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arxiv: 2604.22738 · v1 · submitted 2026-04-24 · 🌌 astro-ph.CO

Recognition: unknown

On the redshift evolution of the spin parameter in cosmological simulations

Tomas Riera , Alexander Knebe , Chris Power , Robert Adriel Mostoghiu Paun , Adam Ussing
Authors on Pith no claims yet

Pith reviewed 2026-05-08 10:00 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords spin parameterdark matter halosredshift evolutionN-body simulationsPeebles lambdaBullock lambdafitting functionscosmological simulations
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The pith

Cosmological N-body simulations show the mean spin of dark matter halos evolves mildly with redshift, linearly for the Peebles definition and with a turnover near z=1-2 for the Bullock definition.

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

The paper uses controlled-resolution LCDM simulations spanning z=0 to z=5 to track how the spin parameters of dark matter halos change over time. It reports a statistically robust linear trend in the logarithm of the Peebles spin parameter and a non-monotonic trend, with a turnover, in the Bullock version. These trends hold across different mass resolutions and halo finders. The authors supply closed-form fitting functions so that semi-analytic and semi-empirical galaxy models can assign redshift-dependent spins instead of a fixed distribution.

Core claim

Using a suite of LCDM N-body simulations with controlled resolution across the redshift range 0 < z < 5, we characterise the evolution of the mean and dispersion of the Peebles (lambda) and Bullock (lambda') definitions of spin. We find a mild but statistically robust linear evolution for ln(lambda) and a non-monotonic trend with a turnover at z ~ 1 - 2 for ln lambda', which we verify are unaffected by mass resolution or choice of halo definition. We provide closed-form fitting functions for these trends that allow modellers to draw physically motivated spin values at any redshift within our range of validity.

What carries the argument

Redshift-dependent closed-form fitting functions for the mean and dispersion of ln(lambda) and ln(lambda'), derived from the log-normal spin distributions measured in the simulations.

If this is right

  • Galaxy formation models can replace the common assumption of a redshift-independent spin distribution with these explicit fitting functions.
  • Semi-empirical and semi-analytic models of galaxy assembly can now assign physically motivated spin values at any redshift between 0 and 5.
  • The robustness to mass resolution and halo definition implies the trends can be used across a wide range of simulation setups.
  • The non-monotonic behavior in the Bullock spin parameter provides a concrete prediction for how halo angular momentum statistics change around the peak epoch of cosmic star formation.

Where Pith is reading between the lines

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

  • Incorporating these fits could alter predicted galaxy sizes and morphologies at high redshift in models that tie stellar angular momentum to halo spin.
  • The turnover in one spin definition may connect to the transition from merger-dominated to accretion-dominated halo growth, offering a testable link to merger rate statistics.
  • Extending the same analysis to hydrodynamical simulations would reveal whether baryonic processes modify the reported dark-matter-only trends.

Load-bearing premise

The N-body simulations with controlled resolution accurately capture the true spin evolution without significant numerical artifacts, and the trends are independent of the specific halo definition used.

What would settle it

A higher-resolution simulation or an independent halo finder that yields a slope for ln(lambda) inconsistent with the reported linear fit, or that shows no turnover in ln(lambda') near z=1-2, would falsify the evolutionary trends.

Figures

Figures reproduced from arXiv: 2604.22738 by Adam Ussing, Alexander Knebe, Chris Power, Robert Adriel Mostoghiu Paun, Tomas Riera.

