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REVIEW 3 major objections 6 minor 4 cited by

THOR: a GPU-accelerated and MPI-parallel radiative transfer code

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read THOR is a portable MPI+SYCL Monte Carlo radiative transfer code that correctly solves resonant emission-line scattering and runs 10-50x faster on GPUs than previous CPU-only codes.

desk verdict A genuinely useful GPU-portable MCRT code with a well-validated meshless engine, but the uniform-grid path that carries the cosmological showcases is never end-to-end validated and the abstract's speedup range outruns the body's measurements. read the letter →

arxiv 2507.11603 v1 pith:MHMYIMIT submitted 2025-07-15 astro-ph.GA astro-ph.IM

Chris Byrohl , Dylan Nelson This is my paper · ORCID
classification astro-ph.GAastro-ph.IM MSC 85A2565C05 PACS 95.30.Jx
keywords radiativetransferMonteCarloresonantlinescatteringLyman-alphaemissionMgIIdoubletGPUaccelerationMPIparallelizationcosmologicalsimulations
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

THOR is a new Monte Carlo radiative transfer code for resonant emission lines, written in C++ with MPI for distributed memory and a portable accelerator abstraction so one codebase runs on CPUs, GPUs, and APUs. The paper's central claim is that this design makes resonant-line transfer both correct and fast: the code reproduces analytic and published benchmark spectra for Lyman-alpha and the MgII doublet, while running roughly 10-50x faster on accelerators than earlier CPU-only MCRT codes. The claimed payoff is that forward modeling of observations becomes routine across scales, from large parameter scans of idealized shell models and parsec-resolved z=6 galaxies to circumgalactic halos, the cosmic web, and synthetic Lyman-alpha forest spectra. A sympathetic reader would take the paper as establishing a portable, high-throughput engine for resonant line radiative transfer, with speed-ups that make previously expensive calculations accessible on consumer and HPC hardware.

What carries the argument

The load-bearing object is the photon-propagation kernel: a per-photon optical-depth integration with sub-cell stepping, rejection sampling of the parallel atom velocity using the comparison function of Zheng and Miralda-Escudé (accelerated by the scheme of Seon and Kim), core-skipping with $x_{\rm crit}=0.2(a\tau_0)^{1/3}$, a mix of isotropic-dipole phase functions, Voigt-profile approximations selectable at compile time, and optional peel-off contributions fused by spatial and spectral proximity. Around this sits a double-buffer, compute-thread/manage-thread MPI architecture that keeps the accelerator busy, coordinates photon exchange across subdomains, and balances loads. The combined mechanism is what converts the same physics into a portable, high-throughput solver rather than a single-machine serial code.

What would settle it

Run THOR's uniform-grid path on a medium with small-scale density clumps deliberately placed below the grid resolution and compare the emergent spectrum and escape fraction to the same clumpy medium realized in the meshless geometry (or an independent unstructured-grid MCRT code); disagreement beyond Monte Carlo noise would show the gridded path biases resonant transfer.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is a computational architecture: a history-based Monte Carlo radiative transfer engine wrapped in an MPI+SYCL double-buffer design that combines portable accelerator execution with domain decomposition and load balancing. The paper claims this engine solves resonant emission-line transfer correctly, verified against the analytic Neufeld double-peak spectra, the analytic slab escape fractions, the published outflow-sphere spectra, and the published MgII doublet profiles. It also claims the engine is fast, with GPU-to-CPU speed-ups of 5-40x across applications and up to about 50x on newer accelerators, while remaining on par with existing codes on CPUs. The same machinery, with separate dataset, driver, interactor, generator, and output abstractions, handles uniform grids, spherical shells, and infinite slabs, so realistic simulations and toy geometries are treated in one code.

Load-bearing premise

The paper assumes that mapping a simulation's gas onto a regular grid for the realistic runs preserves the small, dense clumps that control resonant scattering and column densities; the direct validation tests use smooth spherical or slab geometries, so a subtle interpolation bias would change the predicted escape fractions and halo maps even if the scattering engine is correct.

