dark-matter-only (solid) and hydrodynamical (dashed) sim￾ulations. Bottom panel: The fractional differences be￾tween dark-matter-only and hydrodynamical simulations (Γhydro − ΓDm)/ΓDm. The excellent agreement (≲ 0.1) be￾tween N-body and Hydro runs demonstrates that baryonic processes have minimal effect on mass accretion rates for the halo mass range probed he… view at source ↗
Figure 4
Figure 4. Figure 4: Validation of our universal fitting function across simulations, cosmologies, and redshifts. Each panel shows Γdyn as a function of peak height, with solid lines indicating the median values from simulations and dashed lines showing predictions from our six-parameter fitting function (Equation 7). Colors denote redshift as labeled, with shaded regions representing 1–σ bootstrap uncertainties. The lower sub… view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of Γdyn in bins of peak height ν (rows) and redshift (columns) for Erebos (WMAP7) simulation. The histograms are best described by the Gamma distribution fit with floc = 0 (dashed). However, a log-normal model specified entirely by the fitting functions of Equations 7 and 9 (solid) also provides a reasonable fit, with KS statistics comparable to those of a log-normal fit with µ and σ as free p… view at source ↗
Figure 6
Figure 6. Figure 6: Left: Median ratio of the scale factor at formation to the scale factor at observation, af/ao, as a function of peak height ν200m for the ΛCDM simulations. Colors indicate the observation redshift, ranging from z0 = 0 to z0 = 12. Points show the binned medians measured from the simulation merger trees, and solid lines show the prediction from Equation 11 with f = 0.5 and C(neff ) given by Equation 13. At l… view at source ↗
Figure 7
Figure 7. Figure 7: compares our model for the half-mass red￾shift for halos at z = 0 to models from the literature. The EPS-based prediction of C. Lacey & S. Cole (1993, olive solid line) lies systematically below all other mod￾els, reproducing a well-known underestimate of forma￾tion times (C. Giocoli et al. 2007, see also the discussion in Section 3.4). However, our model matches well with those of C. Giocoli et al. (2012,… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of Γdyn(M, z) from our fitting function (solid lines) with models from the literature, with colors indicating redshift from z = 0 (dark blue) to z = 14 (yellow). All models have been converted to Γdyn measured over one dynamical time (Section 4.2). Top left: the exponential MAH of R. H. Wechsler et al. (2002) with formation redshifts based on our model (dashed) and the F. C. van den Bosch (2002)… view at source ↗
read the original abstract

The formation histories of halos set the baseline rate at which galaxies accrete gas over cosmic time. While a number of models describe these histories and their derivative, the mass accretion rate (MAR), a simple and universal formula has remained elusive. Here we measure the median MARs and half-mass formation times of halos in dark matter-only and hydrodynamical simulations, in extremely different cosmologies ($\Lambda$CDM and Einstein-de Sitter), and across a wide range of redshifts ($z = 0$-$14$). We confirm that MARs increase with mass and redshift, and that they are virtually identical in hydrodynamical and dark matter-only simulations. We show that MARs are accurately described by a universal six-parameter function of three physical variables: the peak height $\nu$, the slope of the linear power spectrum $n_{\rm eff}$, and the effective linear growth rate $\alpha_{\rm eff}$. A complementary two-parameter fit for the formation redshift improves on the function of Lacey \& Cole by fixing one parameter to its physical value and adding a dependence on $n_{\rm eff}$. Our model is broadly consistent with some prescriptions from the literature but provides a larger range and higher accuracy at high redshifts and low masses. Our fitting functions are implemented in the publicly available \textsc{Colossus} toolkit.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper measures median mass accretion rates (MARs) and half-mass formation times from dark matter-only and hydrodynamical simulations in ΛCDM and Einstein-de Sitter cosmologies at z=0–14. It claims that the MARs are accurately described by a universal six-parameter function of three variables (peak height ν, effective spectral index n_eff, and effective growth rate α_eff), and presents a complementary two-parameter fit for formation redshift that improves on Lacey & Cole by fixing one parameter to its physical value and adding n_eff dependence. The functions are implemented in the public Colossus toolkit and stated to be broadly consistent with some literature prescriptions while offering better accuracy at high z and low mass.

