Sherwood-Relics Hydrodynamical Simulation Suite

• Sherwood-Relics is a suite of over 200 cosmological hydrodynamical simulations designed to capture the IGM's evolution during and after hydrogen reionization.
• It extends the original Sherwood programme by expanding parameter space, incorporating hybrid radiative transfer, and using a state-of-the-art P-GADGET-3 framework.
• The suite enables precise investigations into Lyman-α forest statistics, reionization timing, and dark matter properties, serving as a calibrated laboratory for high-redshift IGM physics.

The Sherwood-Relics hydrodynamical simulation suite is a large suite of cosmological simulations designed to model the low-density intergalactic medium during and after hydrogen reionization, with particular emphasis on the high-redshift Lyman-$\alpha$ forest, patchy reionization, pressure smoothing, and related inference problems in dark-matter and IGM physics. It generalizes the earlier Sherwood programme by retaining the P-GADGET-3 numerical backbone while extending the parameter space in reionization history, thermal history, cosmology, and warm dark matter, and by adding a lightweight hybrid radiative-transfer treatment that imprints spatially varying ionization and heating histories on the gas (Puchwein et al., 2022, Bolton et al., 2016).

1. Origins, scope, and relation to the Sherwood programme

Sherwood-Relics was introduced as a suite of over 200 cosmological hydrodynamical simulations aimed at modelling the intergalactic medium during and after the cosmic reionization of hydrogen (Puchwein et al., 2022). Its immediate predecessor, the Sherwood simulation suite, had already established a high-dynamic-range SPH framework for the Lyman-$\alpha$ forest over $2PDFs, flux power spectra, column-density distributions, and line-width statistics (Bolton et al., 2016). Sherwood-Relics preserves that basic strategy while shifting the scientific center of gravity toward the tail end of reionization and the post-reionization thermal “relics” of an inhomogeneous UV radiation field (Puchwein et al., 2022).

In the Sherwood-Relics overview, the principal scientific goals are to model the IGM during and after hydrogen reionization, quantify how patchy reionization imprints large-scale temperature and pressure-smoothing fluctuations, and understand how those fluctuations alter the high-redshift Lyman-$\alpha$ forest and derived constraints on cosmology and dark matter (Puchwein et al., 2022). The suite is therefore not only a generator of synthetic absorption spectra; it is also a calibrated laboratory for reionization timing, IGM thermodynamics, warm-dark-matter free-streaming, and field-level statistical inference. Later work uses the same framework to study the Lyman-limit mean free path at $5$\alpha$ transmission cross-correlation at $4.2\le z \le 7$, machine-learning reconstruction of density fields at $4.1\le z \le 5.0$, and correlated Si III contamination of the 1D Ly$\alpha$ forest power spectrum over $2.2\le z \le 5.0$ (Feron et al., 2024, Conaboy et al., 5 Feb 2025, Artola et al., 2024, Ma et al., 10 Sep 2025).

A defining feature of Sherwood-Relics is that it was designed for direct continuity with Sherwood. The cosmology is generally the same Planck-like flat $\alpha$0CDM model,

$\alpha$1

with primordial helium mass fraction $\alpha$2 or $\alpha$3 in the relevant papers (Bolton et al., 2016, Puchwein et al., 2022). This continuity is central to how Sherwood-Relics is used: homogeneous-UVB Sherwood-style runs provide the baseline grid, and patchy-reionization extensions provide controlled corrections or alternate physical realizations.

2. Numerical architecture and physical prescriptions

Sherwood-Relics hydrodynamical runs are performed with P-GADGET-3, a non-public updated version of GADGET-2, using Tree-PM gravity and entropy- and energy-conserving smoothed particle hydrodynamics (Puchwein et al., 2022). The thermochemistry is followed with a non-equilibrium ionization and cooling solver for primordial H/He, with rate coefficients including Case A recombination from Verner & Ferland (1996), He II dielectronic recombination from Aldrovandi & Pequignot (1973), collisional excitation from Cen (1992), collisional ionization from Voronov (1997), and free–free cooling from Theuns et al. (1998), integrated with CVODE (Puchwein et al., 2022). In later high-resolution metal-line work, the same customized P-Gadget-3 backbone is described as including SPH hydrodynamics and additional non-equilibrium thermo-chemistry (Ma et al., 10 Sep 2025).