Editorial extensions

If this is right

  • Shell-model parameter inference becomes practical: roughly 50,000 RT runs were combined with MCMC to recover the parameters of a nine-dimensional mock spectrum.
  • For a parsec-resolved z=6 galaxy, Lyman-alpha escape fractions of about 4 percent (aperture-restricted roughly 2-3 percent) emerge with strong line-of-sight scatter, and dust suppresses the spectral wings to a few Angstrom.
  • In a z=1-2 Milky Way progenitor, Lyman-alpha and MgII scattering creates extended observable halos, with the MgII doublet peak ratio varying from red-dominant in the center to blue-dominant in the outskirts.
  • In a large cosmological box, Lyman-alpha scattering shifts intrinsic high-surface-brightness emission into a volume-filling low-surface-brightness regime of order $10^{-21}\,\mathrm{erg\,s^{-1}\,cm^{-2}\,arcsec^{-2}}$, relevant for intensity mapping.
  • The raytracing driver produces Lyman-alpha forest spectra and tomographic maps directly from simulation snapshots, and the same machinery scales to a $6144^3$ volume RT calculation.

Reading between the lines

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

  • If the uniform-grid path is accurate, the practical and testable bottleneck becomes the grid-mapping step (SPH-style splatting), which the authors do not directly validate; a native unstructured-mesh dataset would settle whether the mapping preserves the small clumps that control resonant scattering.
  • The composable driver/dataset/interactor design implies that other resonant lines, X-ray lines, or polarization can be added without rewriting the propagation engine; whether that holds depends on whether the doublet treatment generalizes to multiplets with non-resonant channels.
  • The speed-ups suggest that parameter scans and full-volume mock surveys become practical on consumer GPUs, shifting the practical limit of forward modeling from compute time to the fidelity of emission models and input simulations.
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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 / 6 minor

Summary. The paper introduces THOR, a C++/SYCL Monte Carlo radiative transfer code for resonant emission lines (Ly-alpha, MgII) and ray-tracing, with MPI support, domain decomposition, and CPU/GPU/APU backends. The authors validate the meshless spherical/slab physics engine against analytic Neufeld spectra, the slab dust escape fraction, the Faucher-Giguere et al. (2010) outflow spectra, and the Chang & Gronke (2024) MgII doublet. They then present scientific showcases: shell-model MCMC fitting, Ly-alpha escape from a z=6 galaxy, CGM Ly-alpha/MgII halos, cosmic-web emission from TNG50, and Ly-alpha forest absorption spectra, followed by performance benchmarks and scaling tests. The central claim is that THOR is a correct, portable, and highly efficient resonant-line MCRT code with large GPU speedups. The physics engine appears well validated, but the uniform-grid path used for every realistic showcase is not end-to-end validated, and the headline speedup claim is partly extrapolated.

Significance. If the claims hold, THOR would be a valuable community tool: it is one of the first portable, multi-vendor GPU-accelerated resonant-line MCRT codes, with a clean abstraction layer, validated single- and doublet scattering physics, and benchmarks against existing public codes with pinned git revisions. The appendices document the accuracy and performance of the Voigt-profile and u-parallel sampling choices, which is a genuine strength. The scientific showcases demonstrate broad applicability. However, the paper currently overstates the measured speedup range, and more importantly, every realistic showcase relies on a uniform-grid traversal path that is not validated against any analytic or independent numerical result. Since the method paper's credibility rests on both the physics engine and the production data path, this gap must be closed before the showcase results can be considered supported.