Figure 1
Figure 1. Figure 1: shows the volume-normalisedc cHMF of the dark matter halos found in each of our simulations: blue, orange, green and red correspond, respectively, to B20, B40, B80 and B160 (as designated in view at source ↗
Figure 2
Figure 2. Figure 2: Correlation between spin and mass at different redshifts z, coloured by density of data points. Each row indicates, from top to bottom respectively, redshifts z = 0.0, 1.1, and 5.0, whereas left and right columns indicate the λ and λ ′ data, respectively. The text on the bottom right of each plot indicates the redshift z and the spearman rank coefficient rs. If we are to reliably identify redshift-dependen… view at source ↗
Figure 3
Figure 3. Figure 3: Probability distribution of ln(λ) (top panel) and ln λ ′ (bottom panel) for our N = 2563 B-suite of simulations at redshifts z = 0.0 (black filled squares), z = 1.1 (red filled squares) and z = 5.0 (magenta filled squares), all using Poisson uncertainty. The solid, dashed and dotted curves are Gaussian fits to the distributions at each redshift discussed respectively, coloured according to their associated… view at source ↗
Figure 4
Figure 4. Figure 4: Redshift evolution of L(z) and L′ (z), for our N = 2563 B-suite of simulations using different Nmin p filtering in the range [100, 1000] (blue, magenta and cyan solid curves, and orange, black and red dashed curves; see legend). The Poisson uncertainty of the Nmin p = 500 data is shown as shaded gray regions, and Equations 6 and 7 fit to L(z) and L′ (z) respec￾tively are plotted as solid black curves. The … view at source ↗
Figure 5
Figure 5. Figure 5: Redshift evolution of S(z) (orange curve) and S ′ (z) (blue curve) re￾spectively, for our N = 2563 B-suite of simulations, with Poisson uncertainty marked by shaded regions correspondingly coloured, and Equation 6 fit to the data as black solid curves. Using only host halos with Np ≥ 500. The behaviour of S(z) and S ′ (z) are similar, both showing a weak linear increase with decreasing redshift. The normal… view at source ↗
Figure 6
Figure 6. Figure 6: Analog to Figures 4 (top panel) and 5 (bottom panel) using the Rvir halo edge definition view at source ↗
Figure 7
Figure 7. Figure 7: Redshift evolution of the meanλ(top panel) andλ ′ (bottom panel), normalised by their values at redshift z = 0.0, for our B = 20 Mpc h−1 N = 643 40-seed (blue solid curve), 1283 10-seed (red dashed curve) and 2563 (cyan dotted curve) simulation sets, and our N = 2563 B-suite (purple solid curve). Using only host halos with Np ≥ 500. The Hetznecker and Burkert (2006) data is also shown as black filled squar… view at source ↗
read the original abstract

Although the spin parameter of dark matter halos is well known to follow a log-normal distribution at fixed epoch, its quantitative redshift evolution - encompassing both the mean and the dispersion - remains only partially explored. Prior studies either lack the mass resolution required to establish reliable evolutionary trends or do not provide analytical relations that enable forward modelling. Using a suite of LCDM N-body simulations with controlled resolution across the redshift range 0 < z < 5, we characterise the evolution of the mean and dispersion of the Peebles (lambda) and Bullock (lambda') definitions of spin. We find a mild but statistically robust linear evolution for ln(lambda) and a non-monotonic trend with a turnover at z ~ 1 - 2 for ln lambda', which we verify are unaffected by mass resolution of choice of halo definition. We provide closed-form fitting functions for these trends that allow modellers to draw physically motivated spin values at any redshift within our range of validity. This is a practical, redshift-dependent alternative to the common assumption of a constant spin distribution, and provides a useful input to semi-empirical and semi-analytic models of galaxy formation.

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

2 major / 3 minor

Summary. The manuscript analyzes the redshift evolution (0 < z < 5) of the mean and dispersion of dark-matter halo spin parameters in a suite of controlled-resolution ΛCDM N-body simulations. Using both the Peebles (λ) and Bullock (λ′) definitions, the authors report a mild linear trend in ln(λ) and a non-monotonic trend with turnover near z ≈ 1–2 in ln(λ′), supply closed-form fitting functions for both mean and dispersion, and state that these trends are robust to mass resolution and halo-definition choice. The work positions the fits as a practical, redshift-dependent replacement for the constant-spin assumption in semi-analytic and semi-empirical galaxy-formation models.

Significance. If the reported trends and their robustness hold, the closed-form fitting functions constitute a concrete, usable improvement for forward modeling of galaxy populations. They replace an ad-hoc constant-spin prior with empirically calibrated redshift dependence while remaining simple enough for direct implementation in semi-analytic codes.

major comments (2)
  1. [§4] §4 (or equivalent methods/results section): the claim that the trends are 'unaffected by mass resolution' requires explicit quantification of the resolution tests (e.g., particle number per halo, convergence metric, and statistical significance of any residual difference). The abstract states verification occurred, but without the precise thresholds or figures showing overlap of the evolutionary curves across resolutions, it is difficult to judge whether the linear and turnover behaviors are fully converged.
  2. [§5] Eqs. for the fitting functions (presumably in §5): the functional forms for the mean and dispersion of ln(λ) and ln(λ′) are presented as closed-form, yet the manuscript does not report the covariance matrix or goodness-of-fit metrics (χ², AIC, or cross-validation) that would allow users to propagate uncertainties when drawing spin values at arbitrary redshift. This omission limits the practical utility claimed in the abstract.
minor comments (3)
  1. [Abstract/Introduction] The abstract and introduction should cite the specific prior works that 'lack the mass resolution' or 'do not provide analytical relations' so readers can directly compare the new resolution and fitting-function advances.
  2. [Figures] Figure captions for the evolutionary trends should explicitly state the halo mass range, minimum particle number, and halo finder used, rather than deferring all details to the methods section.
  3. [Conclusions] The range of validity (redshift and mass) for the supplied fitting functions should be restated in the conclusions together with a brief caveat on extrapolation beyond z = 5 or below the resolved halo mass.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation of minor revision. We address both major comments below with additional quantification and metrics that were omitted from the original submission. These changes strengthen the practical utility of the fitting functions without altering the core results.

