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The life and times of dark matter haloes: what will I be when I grow up?

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The most massive dark matter haloes do not stay the most massive: only 40% of today's top 100 clusters were still in the top 100 at z=1.

desk verdict Direct measurement of rank churn in MDPL2's top 100 haloes; the 40% survival at z=1 is a useful number but the mass-definition dependence and lack of error bars need attention. read the letter →

arxiv 2508.18778 v1 pith:XGTTFOZD submitted 2025-08-26 astro-ph.GA

Julian Onions , Frazer Pearce , Alexander Knebe , Meghan Gray , Roan Haggar , Ulrike Kuchner , Ana Contreras-Santos , Gustavo Yepes
show 1 more author
Weiguang Cui
This is my paper · ORCID
classification astro-ph.GA
keywords darkmatterhaloeshalomassfunctionclusterselectionmergertreesmajormergersdynamicalstatecosmologicalsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tests a common assumption in cluster cosmology: that the most massive dark matter haloes at one time are also the most massive at other times. Tracing the 100 most massive haloes in a large cosmological simulation from z=0 backwards, the authors find only about 40% were still in the top 100 at z=1, and the top 10 churn even faster. Growth is driven by stochastic major mergers, so objects leap into the highest mass ranks and then gradually fall back. The consequence is that a sample selected by mass at a single redshift is not mass-complete at other redshifts and is biased toward recently merged, dynamically unrelaxed systems. This matters for comparing simulated clusters with observed surveys at high redshift.

What carries the argument

The central device is the 'froth region': the top 100 haloes by virial mass in the simulation volume, where one major merger can change an object's rank dramatically. Haloes are ranked using a redshift-dependent virial mass definition, linked across 50 snapshots by merger trees built from particle membership, and followed along the most massive progenitor branch. The churn rate measured on this ranked sample carries the whole argument.

What would settle it

Recompute the top-100 membership at every snapshot using a fixed overdensity mass definition, such as 200 times the critical density, with the same merger trees; if the fraction surviving from z=1 to z=0 stays near 40%, the churn claim is insensitive to mass definition. Alternatively, compare two observed cluster samples ranked by independent mass proxies, such as X-ray hydrostatic mass versus Sunyaev-Zel'dovich mass, at z~1 and z~0, and ask what fraction of the z~1 top set remains top-ranked at z=0.

Watch

Extended reading notes

Core claim

The paper establishes that rank-order stability of the most massive haloes fails: fewer than half of the 100 most massive haloes at z=1 remain in that set at z=0, and only 40% of the z=0 top 100 were in the top 100 at z=1. The apparent tension with hierarchical growth is resolved by merger-driven 'churn': a major merger can roughly double a halo's mass in a short interval, promoting it into the top set, while later quiescent accretion lets rivals overtake it. The authors quantify the effect by building a mass-complete superset of 268 clusters that includes every halo that was ever among the top 100 between z=0 and z=1, and show that a fixed sample's mean mass evolves differently from a truly

Load-bearing premise

The result depends on how a halo's mass is defined: rankings use a virial mass that changes its overdensity contrast with redshift, and a different standard definition could shift some haloes across the top-100 boundary and change the survival fractions.