Significance. If the quantitative accuracy and universality hold, the result supplies a compact, cosmology-independent parametrization of halo accretion histories that could be adopted in semi-analytic galaxy formation models. The public Colossus implementation and the confirmation that hydrodynamical and dark-matter-only MARs are essentially identical are concrete strengths that aid reproducibility and community use.

major comments (3)
  1. [Abstract] Abstract: the statement that the six-parameter function 'accurately describes' the measured median MARs supplies no quantitative support (χ², residuals, rms error, cross-validation, or parameter uncertainties), so the data-to-claim link cannot be evaluated from the given information.
  2. [Fitting procedure and universality tests] Fitting and universality sections: the six parameters are determined by matching the median MARs extracted from the same ΛCDM+EdS simulation suite used to test the model; without held-out cosmologies, altered power spectra, or different dark-energy evolution, the claim that ν, n_eff and α_eff fully capture all cosmology dependence remains untested and the universality assertion is circular by construction.
  3. [Formation redshift section] Formation-time fit: the two-parameter model is presented as an improvement over Lacey & Cole, but no direct quantitative comparison (e.g., residuals or R² on the same data) is supplied to demonstrate the improvement or to show that fixing one parameter to its physical value is justified across the full redshift and mass range.
minor comments (2)
  1. [Abstract and methods] Abstract and methods: the exact halo mass range, number of halos per bin, and simulation volume/resolution details used for the median MAR extraction should be stated explicitly to allow readers to judge the statistical robustness of the fit.
  2. [Figures and notation] Figure captions and text: labels for the three input variables (ν, n_eff, α_eff) and the six fit parameters should be defined at first use with their precise mathematical definitions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the six-parameter function 'accurately describes' the measured median MARs supplies no quantitative support (χ², residuals, rms error, cross-validation, or parameter uncertainties), so the data-to-claim link cannot be evaluated from the given information.

    Authors: We agree that the abstract would benefit from quantitative support. In the revised manuscript we will add a concise statement of the typical rms residuals (approximately 0.05–0.1 dex across the probed range) and will include parameter uncertainties and a summary of fit quality in a new subsection of the results. These metrics will also be referenced briefly in the abstract. revision: yes

  2. Referee: [Fitting procedure and universality tests] Fitting and universality sections: the six parameters are determined by matching the median MARs extracted from the same ΛCDM+EdS simulation suite used to test the model; without held-out cosmologies, altered power spectra, or different dark-energy evolution, the claim that ν, n_eff and α_eff fully capture all cosmology dependence remains untested and the universality assertion is circular by construction.

    Authors: The two cosmologies employed (flat ΛCDM and Einstein-de Sitter) differ substantially in both expansion history and the redshift evolution of the power spectrum, and the variables ν, n_eff and α_eff were selected precisely because they encode the leading physical dependencies. Nevertheless, we acknowledge that the tests are performed on the same simulation suite. In the revision we will clarify the scope of the universality claim, explicitly note the absence of additional cosmologies, and discuss this as a limitation rather than asserting complete cosmology independence. revision: partial

  3. Referee: [Formation redshift section] Formation-time fit: the two-parameter model is presented as an improvement over Lacey & Cole, but no direct quantitative comparison (e.g., residuals or R² on the same data) is supplied to demonstrate the improvement or to show that fixing one parameter to its physical value is justified across the full redshift and mass range.

    Authors: We agree that a side-by-side quantitative comparison is needed. The revised manuscript will include a table or figure showing residuals and goodness-of-fit statistics for both our model and the Lacey & Cole prescription evaluated on the identical data set. We will also provide a brief physical justification for fixing the relevant parameter and demonstrate that the improvement holds across the full redshift and mass range examined. revision: yes

Circularity Check

0 steps flagged

Empirical fit presented as universal description; no reduction of derivation to inputs by construction

full rationale

The paper measures median MARs directly from a suite of DM-only and hydrodynamical simulations in ΛCDM and EdS cosmologies, then constructs a six-parameter fitting function of ν, n_eff and α_eff to describe those measurements. This is a standard empirical modeling workflow with no claimed first-principles derivation, no self-citation load-bearing step, and no instance in which a fitted parameter is renamed as an independent prediction or where an equation reduces to its inputs by definition. The universality claim rests on the representativeness of the chosen variables and simulation suite, but that is an evidentiary question rather than a circularity in the derivation chain itself. No quoted equations or steps exhibit the specific reductions required for a positive circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on empirical fitting of six free parameters to median MARs measured in a finite set of simulations plus the assumption that those medians and the chosen functional form capture universal behavior.

free parameters (1)
  • six parameters of the MAR fitting function
    Determined by fitting to the median MARs measured across the simulation suite.
axioms (2)
  • domain assumption Median MARs from the dark-matter-only and hydrodynamical runs in the two cosmologies are representative of the physical accretion process.
    The universality claim is built directly on these measured medians.
  • ad hoc to paper The three-variable functional form with six parameters is sufficient to capture all relevant dependencies without additional terms or cosmology-specific adjustments.
    Universality is asserted after fitting the chosen form to the tested cases.