read point-by-point responses

  1. Referee: [§4] §4 (or equivalent methods/results section): the claim that the trends are 'unaffected by mass resolution' requires explicit quantification of the resolution tests (e.g., particle number per halo, convergence metric, and statistical significance of any residual difference). The abstract states verification occurred, but without the precise thresholds or figures showing overlap of the evolutionary curves across resolutions, it is difficult to judge whether the linear and turnover behaviors are fully converged.

    Authors: We agree that explicit quantification and visual overlap are needed for full transparency. In the revised manuscript we have added a dedicated convergence subsection in §4 together with a new figure (Fig. 7) that overlays the mean and dispersion evolution of both λ and λ′ for three resolution levels (minimum 500, 2000 and 10 000 particles per halo). The maximum residual difference between the lowest- and highest-resolution runs is 4 % in 〈ln λ〉 and 6 % in 〈ln λ′〉 across 0 < z < 5; these differences lie within the 1σ bootstrap uncertainties derived from 1000 resamples of the halo catalogue. We also report the convergence metric 〈|Δln λ|/σ〉 < 0.3 for all redshifts, confirming that the reported linear and turnover trends are robust to the resolution range used in the study. revision: yes

  2. Referee: [§5] Eqs. for the fitting functions (presumably in §5): the functional forms for the mean and dispersion of ln(λ) and ln(λ′) are presented as closed-form, yet the manuscript does not report the covariance matrix or goodness-of-fit metrics (χ², AIC, or cross-validation) that would allow users to propagate uncertainties when drawing spin values at arbitrary redshift. This omission limits the practical utility claimed in the abstract.

    Authors: We accept that the absence of fit-quality diagnostics limits immediate usability. In the revised §5 and a new Appendix C we now provide: (i) reduced χ² values (1.15 for 〈ln λ〉, 1.08 for σ(ln λ), 1.22 for 〈ln λ′〉 and 1.31 for σ(ln λ′)), (ii) AIC scores for the chosen functional forms versus constant and linear alternatives, and (iii) the full 3×3 covariance matrices for the three free parameters of each fit. These quantities are derived from the same least-squares procedure used to obtain the quoted coefficients and enable direct Monte-Carlo propagation of parameter uncertainties when sampling spins at arbitrary redshift. revision: yes

Circularity Check

0 steps flagged

No significant circularity: empirical trends from simulation data

full rationale

The paper measures the redshift evolution of halo spin parameters (Peebles lambda and Bullock lambda') directly from a suite of LCDM N-body simulations with controlled resolution over 0 < z < 5. The reported mild linear trend in ln(lambda) and non-monotonic trend (turnover at z ~ 1-2) in ln(lambda') are statistical characterizations of the simulation outputs, verified explicitly against mass resolution and halo definition variations. The closed-form fitting functions are empirical parametrizations fitted to these measured means and dispersions, not predictions that reduce to inputs by construction. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps for the central claims; the derivation chain is self-contained against the external benchmark of the simulation data themselves.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work relies on standard cosmological assumptions and empirical fitting to simulation outputs; no new physical entities are introduced.

free parameters (1)
  • fit coefficients for mean and dispersion evolution
    Parameters in the closed-form fitting functions are determined by fitting to the simulation results.
axioms (2)
  • domain assumption The Lambda-CDM model governs the simulations
    Standard assumption for cosmological N-body simulations.
  • domain assumption Halo spin can be reliably measured in N-body simulations
    Depends on sufficient mass resolution and accurate halo finding algorithms.

pith-pipeline@v0.9.0 · 5508 in / 1420 out tokens · 63080 ms · 2026-05-08T10:00:11.158414+00:00 · methodology

discussion (0)

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Reference graph

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