major comments (3)
  1. [Section 4 vs. Sections 5.2-5.4] The uniform-grid MCRT path used in all realistic showcases is not end-to-end validated. Section 4 explicitly states that the analytic Neufeld and slab tests use the meshless spherical geometry and that 'we do not explicitly realize a discretized gas distribution.' All Section 4 validations (Neufeld sphere, slab escape fraction, Faucher-Giguere outflow, Chang-Gronke MgII) therefore exercise only the meshless code path. In contrast, the z=6 galaxy (Section 5.2), the CGM Ly-alpha/MgII maps (Section 5.3), the TNG50 cosmic web (Section 5.4), and the weak-scaling benchmark (Section 6.3) all use the uniform-grid dataset, fed by SPH splatting of Voronoi/AREPO data onto 3072^3 grids at ~1-50 pc resolution. The grid-specific operations--cell index traversal, piecewise optical-depth integration across cell faces, sub-cell stepping in the presence of velocity and ionization gradients, and boundary handling--are never compared with an analytic solution or an independent numerical code. A bug or a resolution bias in this path would change the quoted escape fraction f_Ly-alpha_esc = 4.1+1.7-1.8% (Section 5.2) and the CGM surface brightness maps while leaving the validated meshless engine untouched. I request at least one end-to-end test of the uniform-grid path (e.g., a grid-resolved Neufeld sphere or slab at matched resolution, plus a grid-convergence study of the z=6 escape fraction) before the showcase results are presented as validated.
  2. [Abstract, Section 6.2, Section 8] The headline speedup claim '~10-50x' in the abstract and Section 8 is not supported by the measurements reported in the paper. Section 6.2 (upper-right panel of Figure 14) reports measured GPU-to-CPU speedups of 6.5, 13.1, 13.2, and 39.9 for the four applications shown, and Section 6.1 reports a workstation GPU-to-CPU speedup of ~5. The 50x figure is an extrapolation based on a statement that the H200 is 40% faster than the A100 and that a 4xH200 node would therefore reach ~50x; this is not a measurement. The abstract and summary should be revised to state the measured range (roughly 5-40x) and to label any extrapolated values as extrapolations.
  3. [Data Availability] For a code paper whose central claims are about a new software tool, the Data Availability statement that 'The thor code will be publicly released in the future' is insufficient for reproducibility. The benchmarks against voroILTIS, RASCAS, and COLT include git revisions (Table 2), which is good, but the THOR version, input decks, and benchmark scripts are not available, so an independent reader cannot reproduce the validation or performance numbers. I recommend making the code, or at minimum a tagged release with validation and benchmark configuration files, publicly available at acceptance, or providing a clear release timeline and archival DOI.
minor comments (6)
  1. [Figure 13] The labels 'thor[g]' and 'thor[c]' in the top panel are confusing; elsewhere the paper uses 'thor[gpu]' and 'thor[cpu]'. Please make the labels consistent and define them in the caption.
  2. [Figure 4] The x-axis label appears garbled as '(a 0)1/3 d' and the text refers to '(a tau0)1/3 tau_a'; the intended quantity is presumably b = (a tau0)^(1/3) tau_d, with tau_d the dust optical depth. Please correct the axis label and the inline expression.
  3. [Sections 5.2, 5.3] The spatial resolutions are written as '30723' and '3072^3' inconsistently; the intended '3072^3' should be used throughout. In addition, the sentence in Section 5.2 that 'we map to a 3072^3 uniform grid' should state the physical cell size explicitly rather than only in the parenthetical.
  4. [Table 2] The table footnotes are mismatched: the column header 'higher orderd' and 'FP modese' refer to notes (d) and (e), but the notes themselves are ordered (a)-(e) with (d) describing higher-order integration and (e) describing reduced-precision mode. Please align the header superscripts with the correct notes.
  5. [Section 3.4.1] The peeling photon-fusing thresholds are described as user-specified (Section 5.2 gives values of 0.01 Angstrom and 0.3 pc), but no defaults or guidance are given in the method section itself; please state the default values and how they affect the spatial/spectral resolution of the peeled contribution.
  6. [Section 3.4.2] The scheme is called 'adaptive core-skipping' in Section 5.2, but Section 3.4.2 defines a fixed x_crit = 0.2(a tau0)^(1/3) without explaining what is adaptive. Please define the term or use consistent terminology.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: THOR's validation is anchored to analytic Neufeld/slab solutions and independent numerical benchmarks; the unvalidated uniform-grid showcase path is a validation gap, not a circular reduction.