pith-pipeline@v0.9.1-grok · 5770 in / 1538 out tokens · 32982 ms · 2026-06-27T15:32:15.726993+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

116 extracted references · 112 canonical work pages · 12 internal anchors

  1. [1]

    Adhikari , S., Dalal , N., & Chamberlain , R. T. 2014, title Splashback in accreting dark matter halos , JCAP, 11, 19, 10.1088/1475-7516/2014/11/019

    work page doi:10.1088/1475-7516/2014/11/019 2014

  2. [2]

    P., Tollerud , E

    Astropy Collaboration , Robitaille , T. P., Tollerud , E. J., et al. 2013, title Astropy: A community Python package for astronomy , , 558, A33, 10.1051/0004-6361/201322068

    work page doi:10.1051/0004-6361/201322068 2013

  3. [3]

    M., Sip o cz , B

    Astropy Collaboration , Price-Whelan , A. M., Sip o cz , B. M., et al. 2018, title The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package , , 156, 123, 10.3847/1538-3881/aabc4f

    work page doi:10.3847/1538-3881/aabc4f 2018

  4. [4]

    M., Lim , P

    Astropy Collaboration , Price-Whelan , A. M., Lim , P. L., et al. 2022, title The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package , , 935, 167, 10.3847/1538-4357/ac7c74

    work page internal anchor Pith review doi:10.3847/1538-4357/ac7c74 2022

  5. [5]

    R., et al

    Avila , S., Knebe , A., Pearce , F. R., et al. 2014, title SUSSING MERGER TREES: the influence of the halo finder , , 441, 3488, 10.1093/mnras/stu799

    work page doi:10.1093/mnras/stu799 2014

  6. [6]

    M., Bond , J

    Bardeen , J. M., Bond , J. R., Kaiser , N., & Szalay , A. S. 1986, title The statistics of peaks of Gaussian random fields , , 304, 15, 10.1086/164143

    work page doi:10.1086/164143 1986

  7. [7]

    H., Hearin , A

    Behroozi , P., Wechsler , R. H., Hearin , A. P., & Conroy , C. 2019, title UNIVERSEMACHINE: The correlation between galaxy growth and dark matter halo assembly from z = 0-10 , , 488, 3143, 10.1093/mnras/stz1182

    work page doi:10.1093/mnras/stz1182 2019

  8. [8]

    S., Wechsler , R

    Behroozi , P. S., Wechsler , R. H., & Wu , H.-Y. 2013 a , title The ROCKSTAR Phase-space Temporal Halo Finder and the Velocity Offsets of Cluster Cores , , 762, 109, 10.1088/0004-637X/762/2/109

    work page internal anchor Pith review doi:10.1088/0004-637x/762/2/109 2013

  9. [9]

    S., Wechsler , R

    Behroozi , P. S., Wechsler , R. H., Wu , H.-Y., et al. 2013 b , title Gravitationally Consistent Halo Catalogs and Merger Trees for Precision Cosmology , , 763, 18, 10.1088/0004-637X/763/1/18

    work page internal anchor Pith review doi:10.1088/0004-637x/763/1/18 2013

  10. [10]

    Benson , A. J. 2017, title The mass function of unprocessed dark matter haloes and merger tree branching rates , , 467, 3454, 10.1093/mnras/stx343

    work page doi:10.1093/mnras/stx343 2017

  11. [11]

    , keywords =

    Benson , A. J., Borgani , S., De Lucia , G., Boylan-Kolchin , M., & Monaco , P. 2012, title Convergence of galaxy properties with merger tree temporal resolution , , 419, 3590, 10.1111/j.1365-2966.2011.20002.x

    work page doi:10.1111/j.1365-2966.2011.20002.x 2012

  12. [12]

    R., Cole , S., Efstathiou , G., & Kaiser , N

    Bond , J. R., Cole , S., Efstathiou , G., & Kaiser , N. 1991, title Excursion set mass functions for hierarchical Gaussian fluctuations , , 379, 440, 10.1086/170520

    work page doi:10.1086/170520 1991

  13. [13]

    T., McCarthy , I

    Brown , S. T., McCarthy , I. G., Diemer , B., et al. 2020, title Connecting the structure of dark matter haloes to the primordial power spectrum , , 495, 4994, 10.1093/mnras/staa1491

    work page doi:10.1093/mnras/staa1491 2020

  14. [14]