Editorial extensions

If this is right

  • Cluster samples selected at a single redshift are biased toward late-forming systems with recent major mergers, not random draws from the mass function.
  • Comparisons between simulations and surveys at high redshift need mass-complete samples, not fixed z=0 selections, or they will miss a large fraction of the most massive progenitors.
  • Mass-growth studies of a fixed set of extreme clusters will overestimate growth before the selection epoch and underestimate it afterward, by roughly (1+z)^-0.5.
  • A rare, very massive cluster is likely dynamically unrelaxed, so mass estimates from equilibrium assumptions can be biased, and its existence is not a strong challenge to standard cosmology.
  • Extending a resimulated cluster sample to be mass-complete back to z=1 requires only modest additions beyond the existing top-324 set.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If churn is as strong in other cosmologies and volumes, high-redshift protocluster surveys selected by galaxy overdensities may trace a different population than z=0 cluster samples; the overlap could be measured by applying the same rank-tracking to mock light cones.
  • The dropout rate likely depends on the chosen mass definition; re-ranking with a fixed overdensity mass (for example, 200 times the critical density) would show whether the 40% figure is a property of the mass hierarchy or of the particular virial-mass boundary chosen.
  • The churn rate may correlate with environment, because early-forming objects in underdense regions are probably underrepresented in z=0 mass-limited samples; the paper notes but does not test this.
  • A similar rank-churn analysis applied to lower mass thresholds or to the galaxy stellar-mass function could show whether the effect is limited to the extreme top of the hierarchy or is general.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper uses the MultiDark Planck 2 (MDPL2) dark-matter-only simulation to track the 100 most massive haloes at z=0 backwards and forwards in time and asks whether the most massive objects at one redshift remain the most massive at another. Using Rockstar halo catalogues and ConsistentTrees merger trees, the authors measure a large degree of 'churn': only ~40% of the top-100 haloes at z=0 are still in the top 100 at z=1. They report that the most massive haloes have experienced more major mergers and are more likely to be dynamically unrelaxed, and they use these results to motivate an extended, mass-complete cluster sample of 268 regions for the Three Hundred Project. They conclude that fixed-epoch mass-selected samples are biased and that the common assumption of a one-to-one correspondence between the most massive clusters across redshifts is incorrect.

Significance. The qualitative conclusion—that rank-order stability of the most massive haloes is poor, especially across z ~ 1—is likely robust and practically relevant for cluster cosmology and for the design of resimulation projects such as The Three Hundred. The paper makes good use of a large public simulation and provides a direct, falsifiable measurement. However, the quantitative headline (the 40% survival fraction) and the proposed 268-cluster superset depend on the adopted halo mass definition (Rockstar Mvir with the Bryan & Norman 1998 overdensity), which itself evolves with redshift. The paper also quotes no uncertainties on the survival fractions, and the (1+z)^-0.5 growth scaling is presented without a derivation or scatter. These are load-bearing issues for the paper's central quantitative claims, though they should be addressable with additional analysis.

major comments (3)
  1. [§2.2, Fig. 1 footnote, §4.3] The headline survival fraction (Fig. 2: only ~40% of the top-100 at z=0 remain in the top 100 at z=1) is computed from ranks based on the Rockstar virial mass Mvir, which uses the redshift-dependent Bryan & Norman (1998) overdensity. As the Fig. 1 footnote itself notes, 'the mass definition evolves with redshift.' Near the steep top-100 boundary, rank membership can therefore change simply because the halo aperture changes with redshift, and §4.3 notes that halo masses can be overestimated by ~50% at merger peaks. The paper provides no test using a fixed-overdensity definition such as M200c or M200m. Please re-run the survival analysis with such a definition and report the effect on the 40% value and on the 268-cluster superset in §4.2.
  2. [§3, Fig. 2] The survival fractions are quoted without any error estimate. The analysis uses a single simulation volume, and the top-100 sample is small; the z=1 survival fraction of ~40% is a single number with no uncertainty. Please provide at least a jackknife or bootstrap over simulation octants, or a Poisson/order-statistics estimate, and state whether the differences between N=100 and N=324 are significant. The claim that 'there is little difference in the dropout rate' (p.5) is currently a visual impression.
  3. [§3, Fig. 3] The text states that the mean mass of a fixed top-100 sample grows faster than the evolving sample by a factor of (1+z)^-0.5 prior to selection, and compares this with the Kaiser (1986) scaling in Eq. (1). No derivation, fit procedure, uncertainty, or redshift range of validity is given; this appears to be an empirical fit to the simulation. Please specify how the exponent was obtained, show its scatter, and avoid implying that it follows from the Kaiser model unless a derivation is provided.
minor comments (5)
  1. [Fig. 4 caption / §3 text] The caption and the text describe the green curves inconsistently. The caption defines 'green dashed line: the minimum mass of the top 100 haloes at each time' while the text says 'green dashed lines show the mass evolution of the smallest of any of the objects that form the original sample.' Please align the descriptions and mark the curves consistently.
  2. [§3.1, Fig. 6] The text in §3.1 says 'those without are shown as dotted lines,' while the Fig. 6 caption says 'Dashed curves indicate clusters without a major merger.' Please standardize the line-style terminology.
  3. [§3.1] The dynamical state is referenced as 'equation one taken from Haggar et al. (2024)' without reproducing the definition. Since the binning into relaxed/unrelaxed sets in Fig. 7 depends on this quantity, please give the equation or a precise description.
  4. [§2.2] The term 'froth' region is used without a definition. Clarify that it refers to the mass range near the top-100 boundary where a single major merger can change rank order.
  5. [§4.2, footnote 2] The construction of the 268-cluster supersets relies on merger-tree identifications and a 2 h^-1 Mpc separation cut. A sentence noting the sensitivity of the final count to these choices would be useful for reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central churn measurement is a direct simulation rank-order statistic, with self-citations limited to auxiliary tools.