full rationale

The paper's central correctness claim is validated externally, not by its own output. Section 4 compares THOR against the analytic Neufeld sphere solution (Neufeld 1990; Dijkstra et al. 2006), the analytic slab escape fraction (Laursen et al. 2009b), the independent numerical outflow-sphere spectra of Faucher-Giguere et al. (2010), and the MgII doublet profiles of Chang & Gronke (2024). These are parameter-free external benchmarks; no fitted THOR value is recycled as a prediction. The performance comparison in Section 6.1 includes the authors' own voroILTIS code, but also independent COLT and RASCAS codes, so the 'on par with existing codes' claim is not self-referential. The Section 5.1 MCMC demonstration generates a mock spectrum with THOR and then fits it with THOR; this is explicitly presented as a capability closure test, not as a physical prediction or external validation. The paper itself flags a real limitation in Section 4: 'For this test we use our meshless spherical shell geometry (Section 3.3), and do not explicitly realize a discretized gas distribution.' Consequently, the uniform-grid MCRT path used in the Sections 5.2-5.4 showcases is not end-to-end validated against an analytic or independent numerical solution. That is an important validation gap and a correctness risk for the grid-based results, but it is not circularity: no equation, fitted parameter, or self-citation chain makes the showcase results equal to their inputs by construction. Self-citations such as Byrohl et al. (2021) and Byrohl & Nelson (2023) are contextual, comparative, or refer to previously published analysis methods; they are not load-bearing for the code's correctness claim. Therefore the derivation chain is self-contained with respect to circularity.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The central method is standard MCRT assembled from literature-sourced physics, so the ledger is modest. The parameters that actually set the showcased science outputs are the emission scalings f_eff (order unity) and the global escape fraction 0.1, plus the dust parameter f_ion = 0.01 and the fusing and skipping heuristics. The most fragile assumption is the SPH-splatting of Voronoi data onto uniform grids, which is unflagged and moves the cold, clumpy gas that dominates resonant scattering. Standard physics inputs adopted from the literature (dust albedo 0.32, g = 0.73, case-B coefficients, Planck 2015 cosmology) are not counted as free parameters. No new entities are invented.

free parameters (7)
  • f_eff (SFR-to-Ly-alpha luminosity conversion) = 1 (order unity)
    Scales absolute Ly-alpha luminosity of every galaxy source in Sections 5.2-5.4 (Eq. 13). Adopted from Dijkstra 2017, not fitted, but all surface brightness and escape fraction numbers scale linearly with it.
  • f_Ly-alpha^esc = 0.1 (global escape fraction) = 0.1
    Ad hoc dust prescription imposed in the TNG50 cosmic-web run (Section 5.4) because dust is not modeled there; lowers all scattered Ly-alpha surface brightness values in Figure 10.
  • f_ion = 0.01 (ionized-gas dust scaling) = 0.01
    Sets the dust number density n_dust = (n_HI + f_ion n_HII) Z/Z0 in the z=6 galaxy run (Section 5.2), adopted from common practice (Smith et al. 2022b).
  • Peel-photon fusing thresholds = 0.01 Angstrom, 0.3 pc
    User-specified heuristics in Section 5.2 that merge peel photons with nearly identical frequency and position; they trade spectral and spatial resolution against memory use and can bias SB maps if too coarse.
  • Core-skipping parameter x_crit coefficient = 0.2 (a*tau0)^(1/3)
    Adopted from Smith et al. 2015; skips line-core scatterings in optically thick media. This is an approximation with problem-dependent accuracy, disabled in the shell-model MCMC grid (Section 5.1) and validation runs.
  • x_cw core-wing transition polynomial coefficients c0..c4 = 1.03489162, -6.17680644e-1, -8.73073343e-2, -7.91384757e-3, -2.76037084e-4
    B25 polynomial fit to the exact Lambert-W core-wing transition (Appendix A.2, Figure A.3). A fit to an analytic function, not to laboratory data; sub-0.5% error across 1 to 1e7 K.
  • Step-size control factor f = 0.01 = 0.01
    Limits each photon step so velocity and density change stay below 1% of thermal velocity and density in the shell-model grid (Section 5.1); affects the accuracy of the roughly 50,000-run MCMC library.
assumptions (8)
  • standard math Monte Carlo photon packets sample the radiative transfer equation, so converged packet statistics reproduce the intensity and escape fraction.
    Underlies the entire MCRT driver in Section 3.4; requires unbiased samplers for optical depth, atom velocities, and phase functions, which the appendices benchmark but do not formally prove.
  • domain assumption The gas is static during post-processing; radiation does not modify temperature, ionization, or velocity fields.
    Section 7.2.1: 'when post-processing hydrodynamical simulations, we always treat the underlying fluid fields as static.' Bounds the applicability of all showcase results.
  • domain assumption The recoil and energy-transfer term in the scattering frequency update Eq. (7) is negligible.
    Section 2.3.1: 'We ignore this transfer in this work as it is negligible (Adams 1971).' Standard for Ly-alpha, but it sets the scattering frequency protocol for all lines.
  • domain assumption Cell properties are piecewise constant (zeroth-order integration) during propagation; sub-cell stepping captures velocity and Hubble gradients.
    Section 3.4: 'We assume zeroth order, i.e. constant physical properties within each gas cell.' Affects accuracy in strong gradients; step-size control is user-set (f = 0.01 in shell runs).
  • domain assumption Two-level-atom resonance approximation with adopted phase function (1-to-2 isotropic-dipole mix near line center, pure dipole in wings) and case-B recombination.
    Sections 2.1 and 2.3.1: standard Ly-alpha RT assumptions inherited from Dijkstra & Loeb 2008 and Scholz et al. 1990; not re-derived.
  • standard math Independent pseudorandom streams per photon (xoshiro128++ seeded by rank, photon ID, and step ID) are statistically equivalent to fresh draws.
    Section 3.4.3; verified with PractRand, but stream independence is assumed rather than proven for derived distributions.
  • domain assumption CLOUDY collisional plus photoionization equilibrium determines MgII ionization and emissivity in each gas cell.
    Section 5.3 and Section 2.4: tabulated CLOUDY emissivities following Nelson et al. 2021; a modeling assumption that sets the MgII source distribution.
  • ad hoc to paper SPH-splatting Voronoi/AREPO data onto a uniform grid conserves the fields relevant to resonant scattering.
    Sections 5.2 and 5.3 map 40-400 pc CGM structure onto 1-50 pc grids with a cubic-spline kernel (Nelson et al. 2016); whether clumping and column densities survive the mapping is not validated. This is the paper's weakest explicit modeling step.