    D., & Pudritz, R

    Cole , S., Lacey , C. G., Baugh , C. M., & Frenk , C. S. 2000, title Hierarchical galaxy formation , , 319, 168, 10.1046/j.1365-8711.2000.03879.x

    work page doi:10.1046/j.1365-8711.2000.03879.x 2000

  15. [15]

    A., Wyithe , J

    Correa , C. A., Wyithe , J. S. B., Schaye , J., & Duffy , A. R. 2015 a , title The accretion history of dark matter haloes - I. The physical origin of the universal function , , 450, 1514, 10.1093/mnras/stv689

    work page doi:10.1093/mnras/stv689 2015

  16. [16]

    A., Wyithe , J

    Correa , C. A., Wyithe , J. S. B., Schaye , J., & Duffy , A. R. 2015 b , title The accretion history of dark matter haloes - III. A physical model for the concentration-mass relation , , 452, 1217, 10.1093/mnras/stv1363

    work page doi:10.1093/mnras/stv1363 2015

  17. [17]

    Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl

    Cranmer , M. 2023, title Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl , arXiv e-prints, arXiv:2305.01582, 10.48550/arXiv.2305.01582

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2305.01582 2023

  18. [18]

    2006, title Transients from initial conditions in cosmological simulations , , 373, 369, 10.1111/j.1365-2966.2006.11040.x

    Crocce , M., Pueblas , S., & Scoccimarro , R. 2006, title Transients from initial conditions in cosmological simulations , , 373, 369, 10.1111/j.1365-2966.2006.11040.x

    work page doi:10.1111/j.1365-2966.2006.11040.x 2006

  19. [19]

    2010, title The Origin of Dark Matter Halo Profiles , arXiv:1010.2539

    Dalal , N., Lithwick , Y., & Kuhlen , M. 2010, title The Origin of Dark Matter Halo Profiles , arXiv:1010.2539. 1010.2539

    Pith/arXiv arXiv 2010

  20. [20]

    R., & Shirokov , A

    Dalal , N., White , M., Bond , J. R., & Shirokov , A. 2008, title Halo Assembly Bias in Hierarchical Structure Formation , , 687, 12, 10.1086/591512

    work page doi:10.1086/591512 2008

  21. [21]

    2009, title Cold streams in early massive hot haloes as the main mode of galaxy formation , , 457, 451, 10.1038/nature07648

    Dekel , A., Birnboim , Y., Engel , G., et al. 2009, title Cold streams in early massive hot haloes as the main mode of galaxy formation , , 457, 451, 10.1038/nature07648

    work page internal anchor Pith review doi:10.1038/nature07648 2009

  22. [22]

    2017, title The Splashback Radius of Halos from Particle Dynamics

    Diemer , B. 2017, title The Splashback Radius of Halos from Particle Dynamics. I. The SPARTA Algorithm , , 231, 5, 10.3847/1538-4365/aa799c

    work page doi:10.3847/1538-4365/aa799c 2017

  23. [23]

    2018, ApJS, 239, 35, doi: 10.3847/1538-4365/aaee8c

    Diemer , B. 2018, title COLOSSUS: A Python Toolkit for Cosmology, Large-scale Structure, and Dark Matter Halos , , 239, 35, 10.3847/1538-4365/aaee8c

    work page doi:10.3847/1538-4365/aaee8c 2018

  24. [24]

    2020, title The Splashback Radius of Halos from Particle Dynamics

    Diemer , B. 2020, title The Splashback Radius of Halos from Particle Dynamics. III. Halo Catalogs, Merger Trees, and Host-Subhalo Relations , , 251, 17, 10.3847/1538-4365/abbf51

    work page doi:10.3847/1538-4365/abbf51 2020

  25. [25]

    2022, title A dynamics-based density profile for dark haloes - I

    Diemer , B. 2022, title A dynamics-based density profile for dark haloes - I. Algorithm and basic results , , 513, 573, 10.1093/mnras/stac878

    work page doi:10.1093/mnras/stac878 2022

  26. [26]

    2019, ApJ, 871, 168, doi: 10.3847/1538-4357/aafad6

    Diemer , B., & Joyce , M. 2019, title An Accurate Physical Model for Halo Concentrations , , 871, 168, 10.3847/1538-4357/aafad6

    work page doi:10.3847/1538-4357/aafad6 2019

  27. [27]

    Diemer , B., & Kravtsov , A. V. 2014, title Dependence of the Outer Density Profiles of Halos on Their Mass Accretion Rate , , 789, 1, 10.1088/0004-637X/789/1/1

    work page doi:10.1088/0004-637x/789/1/1 2014

  28. [28]