full rationale

The paper's central claim—that only ~40% of the top-100 haloes at z=0 are still in the top 100 at z=1—is a direct rank-order measurement from the MDPL2 simulation, not a derivation from a model. The top-100 sample is defined by sorting Rockstar virial masses at each snapshot, and the survival fraction is read off from merger-tree progenitor links. No fitted parameter is renamed as a prediction. The only fitted-looking curve, the (1+z)^-0.5 growth scaling in Fig. 3, is presented as an empirical characterization of the measured fixed-sample mass evolution ('For mean mass, the rates of growth of the fixed samples are more rapid ... by a factor of (1+z)^-0.5'), not as a first-principles prediction. Self-citations appear for auxiliary tools: Onions et al. (2012) and Srisawat et al. (2013) for reliability of Rockstar/ConsistentTrees, Contreras-Santos et al. (2022) for the major-merger identification used in Fig. 6, and Haggar et al. (2024) for the dynamical-state measure used in Fig. 7. None of these is used to construct the central churn statistic; they support secondary interpretation. The Fig. 1 footnote acknowledges that the Rockstar/Bryan & Norman mass definition evolves with redshift. This is an important robustness caveat—top-100 membership could shift under a fixed-overdensity definition—but it is a sensitivity limitation, not circularity: the paper does not define the churn result in terms of that mass definition, and the measurement remains a legitimate simulation-based statistic under the stated definition. No step in the paper reduces by construction to its own input, so no circularity is found.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central measurement is an analysis of an existing simulation; the load-bearing inputs are the simulation itself, the halo finder and merger tree, the mass definition, and the choice of N=100. No new physical entities are introduced.

free parameters (2)
  • Sample size N=100
    The top-100 threshold is motivated by the Sheth-Tormen mass function giving ~100 haloes within a factor of 3 of the most massive, but is ultimately arbitrary; the central results depend on this choice (Section 2.2).
  • (1+z)^-0.5 growth exponent = -0.5
    The relative mass growth rate of fixed vs evolving samples is measured to follow (1+z)^-0.5; this is an empirical fit to the simulation, not a derived quantity (Section 3).
assumptions (4)
  • domain assumption MDPL2 simulation and its halo catalogues accurately represent halo growth and masses
    The paper relies on the publicly available MDPL2 N-body simulation and Rockstar/ConsistentTrees catalogues without independent validation in this work beyond citing previous tests (Section 2.1).
  • domain assumption Most massive progenitor defines the main branch
    Tracing halo histories uses the most massive progenitor in the merger tree; if this choice misidentifies the true main branch, survival fractions could change (Section 2.1).
  • domain assumption Bryan & Norman (1998) virial mass is the appropriate ranking mass
    The mass definition evolves with redshift and affects which haloes are in the top 100 at each epoch (Section 2.2 footnote).
  • domain assumption The major merger definition from Contreras-Santos et al. (2022) is adopted
    The study uses a fractional mass growth technique to identify major mergers without re-deriving or validating it in this paper (Section 3.1).