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Pith. "Pith review of THOR: a GPU-accelerated and MPI-parallel radiative transfer code." pith.science (2026). https://pith.science/paper/MHMYIMIT

@misc{pith2026250711603,
  author       = {Pith},
  title        = {Pith review of: THOR: a GPU-accelerated and MPI-parallel radiative transfer code},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHMYIMIT}},
  note         = {Machine review of arXiv:2507.11603}
}
abstract

Emission and absorption line features are important diagnostics for the physics underlying extragalactic astronomy. The interpretation of observed signatures involves comparing against forward modeled spectra from galaxy formation simulations as well as more simplified geometries, while including the complex scattering radiative transfer (RT) of resonant emission lines. Here, we present thor, a modern C++ radiative transfer code focused initially on resonant emission lines. thor is a high-performance, distributed memory MPI-parallel, multi-target code, running on CPUs, GPUs and other accelerators, yielding large $\sim 10-50\rm{x}$ speed-ups compared to previous CPU-only codes. We support multiple grid-based and gridless data structures, enabling comparisons across different hydrodynamical codes as well as toy model geometries. We demonstrate its science capabilities with a number of example use cases across scales: (i) Lyman-alpha RT on simple shell-like gas distributions; (ii) Lyman-alpha RT applied to a high-resolution, high-redshift $z \sim 6$ cosmological hydrodynamical galaxy formation simulation; (iii) Lyman-alpha and Magnesium-II halos, i.e. scattering and emission from the circumgalactic medium of $z \simeq 1-2$ galaxies drawn from cosmological magnetohydrodynamical simulations; (iv) the large-scale cosmic web in gas emission, a $6144^3$ volume-element RT scaling calculation; and (v) synthetic absorption spectra of the Lyman-alpha forest. Extensive verification and benchmarking validates our approach and its computational efficiency.

Figures

Figures reproduced from arXiv: 2507.11603 by the authors.