    Diemer , B., & Kravtsov , A. V. 2015, title A Universal Model for Halo Concentrations , , 799, 108, 10.1088/0004-637X/799/1/108

    work page doi:10.1088/0004-637x/799/1/108 2015

  29. [29]

    V., & More , S

    Diemer , B., Kravtsov , A. V., & More , S. 2013 a , title On the Evolution of Cluster Scaling Relations , , 779, 159, 10.1088/0004-637X/779/2/159

    work page doi:10.1088/0004-637x/779/2/159 2013

  30. [30]

    Diemer , B., More , S., & Kravtsov , A. V. 2013 b , title The Pseudo-evolution of Halo Mass , , 766, 25, 10.1088/0004-637X/766/1/25

    work page doi:10.1088/0004-637x/766/1/25 2013

  31. [31]

    doi:10.1111/j.1365-2966.2009.15868.x , eprint =

    Dolag , K., Borgani , S., Murante , G., & Springel , V. 2009, title Substructures in hydrodynamical cluster simulations , , 399, 497, 10.1111/j.1365-2966.2009.15034.x

    work page doi:10.1111/j.1365-2966.2009.15034.x 2009

  32. [32]

    S., White , S

    Efstathiou , G., Frenk , C. S., White , S. D. M., & Davis , M. 1988, title Gravitational clustering from scale-free initial conditions. , , 235, 715, 10.1093/mnras/235.3.715

    work page doi:10.1093/mnras/235.3.715 1988

  33. [33]

    J., & Hu , W

    Eisenstein , D. J., & Hu , W. 1998, title Baryonic Features in the Matter Transfer Function , , 496, 605, 10.1086/305424

    work page doi:10.1086/305424 1998

  34. [34]

    doi:10.1111/j.1365-2966.2009.15868.x , eprint =

    Fakhouri , O., & Ma , C.-P. 2009, title Environmental dependence of dark matter halo growth - I. Halo merger rates , , 394, 1825, 10.1111/j.1365-2966.2009.14480.x

    work page doi:10.1111/j.1365-2966.2009.14480.x 2009

  35. [35]

    M., 2011, @doi [ ] 10.1111/j.1365-2966.2010.17821.x , 411, 1917

    Fakhouri , O., Ma , C.-P., & Boylan-Kolchin , M. 2010, title The merger rates and mass assembly histories of dark matter haloes in the two Millennium simulations , , 406, 2267, 10.1111/j.1365-2966.2010.16859.x

    work page doi:10.1111/j.1365-2966.2010.16859.x 2010

  36. [36]

    , keywords =

    Faucher-Gigu \`e re , C.-A., Kere s , D., & Ma , C.-P. 2011, title The baryonic assembly of dark matter haloes , , 417, 2982, 10.1111/j.1365-2966.2011.19457.x

    work page doi:10.1111/j.1365-2966.2011.19457.x 2011

  37. [37]

    Gao , L., Springel , V., & White , S. D. M. 2005, title The age dependence of halo clustering , , 363, L66, 10.1111/j.1745-3933.2005.00084.x

    work page doi:10.1111/j.1745-3933.2005.00084.x 2005

  38. [38]

    2022, title The THESAN project: properties of the intergalactic medium and its connection to reionization-era galaxies , , 512, 4909, 10.1093/mnras/stac257

    Garaldi , E., Kannan , R., Smith , A., et al. 2022, title The THESAN project: properties of the intergalactic medium and its connection to reionization-era galaxies , , 512, 4909, 10.1093/mnras/stac257

    work page doi:10.1093/mnras/stac257 2022

  39. [39]

    2010, title The Growth of Dark Matter Halos: Evidence for Significant Smooth Accretion , , 719, 229, 10.1088/0004-637X/719/1/229

    Genel , S., Bouch \'e , N., Naab , T., Sternberg , A., & Genzel , R. 2010, title The Growth of Dark Matter Halos: Evidence for Significant Smooth Accretion , , 719, 229, 10.1088/0004-637X/719/1/229

    work page doi:10.1088/0004-637x/719/1/229 2010

  40. [40]

    2008, title Mergers and Mass Accretion Rates in Galaxy Assembly: The Millennium Simulation Compared to Observations of z 2 Galaxies , , 688, 789, 10.1086/592241

    Genel , S., Genzel , R., Bouch \'e , N., et al. 2008, title Mergers and Mass Accretion Rates in Galaxy Assembly: The Millennium Simulation Compared to Observations of z 2 Galaxies , , 688, 789, 10.1086/592241

    work page doi:10.1086/592241 2008

  41. [41]

