HYPERION: An open-source parallelized three-dimensional dust continuum radiative transfer code

Thomas P. Robitaille

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HYPERION: An open-source parallelized three-dimensional dust continuum radiative transfer code

Thomas P. Robitaille

arXiv:1112.1071v1Dec 5, 2011astro-ph.IMastro-ph.COastro-ph.GAastro-ph.SR

TL;DR

Astrophysical dust radiative transfer often requires numerical treatment, especially for arbitrary three-dimensional structures and optically thick regions. Hyperion provides a modular, parallel Monte Carlo code with flexible grids and sources, and it agrees excellently with published disk benchmarks while modeling a low-mass star-formation simulation. Its speedup depends on the model setup, and PAH/VSG feature shapes are only accurate to first order.

Problem
Most dust-and-gas radiation problems require numerical solutions, while optically thick regions can trap photon packets and make Monte Carlo transport inefficient.
Method
Hyperion uses a problem-independent three-dimensional Monte Carlo core with iterative absorption calculations, flexible grids, and parallel execution.
Results
Hyperion scales well to hundreds or thousands of processes, agrees excellently with published circumstellar-disk benchmarks, and predicts synthetic observations for a low-mass star-formation simulation.
Takeaways & Limitations
The star-formation case study found that three-dimensional accretion flows produced radiation beaming and fairly symmetric structures usually associated with bipolar outflow cavities.
Takeaways & Limitations
Speedup depends on model setup, while PAH/VSG feature shapes are only accurate to first order because emissivities are pre-computed using total absorbed-energy ratios.

Abstract

from arXiv · show

HYPERION is a new three-dimensional dust continuum Monte-Carlo radiative transfer code that is designed to be as generic as possible, allowing radiative transfer to be computed through a variety of three-dimensional grids. The main part of the code is problem-independent, and only requires an arbitrary three-dimensional density structure, dust properties, the position and properties of the illuminating sources, and parameters controlling the running and output of the code. HYPERION is parallelized, and is shown to scale well to thousands of processes. Two common benchmark models for protoplanetary disks were computed, and the results are found to be in excellent agreement with those from other codes. Finally, to demonstrate the capabilities of the code, dust temperatures, SEDs, and synthetic multi-wavelength images were computed for a dynamical simulation of a low-mass star formation region. HYPERION is being actively developed to include new features, and is publicly available (http://www.hyperion-rt.org).

1. Introduction

Three-dimensional dust radiative transfer generally requires numerical methods, and Monte Carlo methods offer a flexible alternative for arbitrary geometries but face efficiency challenges in optically thick regions. Hyperion addresses these needs as a modular, parallel dust-continuum code incorporating performance optimizations and supporting synthetic observations.

Most astrophysical dust-and-gas radiation problems require numerical radiative-transfer solutions to infer source geometrical, physical, and chemical properties.
Monte Carlo radiative transfer propagates sampled photon packets through three-dimensional grids, producing temperatures, SEDs, and images from escaping packets.In LTE, absorbed energy is iteratively converted into equilibrium dust temperatures because emissivity depends on temperature.
Performance optimizations include continuous absorption, immediate temperature correction, peeling-off for higher observation signal-to-noise, and forced first scattering in optically thin cases.
Optically thick cells can trap photon packets, with interaction counts increasing approximately as the square of density; diffusion-based random walks reduce escape steps.
Hyperion is designed for wide-ranging dust-continuum problems, combines recent Monte Carlo optimizations with modularity, and is parallelized to scale to thousands of processes.

2. Code overview

Hyperion separates a problem-independent high-performance radiative-transfer core from a Python setup and analysis library. It accepts arbitrary three-dimensional structures, supports multiple grids and sources, and models wavelength-dependent scattering and polarization.

The Fortran core accepts arbitrary three-dimensional density structures, dust properties, sources, and output parameters to compute temperatures, SEDs, and images.
A Python library creates input files, provides analytical density structures and simulation-import tools, and supports post-processing of radiative-transfer results.
The code propagates photon packets, iterates absorbed-energy calculations until convergence, then computes SEDs and images.
Hyperion supports isotropic point, spherical, diffuse, and external isotropic sources, with user-defined spectra and configurable photon counts.
Photon packets carry position, direction, frequency, and Stokes vectors describing total intensity and linear and circular polarization.
Supported grids include Cartesian, spherical-polar, cylindrical-polar, octree, and AMR geometries, concentrating resolution where needed.
Dust modeling supports frequency-dependent extinction, albedo, and anisotropic scattering for randomly oriented grains using a four-element Mueller matrix.Support for aligned non-spherical grains using a full 16-element matrix is planned for future implementation.
For LTE dust, pre-computed mean opacities and emissivities are tabulated as functions of specific energy absorption rate rather than temperature.

2.2. Photon packet propagation

Hyperion propagates source-emitted photon packets through the grid while addressing inefficient transport in very optically thick regions with a modified random-walk approach.

Photon packets are sampled from source luminosities, with standard luminosity-proportional emission or equal source counts using energy weighting.
Very optically thick regions can require millions of interactions, so the modified random walk groups many scatterings and absorptions into single larger propagation steps.