Figure 1
Figure 1. Schematic diagram of the MCRT driver and the process of calculating resonant line emission and scattering in thor. The source model produces initial photon emission. These photons then propagate through, and interact with, the gas medium. depth. In Appendix A.3, we evaluate different approximations with respect to their performance and accuracy.6 We assume zeroth order, i.e. constant physical properties within each … view at source ↗
Figure 2
Figure 2. Schematic diagram of the parallelism and communication of thor. Two distributed-memory MPI ranks are shown. On each, a man￾agement thread handles MPI communication, output (red), sorting and pre-processing, and similar tasks. Simultaneously, a compute thread runs driver-specific kernels that execute on the device (CPU, GPU, or APU). The two communicate with thread-safe swaps of double buffers containing photon data.… view at source ↗
Figure 3
Figure 3. Left: Emergent Ly𝛼 spectrum for a uniform density sphere with a line-center optical depth of 𝜏 = 106 and temperature of 𝑇 = 2 · 104 K. The dashed lines show the analytic solution in the limit 𝑎𝜏0 ≫ 1 (Neufeld 1990; Dijkstra et al. 2006). Right: Emergent Ly𝛼 spectrum for a homogeneous sphere with a column density of 𝑁HI = 2 · 1020 cm2 , temperature 𝑇 = 2 · 104 K, and a differential outflow of 𝑣𝑟 (𝑟) = 𝑣max (𝑟/𝑟max). D… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Validation of Ly𝛼 escape fraction for photons injected in the line center within an infinite slab. Parameterized by (𝑎𝜏0) 1/3 𝜏𝑎 an analytic solutions exists for 𝑎𝜏0 ≫ 1 and 𝑎𝜏0 ≫ 𝜏 3 𝑎 (Laursen 2010). We find good agreement between the thor calculations and the analyt…
Figure 5
Figure 5. Figure 5: Validation of the doublet implementation for MgII. We initialize a sphere of constant density with a differential velocity gradient as for Ly𝛼, with NMgII = 1014.5 cm−2 and 𝑇 ∼ 104 K, and consider four different outflow velocities 𝑣outflow. An initially flat continuum …
Figure 6
Figure 6. Figure 6: Corner plot of the posterior distribution for logHI, 𝑣max, log𝑇, 𝜎int, EWint, 𝜏𝑑 from Ly𝛼 mock spectrum using ∼ 50, 000 thor RT simulations, and emcee for sampling. Blue contours show the 0.5𝜎, 1𝜎, and 2𝜎 levels. In the upper right corner, we show the true (i.e. ‘obser…
Figure 7
Figure 7. Figure 7: Application of thor raytracing and Ly𝛼 MCRT for a highly resolved, high-redshift galaxy formation simulation at 𝑧 = 6. Left column: Ly𝛼 surface brightness maps. The top panel shows the intrinsic emission from recombinations due to local stellar ionizing photons. The mi…
Figure 8
Figure 8. Figure 8: Impact of resonant scattering on Ly𝛼 emission in the circumgalactic medium of the highly-resolved cosmological hydrodynamical galaxy formation simulation GIBLE at 𝑧 = 2 (S167RF4096). Ly𝛼 is emitted proportional to the star-formation rate of the galaxy, and its satellit…
Figure 9
Figure 9. Figure 9: Extended MgII emission on the scales of the circumgalactic medium of a star-forming galaxy at 𝑧 = 1 from the GIBLE simulations. Left: surface brightness map after accounting for scattering. The inset shows the intrinsic emission in the inner region. Right: Spectral pro…
Figure 10
Figure 10. Figure 10: Application of thor MCRT to the problem of Ly𝛼 emission on the largest scales of the cosmic web. We use the cosmological galaxy formation simulation TNG50 at 𝑧 = 2, and apply a simple galaxy-centric Ly𝛼 emission model. The true, mean neutral hydrogen density field is …
Figure 11
Figure 11. Figure 11: Volume rendering using a simple transfer function for cold (blue) and hot (red/orange) gas in TNG50 centered on the most massive halo at 𝑧 = 2. The temperature-dependent transfer function is visualized as a line within the inset where the line color shows the RGB valu…
Figure 12
Figure 12. Figure 12: Ly𝛼 forest application of thor to the TNG50 cosmological galaxy formation simulation at 𝑧 = 2. Top: Residual continuum flux for two randomly drawn lines of sight using periodic boundary conditions. We show relative flux i.e. with respect to the continuum, as a functio…
Figure 13
Figure 13. Figure 13: Benchmark and code performance comparison. Here we con￾sider the Neufeld test problem and its analytic solution in the optically thick limit. The top panel shows a comparison of the emergent (final) spectra produced by each code, while the middle (bottom) panels show …
Figure 14
Figure 14. Figure 14: Runtime benchmarks and scaling tests for the thor radiative transfer code. The application is always Ly𝛼 MCRT, although we apply it in several different regimes. Upper left: a spherical setup for varying line-center optical depth 𝜏0 with and without core-skipping acce…

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