    , keywords =

    Giocoli , C., Moreno , J., Sheth , R. K., & Tormen , G. 2007, title An improved model for the formation times of dark matter haloes , , 376, 977, 10.1111/j.1365-2966.2007.11520.x

    work page doi:10.1111/j.1365-2966.2007.11520.x 2007

  42. [42]

    Giocoli , C., Tormen , G., & Sheth , R. K. 2012, title Formation times, mass growth histories and concentrations of dark matter haloes , , 422, 185, 10.1111/j.1365-2966.2012.20594.x

    work page doi:10.1111/j.1365-2966.2012.20594.x 2012

  43. [43]

    2021, title Shape and connectivity of groups and clusters: Effect of the dynamical state and accretion history , , 651, A56, 10.1051/0004-6361/202140327

    Gouin , C., Bonnaire , T., & Aghanim , N. 2021, title Shape and connectivity of groups and clusters: Effect of the dynamical state and accretion history , , 651, A56, 10.1051/0004-6361/202140327

    work page doi:10.1051/0004-6361/202140327 2021

  44. [44]

    , year = 1972, month = aug, volume =

    Gunn , J. E., & Gott , III, J. R. 1972, title On the Infall of Matter Into Clusters of Galaxies and Some Effects on Their Evolution , , 176, 1, 10.1086/151605

    work page doi:10.1086/151605 1972

  45. [45]

    Harris and K

    Harris , C. R., Millman , K. J., van der Walt , S. J., et al. 2020, title Array programming with NumPy , , 585, 357, 10.1038/s41586-020-2649-2

    work page doi:10.1038/s41586-020-2649-2 2020

  46. [46]

    P., Chaves-Montero , J., Becker , M

    Hearin , A. P., Chaves-Montero , J., Becker , M. R., & Alarcon , A. 2021, title A Differentiable Model of the Assembly of Individual and Populations of Dark Matter Halos , The Open Journal of Astrophysics, 4, 7, 10.21105/astro.2105.05859

    work page doi:10.21105/astro.2105.05859 2021

  47. [47]

    Henriques , B. M. B., White , S. D. M., Thomas , P. A., et al. 2015, title Galaxy formation in the Planck cosmology - I. Matching the observed evolution of star formation rates, colours and stellar masses , , 451, 2663, 10.1093/mnras/stv705

    work page doi:10.1093/mnras/stv705 2015

  48. [48]

    Hunter , J. D. 2007, title Matplotlib: A 2D Graphics Environment , Computing in Science and Engineering, 9, 90, 10.1109/MCSE.2007.55

    work page doi:10.1109/mcse.2007.55 2007

  49. [49]

    Jing , Y. P. 1998, title Accurate Fitting Formula for the Two-Point Correlation Function of Dark Matter Halos , , 503, L9, 10.1086/311530

    work page doi:10.1086/311530 1998

  50. [50]

    2021, title Quantifying resolution in cosmological N-body simulations using self-similarity , , 501, 5051, 10.1093/mnras/staa3434

    Joyce , M., Garrison , L., & Eisenstein , D. 2021, title Quantifying resolution in cosmological N-body simulations using self-similarity , , 501, 5051, 10.1093/mnras/staa3434

    work page doi:10.1093/mnras/staa3434 2021

  51. [51]

    2022, title Introducing the THESAN project: radiation-magnetohydrodynamic simulations of the epoch of reionization , , 511, 4005, 10.1093/mnras/stab3710

    Kannan , R., Garaldi , E., Smith , A., et al. 2022, title Introducing the THESAN project: radiation-magnetohydrodynamic simulations of the epoch of reionization , , 511, 4005, 10.1093/mnras/stab3710

    work page doi:10.1093/mnras/stab3710 2022

  52. [52]

    , keywords =

    Kere s , D., Katz , N., Weinberg , D. H., & Dav \'e , R. 2005, title How do galaxies get their gas? , , 363, 2, 10.1111/j.1365-2966.2005.09451.x

    work page doi:10.1111/j.1365-2966.2005.09451.x 2005

  53. [53]

    A., Trujillo-Gomez , S., & Primack , J

    Klypin , A. A., Trujillo-Gomez , S., & Primack , J. 2011, title Dark Matter Halos in the Standard Cosmological Model: Results from the Bolshoi Simulation , , 740, 102, 10.1088/0004-637X/740/2/102

    work page doi:10.1088/0004-637x/740/2/102 2011

  54. [54]

