GUREFT: Ultra High-z Dark Matter Suite

• GUREFT is a dark matter simulation suite focused on characterizing halo demographics and merger histories in the ultra-high-redshift (z>10) universe.
• It uses four 1024³-particle simulations with extra-fine temporal sampling to accurately resolve rapid halo growth and short-lived progenitors.
• The suite calibrates halo mass functions and internal structure metrics, challenging low-z extrapolations and enhancing semi-analytic and abundance matching models.

The GUREFT dark-matter-only cosmological simulation suite—“Gadget at Ultrahigh Redshift with Extra-Fine Timesteps”—is a set of simulations designed to characterise dark matter halo demographics, structural properties, and assembly histories in the ultra-high-redshift universe, especially across the $z>10$ regime newly foregrounded by JWST (Yung et al., 2023). Its central purpose is to provide merger trees and halo statistics suitable for applications such as semi-analytic models (SAMs), sub-halo abundance matching (SHAM), and decorated halo occupation distribution models, while resolving the rapid halo growth and short-lived progenitor population that become prominent at early cosmic times. The suite comprises four $1024^3$-particle simulations with box sizes of $5$, $15$, $35$, and $90\ \mathrm{Mpc}\ h^{-1}$, with outputs densely sampled from $z\simeq40$ to $z=6$ in order to recover halo growth and merger histories at temporal resolution tied to the halo dynamical time (Yung et al., 2023).

1. Scientific scope and motivation

GUREFT is motivated by the need to model halo populations and merger histories in the earliest epochs of cosmic history, where dark matter halo assembly is sufficiently rapid that conventional temporal sampling can miss short-lived progenitors or introduce spurious links across widely separated outputs (Yung et al., 2023). The suite is therefore explicitly aimed at the “ultra-z” regime, with emphasis on halo mass functions from $z\sim20$ to $z=6$, halo structural properties such as concentration and spin, and assembly metrics including mass growth and merger rates.

Within this framing, merger trees are treated as fundamental inputs for several modelling pipelines. The suite is intended to support SAMs, SHAM, and decorated HOD analyses by supplying halo catalogues and temporally resolved progenitor–descendant relations in a regime where older fitting functions and analytic approximations can fail substantially. A common misconception in this area is that low-redshift halo fits can be extrapolated straightforwardly into the $1024^3$0 domain; GUREFT directly tests that assumption and finds substantial discrepancies for several standard forms (Yung et al., 2023).

2. Numerical design of the suite

All four simulations assume the Planck-compatible cosmological parameters

$1024^3$1

Each box contains $1024^3$2 dark-matter particles. In $1024^3$3-scaled masses and lengths, the suite spans particle masses from $1024^3$4 to $1024^3$5 and Plummer softenings from $1024^3$6 to $1024^3$7 (Yung et al., 2023).

Box	$1024^3$8 and $1024^3$9	Snapshots
GUREFT–05 ($5$0)	$5$1; $5$2	171
GUREFT–15 ($5$3)	$5$4; $5$5	171
GUREFT–35 ($5$6)	$5$7; $5$8	171
GUREFT–90 ($5$9)	$15$0; $15$1	171

Snapshots are stored at 171 epochs uniformly spaced at one-tenth of the halo dynamical time,

$15$2

from $15$3 down to $15$4 (Yung et al., 2023). This “extra-fine” temporal sampling is one of the defining features of the suite. It is specifically justified by the statement that, at ultra-high redshift, halo assembly is extremely rapid and therefore requires $15$5 to reconstruct merger histories without missing short-lived progenitors or spuriously linking halos across widely separated epochs.

The box configuration is strategically chosen to cover a dynamic range relevant to emerging halo populations in the early universe. A plausible implication is that the four-box design is meant to trade off mass resolution and cosmological volume so that halo demographics can be measured over a broad mass interval while preserving temporal resolution.

3. Halo definition, resolution threshold, and merger trees

Halo identification is performed with the 6D phase-space finder ROCKSTAR using default settings (Yung et al., 2023). Halo mass is defined through the Bryan and Norman (1998) spherical-overdensity virial mass,

$15$6

with

$15$7

Only halos with at least $15$8 particles are treated as resolved. This resolution criterion sets the effective lower limit of halo measurements in each box and underlies the suite’s reported ability to trace the halo mass function down to $15$9.

Merger trees are constructed with the consistent-trees algorithm of Behroozi et al. (2013c), which identifies descendant–progenitor links by matching particle IDs across multiple snapshots, uses a merit function that maximizes shared particles with weighting toward inner, bound particles, and enforces gravitational consistency through smooth mass and velocity evolution (Yung et al., 2023). The stated consequence is a strong reduction in spurious branches and in “stranded” halos lacking a descendant or progenitor.

In the context of GUREFT, this pipeline is not merely a catalogue-building step but part of the scientific design. The dense output cadence and the tree-construction algorithm are jointly presented as necessary for robust measurements of halo assembly at early times, where halo growth is both fast and episodic.

4. Halo mass function and its ultra-high-redshift calibration

The differential comoving halo mass function is written as

$35$0

where $35$1 is today’s mean matter density and $35$2 with $35$3 the linear growth factor (Yung et al., 2023). The multiplicity function is parameterized as

$35$4

For the ultra-high-$35$5 calibration, each of the four parameters is allowed to vary quadratically with redshift,

$35$6

Fitting GUREFT plus MultiDark halos over $35$7 yields

$35$8

$35$9

$90\ \mathrm{Mpc}\ h^{-1}$0

$90\ \mathrm{Mpc}\ h^{-1}$1

in simulation units of $90\ \mathrm{Mpc}\ h^{-1}$2 and $90\ \mathrm{Mpc}\ h^{-1}$3 (Yung et al., 2023). The full tabulations are referred to Appendix A.