Two UV-background modes are used. In homogeneous runs, the radiation field is spatially uniform but time dependent, based on Puchwein et al. (2019), with variants generated by rescaling the photoheating rates and shifting the effective redshift of reionization (Puchwein et al., 2022). In hybrid patchy runs, the H I photoionization rate becomes a spatial field, $\alpha$4, derived from radiative-transfer post-processing and then applied in a second hydrodynamical simulation (Puchwein et al., 2022, Feron et al., 2024). This distinction between homogeneous-UVB and spatially varying UVB runs is foundational across the suite.

Dense gas is treated with the usual Sherwood “quick-Ly$\alpha$5” prescription: gas with overdensity $\alpha$6 and temperature $\alpha$7 is converted into collisionless star particles (Puchwein et al., 2022, Feron et al., 2024, Ma et al., 10 Sep 2025). The rationale, stated repeatedly, is that the target observables arise in low-density gas rather than in the ISM. This expedient removes dense star-forming material cheaply while preserving the forest statistics of interest. In the mean-free-path analysis, the same approximation is noted to remove cold, dense ISM gas and most of the high-column DLA regime, while having only a modest effect on $\alpha$8 at $\alpha$9 (Feron et al., 2024).

The thermal state of the low-density IGM is described by the usual power-law equation of state,

$2

with $2Puchwein et al., 2022, Artola et al., 2024, Ma et al., 10 Sep 2025). Sherwood-Relics is unusual in that it models not only the instantaneous parameters $2Molaro et al., 2023).

3. Simulation inventory, representative runs, and parameter space

The suite spans box sizes

$2

with particle loads from $2Puchwein et al., 2022). Representative high-resolution and large-volume configurations recur across the literature.

Configuration	Size and resolution	Typical role
40-2048	$2$\alpha$0, $\alpha$1	Fiducial high-resolution patchy-reionization and mean-free-path studies
160-2048	$\alpha$2, $\alpha$3, $\alpha$4, $\alpha$5	Large-volume late-reionization and halo-environment statistics
20 $\alpha$6 WDM grid	$\alpha$7, $\alpha$8 dark matter + $\alpha$9 gas	$5

The 40-2048 configuration is the fiducial high-resolution Sherwood-Relics run in the late-reionization mean-free-path paper, with gravitational softening $5Feron et al., 2024). The 160-2048 run uses the same particle number in a $5Feron et al., 2024). In the Si III power-spectrum analysis, a single $5Ma et al., 10 Sep 2025).

Sherwood-Relics varies several classes of physics. The 2022 overview lists CDM and WDM runs with thermal relic masses

$5

reionization histories with completion redshifts $5$\alpha$0–9.1, and photoheating amplitudes obtained by multiplying H I and He I photoheating by factors $\alpha$1, with corresponding He II factors $\alpha$2 (Puchwein et al., 2022). In the WDM machine-learning study, a specific Sherwood-Relics subset consists of the runs L20-ref, L20-ref-hot, and L20-ref-cold, each with the six WDM settings

$\alpha$3

corresponding to CDM and thermal relic masses $\alpha$4, with $\alpha$5 (“ref”), $\alpha$6 (“hot”), and $\alpha$7 (“cold”) (Artola et al., 2024).

For late-reionization studies, the emissivity history is calibrated to observed Ly$\alpha$8 transmission. In Feron et al., the 40-2048 run is calibrated to Bosman et al. (2018) and Eilers et al. (2018), while 160-2048 is calibrated to the XQR-30 compilation of Bosman et al. (2022); the resulting midpoint redshifts are $\alpha$9 and 7.2, with reionization completion $4.2\le z \le 7$0 and 5.3, respectively (Feron et al., 2024). The emissivity at $4.2\le z \le 7$1 settles to $4.2\le z \le 7$2 in both models (Feron et al., 2024).

4. Hybrid radiative transfer, patchy reionization, and data products

The most distinctive Sherwood-Relics development is the hybrid radiation–hydrodynamical scheme. The workflow has three stages: a baseline hydrodynamical simulation with a homogeneous UVB, post-processing radiative transfer with ATON on snapshots separated by $4.2\le z \le 7$3 Myr, and a second hydrodynamical simulation in which gas elements experience the spatially varying $4.2\le z \le 7$4 inferred from ATON (Puchwein et al., 2022). ATON uses a moment-based RT solver with M1 closure and the full speed of light, on a fixed Eulerian grid with the same number of cells as gas particles in the patchy runs, such as $4.2\le z \le 7$5 cells for the $4.2\le z \le 7$6 realizations (Puchwein et al., 2022).