    , keywords =

    Knebe , A., Knollmann , S. R., Muldrew , S. I., et al. 2011, title Haloes gone MAD: The Halo-Finder Comparison Project , , 415, 2293, 10.1111/j.1365-2966.2011.18858.x

    work page doi:10.1111/j.1365-2966.2011.18858.x 2011

  55. [55]

    A., Bridle, A

    Knollmann , S. R., Power , C., & Knebe , A. 2008, title Dark matter halo profiles in scale-free cosmologies , , 385, 545, 10.1111/j.1365-2966.2008.12857.x

    work page doi:10.1111/j.1365-2966.2008.12857.x 2008

  56. [56]

    M., Dunkley , J., et al

    Komatsu , E., Smith , K. M., Dunkley , J., et al. 2011, title Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation , , 192, 18, 10.1088/0067-0049/192/2/18

    work page internal anchor Pith review doi:10.1088/0067-0049/192/2/18 2011

  57. [57]

    1993, title Merger rates in hierarchical models of galaxy formation , , 262, 627

    Lacey , C., & Cole , S. 1993, title Merger rates in hierarchical models of galaxy formation , , 262, 627

    1993

  58. [58]

    1994, title Merger Rates in Hierarchical Models of Galaxy Formation - Part Two - Comparison with N-Body Simulations , , 271, 676, 10.1093/mnras/271.3.676

    Lacey , C., & Cole , S. 1994, title Merger Rates in Hierarchical Models of Galaxy Formation - Part Two - Comparison with N-Body Simulations , , 271, 676, 10.1093/mnras/271.3.676

    work page doi:10.1093/mnras/271.3.676 1994

  59. [59]

    2021, title Testing dark matter halo properties using self-similarity , , 501, 5064, 10.1093/mnras/staa3435

    Leroy , M., Garrison , L., Eisenstein , D., Joyce , M., & Maleubre , S. 2021, title Testing dark matter halo properties using self-similarity , , 501, 5064, 10.1093/mnras/staa3435

    work page doi:10.1093/mnras/staa3435 2021

  60. [60]

    2000, title Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann-Robertson-Walker Models , , 538, 473, 10.1086/309179

    Lewis , A., Challinor , A., & Lasenby , A. 2000, title Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann-Robertson-Walker Models , , 538, 473, 10.1086/309179

    work page doi:10.1086/309179 2000

  61. [61]

    D., Bose , S., Angulo , R

    Ludlow , A. D., Bose , S., Angulo , R. E., et al. 2016, title The mass-concentration-redshift relation of cold and warm dark matter haloes , , 460, 1214, 10.1093/mnras/stw1046

    work page doi:10.1093/mnras/stw1046 2016

  62. [62]

    D., Navarro , J

    Ludlow , A. D., Navarro , J. F., Boylan-Kolchin , M., et al. 2013, title The mass profile and accretion history of cold dark matter haloes , , 432, 1103, 10.1093/mnras/stt526

    work page doi:10.1093/mnras/stt526 2013

  63. [63]

    A., Bridle, A

    Macci \`o , A. V., Dutton , A. A., & van den Bosch , F. C. 2008, title Concentration, spin and shape of dark matter haloes as a function of the cosmological model: WMAP1, WMAP3 and WMAP5 results , , 391, 1940, 10.1111/j.1365-2966.2008.14029.x

    work page doi:10.1111/j.1365-2966.2008.14029.x 2008

  64. [64]

    2018, title First results from the IllustrisTNG simulations: radio haloes and magnetic fields , , 480, 5113, 10.1093/mnras/sty2206

    Marinacci , F., Vogelsberger , M., Pakmor , R., et al. 2018, title First results from the IllustrisTNG simulations: radio haloes and magnetic fields , , 480, 5113, 10.1093/mnras/sty2206

    work page internal anchor Pith review doi:10.1093/mnras/sty2206 2018

  65. [65]

    Massey, F. J. 1951, title The Kolmogorov-Smirnov Test for Goodness of Fit, Journal of the American Statistical Association, 46, 68. http://www.jstor.org/stable/2280095

    arXiv 1951

  66. [66]

    2007, title The Dependence of the Mass Assembly History of Cold Dark Matter Halos on Environment , , 654, 53, 10.1086/509706

    Maulbetsch , C., Avila-Reese , V., Col \' n , P., et al. 2007, title The Dependence of the Mass Assembly History of Cold Dark Matter Halos on Environment , , 654, 53, 10.1086/509706

    work page doi:10.1086/509706 2007

  67. [67]

    doi:10.1111/j.1365-2966.2009.15868.x , eprint =

    McBride , J., Fakhouri , O., & Ma , C.-P. 2009, title Mass accretion rates and histories of dark matter haloes , , 398, 1858, 10.1111/j.1365-2966.2009.15329.x

    work page doi:10.1111/j.1365-2966.2009.15329.x 2009

  68. [68]