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Cite this review

Pith. "Pith review of The life and times of dark matter haloes: what will I be when I grow up?." pith.science (2026). https://pith.science/paper/XGTTFOZD

@misc{pith2026250818778,
  author       = {Pith},
  title        = {Pith review of: The life and times of dark matter haloes: what will I be when I grow up?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGTTFOZD}},
  note         = {Machine review of arXiv:2508.18778}
}
abstract

Are the most massive objects in the Universe today the direct descendants of the most massive objects at higher redshift? We address this question by tracing the evolutionary histories of haloes in the MultiDark Planck2 simulation. By following the 100 most massive halos at $z = 0$ across cosmic time, we find that only 40\% of them were among the largest 100 halos at $z = 1$. This suggests that many of today's most massive clusters were not the most dominant structures at earlier times, while some of the most massive objects at high redshift do not remain in the top mass ranks at later epochs. The hierarchical nature of structure formation predicts that, on average, massive haloes grow over time, with their abundance in comoving space decreasing rapidly at higher redshifts. However, individual clusters exhibit diverse evolutionary paths: some undergo early rapid growth, while others experience steady accretion or significant merger-driven mass changes. A key assumption in self-similar models of cluster evolution is that the most massive objects maintain their rank in the mass hierarchy across cosmic time. In this work, we test this assumption by constructing a mass-complete sample of haloes within the $(1 h^{-1}{\rm Gpc})^3$ volume of MultiDark and analysing when clusters enter and exit a high-mass-selected sample. Our results demonstrate that cluster selections must be carefully constructed, as significant numbers of objects can enter and leave the sample over time. These findings have important implications for observational cluster selection and comparisons between simulations and surveys, especially at high redshift.

Figures

Figures reproduced from arXiv: 2508.18778 by the authors.

Figure 1
Figure 1. The cumulative number of halos expected within a volume of side 1Gpc/ℎ as a multiple of the mass of the largest halo expected as a function of redshift. The points indicate the measured mass ratio for haloes found within the MDPL2 volume at 𝑧 = 0. The curves indicate the analytic result found by integrating under the Sheth-Tormen mass function scaled to the MDPL2 volume (various redshifts as indicated). At low redsh… view at source ↗
Figure 3
Figure 3. Mass evolution of the top 100 clusters at different epochs from 𝑧 = 2 forwards as a fraction of the mass of the largest 100 haloes at the indicated redshift. The blue, orange, green, and red lines show the fractional mass of a fixed sample of the largest 100 haloes selected at 𝑧 = 0, 0.5, 1, 2 respectively as they evolve over time, relative to the mass of the top 100 clusters selected at any given redshift 𝑧. Solid … view at source ↗
Figure 4
Figure 4. The mass evolution of various quantities. The left panel is for samples selected at 𝑧 = 0 tracked back to 𝑧 = 2. The right panel is the reverse: i.e. samples selected at 𝑧 = 2 tracked to 𝑧 = 0. The various samples are: blue solid line: the most massive object at the indicated time. Blue dashed line: maximum mass of any member in the original sample at this time. When this differs from the blue line, none of the orig… view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: Mass at 𝑧 = 0 compared to mass at 𝑧 = 1 for the largest 100 haloes. Smaller blue filled circles indicate objects within the largest 100 at 𝑧 = 0 and their progenitor mass at 𝑧 = 1. Larger open orange circles indicate the objects found within the top 100 objects at 𝑧 = …
Figure 6
Figure 6. Figure 6: The mass growth of haloes. Left panel (a): the largest 30 haloes in the volume at 𝑧 = 0. Clusters undergoing a major merger since 𝑧 = 1 (shown via the dotted vertical line) are indicated as solid curves with the start and finish time of the merger indicated via the fil…
Figure 7
Figure 7. Figure 7: Splitting the 100 clusters in the 𝑧 = 0 sample into three roughly equal sized bins according to dynamical state (taken from Haggar et al. (2024)), the fraction of each of these groups that remain in the top 100 sample at earlier times. Most of the unrelaxed clusters en…

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.