This scheme outputs both $4.2\le z \le 7$7 and a local reionization-redshift field $4.2\le z \le 7$8, defined as the redshift when the local H II fraction first exceeds $4.2\le z \le 7$9 (Puchwein et al., 2022). In the second hydrodynamical run, gas is unilluminated before local reionization, and after front passage it receives local photoionization and photoheating. The adopted monochromatic photon energy is $4.1\le z \le 5.0$0, implying H I heating per ionization

$4.1\le z \le 5.0$1

with $4.1\le z \le 5.0$2, जबकि He II photoheating remains tied to the homogeneous UVB (Puchwein et al., 2022). The hydrodynamical response to this inhomogeneous heating produces spatially varying pressure smoothing and long-lived temperature fluctuations.

Sherwood-Relics also provides a large set of directly usable observables. Across several studies, standard products are 1D Ly$4.1\le z \le 5.0$3 skewers, transmitted-flux spectra, density and temperature fields, halo catalogues, and local reionization-redshift maps (Puchwein et al., 2022, Conaboy et al., 5 Feb 2025). The extraction conventions are consistent enough to support secondary analyses. The WDM density-field paper extracts $4.1\le z \le 5.0$4 random Ly$4.1\le z \le 5.0$5 sightlines per simulation box and redshift, each with $4.1\le z \le 5.0$6 pixels, together with $4.1\le z \le 5.0$7, $4.1\le z \le 5.0$8, and the optical-depth-weighted density field

$4.1\le z \le 5.0$9

which is then used as a supervised-learning target (Artola et al., 2024). The Si III study similarly extracts $\alpha$0 periodic sightlines per redshift snapshot from a $\alpha$1 box, including $\alpha$2, $\alpha$3, $\alpha$4, $\alpha$5, and $\alpha$6, and then computes Ly$\alpha$7 and Si III optical depths in post-processing (Ma et al., 10 Sep 2025).

The suite is explicitly presented as a public community resource. Both the 2022 overview and later application papers note data access through the Nottingham Sherwood-Relics site: $\alpha$8 This institutionalized release model is part of the suite’s role as common infrastructure rather than a one-off simulation campaign (Puchwein et al., 2022, Ma et al., 10 Sep 2025).

5. Principal scientific uses and derived results

Sherwood-Relics has been used to establish several recurrent results about reionization-era IGM structure. The 2022 overview argues that patchy reionization causes large-scale temperature fluctuations that persist well after the end of reionization, that these fluctuations increase the Lyman-$\alpha$9 forest flux power spectrum on large scales, that pressure smoothing varies spatially and correlates with the local reionization redshift, and that photoheated structures can generate flat-bottom or double-dip absorption features in Ly$2.2\le z \le 5.0$0 spectra (Puchwein et al., 2022). In a later power-spectrum analysis, Molaro et al. use Sherwood-Relics to compare homogeneous-UVB and patchy-reionization templates against new data at $2.2\le z \le 5.0$1, finding a $2.2\le z \le 5.0$2 preference for a large-scale enhancement in the 1D Ly$2.2\le z \le 5.0$3 forest power spectrum relative to a spatially uniform UVB, while also emphasizing that the statistical precision is not yet sufficient for a robust detection (Molaro et al., 2023).

In late-reionization mean-free-path studies, the suite is used to measure the free path of H I-ionizing photons through the inhomogeneous IGM. Feron et al. find that Sherwood-Relics models calibrated to a late end to reionization at $2.2\le z \le 5.0$4 are consistent with recent mean-free-path measurements at $2.2\le z \le 5.0$5, while lying $2.2\le z \le 5.0$6 and $2.2\le z \le 5.0$7 above the highest-redshift point at $2.2\le z \le 5.0$8 for the 40-2048 and 160-2048 realizations, respectively (Feron et al., 2024). A central physical conclusion is that, near the end of reionization, the majority of the Lyman-limit opacity is attributable to highly ionized Ly$2.2\le z \le 5.0$9 forest absorbers with

$\alpha$00

rather than only to classically self-shielded neutral systems (Feron et al., 2024). The same work shows a strong environmental dependence: after reionization, overdense gas reduces the mean free path by up to $\alpha$01 around haloes with $\alpha$02, whereas during reionization ionized bubbles can boost the local mean free path around haloes by up to an order of magnitude when the IGM is as much as $\alpha$03 neutral by volume (Feron et al., 2024).