A major result is that, at $90\ \mathrm{Mpc}\ h^{-1}$4, commonly used Press–Schechter, Sheth–Tormen, Tinker (2008), and Reed (2007) forms can differ from the measured GUREFT halo mass function by factors of two to ten (Yung et al., 2023). This is one of the suite’s most consequential findings because it directly challenges the routine extrapolation of lower-redshift analytic or semi-empirical abundance fits into the JWST era. The paper therefore positions direct ultra-high-redshift calibration, rather than extrapolation, as necessary for robust halo demographics in this regime.

5. Structural properties of ultra-$90\ \mathrm{Mpc}\ h^{-1}$5 halos

GUREFT reports updated measurements for maximum circular velocity, concentration, and spin (Yung et al., 2023). For $90\ \mathrm{Mpc}\ h^{-1}$6, the $90\ \mathrm{Mpc}\ h^{-1}$7–$90\ \mathrm{Mpc}\ h^{-1}$8 relation is fitted by a redshift-dependent power law in $90\ \mathrm{Mpc}\ h^{-1}$9, with

$z\simeq40$0

$z\simeq40$1

and $z\simeq40$2. This provides a compact description of how halo internal velocity structure scales with mass and cosmic time in the ultra-high-redshift regime.

For concentration, the suite measures NFW concentrations $z\simeq40$3 up to $z\simeq40$4 and finds a flattening and weak rise of $z\simeq40$5 at fixed mass toward earlier times, reversing the decline seen at $z\simeq40$6 (Yung et al., 2023). When concentration is expressed as a function of peak height, $z\simeq40$7, the resulting $z\simeq40$8–$z\simeq40$9 relation shows negligible evolution over $z=6$0, which the paper interprets as self-similarity. No simple closed-form $z=6$1 fit is provided, but the Diemer and Kravtsov (2015) universal model is reported to reproduce the behaviour.

The suite computes both $z=6$2 and $z=6$3 spin definitions; for the latter,

$z=6$4

The $z=6$5 distribution is well fitted by a Schechter-like form,

$z=6$6

with parameters evolving mildly with redshift (Yung et al., 2023). At $z=6$7, the reported best-fit values are $z=6$8, $z=6$9, and $z\sim20$0. Fits for $z\sim20$1 and for other redshifts are tabulated in Appendix C. An explicit caution is that a simple log-normal does not reproduce the low-$z\sim20$2 tail, making the Schechter-like representation materially more accurate for this dataset.

6. Assembly histories, comparisons with older prescriptions, and downstream uses

GUREFT measures halo assembly through specific mass-accretion rates, main-progenitor growth histories, and merger activity (Yung et al., 2023). Averaged over a dynamical time, the specific mass-accretion rate $z\sim20$3 continues the low-$z\sim20$4 trend of rising with redshift and is fitted for $z\sim20$5 by a redshift-dependent power law in $z\sim20$6 with

$z\sim20$7

$z\sim20$8

This result places ultra-high-redshift halo growth on the same general evolutionary trajectory seen at lower redshift, but with quantitatively updated coefficients calibrated from the simulation suite itself.

For median mass-growth histories, tracing the main progenitor back from $z\sim20$9 shows that halo masses grow more slowly than simple exponential models such as Dekel et al. (2013) predict at $z=6$0 (Yung et al., 2023). No simple closed form for $z=6$1 is judged adequate; the paper instead presents the full mass-accretion histories in figure form. This is an important qualification: it indicates that compact analytic summaries may be insufficient for some ultra-high-redshift applications even when broad trends are known.

The suite also enables robust measurements of major mergers, defined as mass ratio $z=6$2, and minor merger rates up to $z=6$3 using the consistent-trees outputs, although a detailed fit for $z=6$4 is deferred to a companion study by Nguyen et al. (2023) (Yung et al., 2023). The deferment of that fit is itself notable, because it marks a boundary between what is fully parameterized in the current release and what remains to be systematized.

In comparison with older prescriptions, GUREFT reports that widely used low-$z=6$5 concentration and mass-accretion-history fits underpredict concentrations and mass-growth rates at ultra-high redshift, alongside the factor-of-two-to-ten halo-mass-function discrepancies already noted. The astrophysical significance identified in the paper is threefold. For SAMs, high-temporal-resolution merger trees and halo mass functions at $z=6$6 avoid biases associated with extrapolated Extended-Press-Schechter trees. For abundance matching, accurate $z=6$7 up to $z=6$8 links observed UV luminosity functions and stellar mass functions to halo masses without ad hoc extrapolations. For early galaxy formation, higher concentrations and mass-accretion rates at $z=6$9 imply deeper potential wells and faster gas infall, affecting star-formation efficiencies, feedback thresholds, and the timing of reionization (Yung et al., 2023).

As a dark-matter-only suite, GUREFT is therefore best understood as a calibrated infrastructure for halo-based modelling rather than as a direct simulation of baryonic galaxy formation. Its planned public products—halo catalogues, merger trees, and the fit-parameter tables in Appendices A–C—are intended to support subsequent high-redshift galaxy and reionization studies.