    R., & Sun , G

    Mirocha , J., Furlanetto , S. R., & Sun , G. 2017, title The global 21-cm signal in the context of the high- z galaxy luminosity function , , 464, 1365, 10.1093/mnras/stw2412

    work page doi:10.1093/mnras/stw2412 2017

  69. [69]

    C., & White , S

    Mo , H., van den Bosch , F. C., & White , S. 2010, Galaxy Formation and Evolution , 10.1017/CBO9780511807244

    work page doi:10.1017/cbo9780511807244 2010

  70. [70]

    J., & White , S

    Mo , H. J., & White , S. D. M. 1996, title An analytic model for the spatial clustering of dark matter haloes , , 282, 347, 10.1093/mnras/282.2.347

    work page doi:10.1093/mnras/282.2.347 1996

  71. [71]

    P., Naab , T., & White , S

    Moster , B. P., Naab , T., & White , S. D. M. 2018, title EMERGE - an empirical model for the formation of galaxies since z 10 , , 477, 1822, 10.1093/mnras/sty655

    work page doi:10.1093/mnras/sty655 2018

  72. [72]

    P., Pillepich , A., Springel , V., et al

    Naiman , J. P., Pillepich , A., Springel , V., et al. 2018, title First results from the IllustrisTNG simulations: a tale of two elements - chemical evolution of magnesium and europium , , 477, 1206, 10.1093/mnras/sty618

    work page internal anchor Pith review doi:10.1093/mnras/sty618 2018

  73. [73]

    F., Frenk , C

    Navarro , J. F., Frenk , C. S., & White , S. D. M. 1997, title A Universal Density Profile from Hierarchical Clustering , , 490, 493, 10.1086/304888

    work page doi:10.1086/304888 1997

  74. [74]

    , keywords =

    Neistein , E., & Dekel , A. 2008, title Constructing merger trees that mimic N-body simulations , , 383, 615, 10.1111/j.1365-2966.2007.12570.x

    work page doi:10.1111/j.1365-2966.2007.12570.x 2008

  75. [75]

    2018, title First results from the IllustrisTNG simulations: the galaxy colour bimodality , , 475, 624, 10.1093/mnras/stx3040

    Nelson , D., Pillepich , A., Springel , V., et al. 2018, title First results from the IllustrisTNG simulations: the galaxy colour bimodality , , 475, 624, 10.1093/mnras/stx3040

    work page internal anchor Pith review doi:10.1093/mnras/stx3040 2018

  76. [76]

    2019, title The IllustrisTNG simulations: public data release , Computational Astrophysics and Cosmology, 6, 2, 10.1186/s40668-019-0028-x

    Nelson , D., Springel , V., Pillepich , A., et al. 2019, title The IllustrisTNG simulations: public data release , Computational Astrophysics and Cosmology, 6, 2, 10.1186/s40668-019-0028-x

    work page doi:10.1186/s40668-019-0028-x 2019

  77. [77]

    2019, title Inferring the astrophysics of reionization and cosmic dawn from galaxy luminosity functions and the 21-cm signal , , 484, 933, 10.1093/mnras/stz032

    Park , J., Mesinger , A., Greig , B., & Gillet , N. 2019, title Inferring the astrophysics of reionization and cosmic dawn from galaxy luminosity functions and the 21-cm signal , , 484, 933, 10.1093/mnras/stz032

    work page doi:10.1093/mnras/stz032 2019

  78. [78]

    , keywords =

    Parkinson , H., Cole , S., & Helly , J. 2008, title Generating dark matter halo merger trees , , 383, 557, 10.1111/j.1365-2966.2007.12517.x

    work page doi:10.1111/j.1365-2966.2007.12517.x 2008

  79. [79]

    2018 b , title Simulating galaxy formation with the IllustrisTNG model , , 473, 4077, 10.1093/mnras/stx2656

    Pillepich , A., Springel , V., Nelson , D., et al. 2018, title Simulating galaxy formation with the IllustrisTNG model , , 473, 4077, 10.1093/mnras/stx2656

    work page internal anchor Pith review doi:10.1093/mnras/stx2656 2018

  80. [80]

    Planck Collaboration , Ade , P. A. R., Aghanim , N., et al. 2014, title Planck 2013 results. XVI. Cosmological parameters , , 571, A16, 10.1051/0004-6361/201321591

    work page doi:10.1051/0004-6361/201321591 2014

Showing first 80 references.