The suite has also been used to connect galaxies to Ly$\alpha$04 transmission. In the galaxy–forest cross-correlation paper, Sherwood-Relics predicts that the shape of the galaxy–Ly$\alpha$05 transmission cross-correlation is sensitive to both the halo mass of the ionizing sources and the volume-averaged neutral fraction $\alpha$06 (Conaboy et al., 5 Feb 2025). The reported excess transmission on scales $\alpha$07 cMpc at $\alpha$08, measured using C IV absorbers as galaxy proxies, is quantitatively reproduced by Sherwood-Relics at $\alpha$09 if the ionizing galaxies occupy haloes with

$\alpha$10

but the same paper argues that this redshift mismatch is equivalent to requiring $\alpha$11 at $\alpha$12, in tension with the observed Ly$\alpha$13 effective-optical-depth distribution (Conaboy et al., 5 Feb 2025). After reionization, the same study shows that relic IGM temperature fluctuations continue to influence the cross-correlation on scales of a few comoving Mpc at $\alpha$14 (Conaboy et al., 5 Feb 2025).

Two later methodological applications illustrate the suite’s broader role as inference infrastructure. First, the WDM density-field study trains a Bayesian neural network on Sherwood-Relics flux–density pairs over $\alpha$15, achieving an in-simulation validation rate in which about $\alpha$16 of pixels lie within the predicted $\alpha$17 interval and $\alpha$18 within $\alpha$19, and then uses reconstructed $\alpha$20 PDFs to derive lower bounds $\alpha$21 and $\alpha$22 at $\alpha$23 from small UVES and GHOST samples (Artola et al., 2024). Second, the Si III contamination paper uses Sherwood-Relics plus Cloudy post-processing to derive an improved analytic model for correlated Si III absorption, showing that distinct Ly$\alpha$24 and Si III line profiles and a variable coeval optical-depth ratio produce additional small-scale power relative to the McDonald (2006) ansatz; the resulting fitting function is validated for $\alpha$25 and $\alpha$26 (Ma et al., 10 Sep 2025).

6. Limitations, tensions, and methodological significance

The suite’s major approximations are explicit in the source papers. The hybrid RT scheme is one-way coupled: ATON sees the density field of the baseline hydrodynamical run rather than the final density field of the patchy simulation, so hydrodynamic back-reaction does not modify the radiative-transfer solution itself (Puchwein et al., 2022). The radiation transport is monochromatic, which simplifies spectral hardening and prevents an inhomogeneous treatment of He II reionization (Puchwein et al., 2022, Feron et al., 2024). The quick-Ly$\alpha$27 conversion suppresses detailed modelling of dense halo gas and the highest-$\alpha$28 population, which is acceptable for the low-density IGM but limits fidelity for the LLS/DLA tail and CGM-scale gas (Feron et al., 2024, Conaboy et al., 5 Feb 2025). In the Si III work, metals are not tracked self-consistently but are painted in post-processing from an observationally motivated abundance model and Cloudy ionization fractions, which is sufficient for low-density IGM Si III but not for a self-consistent CGM enrichment history (Ma et al., 10 Sep 2025).

There are also substantive astrophysical tensions. The mean-free-path paper notes that the emissivity calibration required by the Ly$\alpha$29 forest produces a photon-starved end stage of reionization, and explicitly connects this to the broader “photon budget crisis” discussed in the literature (Feron et al., 2024). The galaxy–Ly$\alpha$30 cross-correlation paper finds a tension between reproducing the Meyer et al. signal with $\alpha$31 at $\alpha$32 and the observed $\alpha$33 distribution, suggesting instead that the host halo masses of high-$\alpha$34 C IV absorbers may have been underestimated (Conaboy et al., 5 Feb 2025). In the WDM-density-field study, the authors note that their Sherwood-Relics training set does not vary $\alpha$35, even though additional runs varying $\alpha$36 exist elsewhere; the paper interprets mild discrepancies in the low-density tail as likely reflecting limitations of the thermal parameter coverage rather than a failure of the WDM modelling (Artola et al., 2024).

Taken together, these properties make Sherwood-Relics a highly structured simulation suite rather than a monolithic single model. It combines a Sherwood-style homogeneous-UVB backbone, an efficient patchy-reionization augmentation, and a parameter grid broad enough to support forward modelling, emulation, and field-level inference. A plausible implication is that its greatest methodological importance lies not in any one flagship result, but in providing a common, internally consistent basis for moving between flux statistics, halo-environment diagnostics, reconstructed density fields, and contamination models within the same high-redshift IGM framework (Puchwein et al., 2022, Artola et al., 2024).