2.3. Temperature/Energy absorption rate calculation

Hyperion iteratively estimates cell energy absorption from photon paths, derives dust emission properties and temperatures under LTE, and uses diffusion and robust percentile criteria where direct estimates are unreliable.

Hyperion uses Lucy’s iterative continuous-absorption method to compute each cell’s specific energy absorption rate from photon-packet paths.
Under LTE, dust temperature is obtained by balancing absorbed and emitted energy; Hyperion instead tabulates opacities and emissivities versus absorption rate and computes temperature on demand.
In high-optical-depth regions with too few packets, the partial diffusion approximation uses reliable cells as boundary conditions to estimate absorption and temperature.
Convergence is evaluated from iteration-to-iteration changes in absorbed energy using a ratio-based difference measure that is insensitive to change direction.
Convergence requires percentile-based changes to fall below user thresholds, allowing outliers to be ignored and requirements to be tailored to the scientific problem.For example, p = 99.9%, Qthres = 2, and Δthres = 1.1 require most cell differences below a factor of 2 and percentile change below about 10%.
If noise prevents convergence, users can increase photon packets, raise the iteration limit, or relax convergence requirements.

2.5. PAH/VSG emission

HYPERION approximates emission from PAHs and VSGs using emissivities pre-computed as a function of absorbed energy. This supports first-order SED and image studies, but PAH feature shapes require caution.

PAH and VSG populations are supported when opacity is temperature- and density-independent and emissivity depends on specific energy absorption.This extends the code beyond dust continuum transfer to an approximation of stochastically heated PAHs and very small non-thermal grains.
The method pre-computes emissivities versus absorbed energy for a given irradiating spectrum and uses them as lookup tables.
UV and optical emission dominate excitation because PAH and VSG opacities peak strongly at those wavelengths.The emissivity choice is based primarily on total absorbed UV and optical energy relative to the template spectrum.
PAH feature strengths and VSG continua should be accurate to first order, whereas PAH feature shapes should be treated cautiously.The template spectrum has a smaller secondary impact on the pre-computed emissivities.
HYPERION selects emissivities using energy absorbed by PAHs and VSGs rather than mean intensity, distinguishing excitation by spectral location.

2.6. SEDs and images

HYPERION provides multiple methods for producing SEDs and images after energy-absorption convergence, ranging from inefficient binning to efficient raytracing. Peeling-off improves signal-to-noise for observer-directed contributions.

After specific energy absorption converges, HYPERION can compute SEDs and images using several implemented methods.
Binning: Direct photon-packet binning is inefficient because each packet contributes once to one viewing angle and outputs are averaged over finite angle bins.
Peeling-off: Peeling-off adds observer-directed photon contributions at each scattering or re-emission, weighted by p exp(-τ), improving signal-to-noise over binning.
Raytracing: Raytracing determines the source function throughout the grid and solves radiative transfer along lines of sight in post-processing.For thermal emission, the source function is related to cell mass and temperature or energy.
Spectral sampling: Finite-width wavelength or frequency bins are the default, while exact-wavelength calculations require modified peeling-off treatment for scattered light.

2.7. Additional user options

HYPERION offers uncertainty estimation, photon-origin tracking, dust sublimation controls, and forced first scattering. These options support error assessment, component decomposition, and treatment of optically thin or thick regions.

Uncertainties are estimated from scatter in photon-packet fluxes for each wavelength or frequency and each aperture or pixel.The implementation accounts for combining techniques with different signal-to-noise properties.
Photon-origin tracking can split SEDs and images by sources, dust types, direct photons, and scattered photons.
Dust sublimation can cap absorption, remove dust completely, or reduce density without setting it to zero.The density-reduction mode addresses optically thick cells where trapped internally generated radiation raises absorption rates.
In optically thick cells with internally generated radiation, reducing rather than eliminating dust density can represent the sublimation response.
Forced first scattering is available to improve signal-to-noise for scattered radiation in optically thin dust.

3. Parallelized performance

HYPERION parallelizes photon-packet propagation with MPI, while serial work limits speedup according to the model and packet count. Disk benchmark temperatures agree with other tested codes, and measured speedups are illustrative rather than universal.

Implementation: MPI distributes photon packets in many small chunks, balancing heterogeneous cores or nodes with low per-batch communication overhead.Results are combined only after all processes finish an iteration.
Scaling model: The parallel fraction P and process count N determine speedup through Amdahl’s law, with serial startup and inter-iteration work limiting scaling.
Performance experiment: 10 repeated wall-clock runs compare a protoplanetary-disk model across N = 1 to N = 512, including a case with 10 times more photon packets.
Benchmark results: Temperature profiles for the τV = 100 disk benchmark compare Hyperion with RADICAL and other tested codes across radial and vertical cuts.The radial cut is near the mid-plane at θ = 2.5°, and the vertical cut is at cylindrical radius 2 AU.
Performance experiment: The two packet-count cases approach the same runtime because their serial portions are identical, despite nearly order-of-magnitude differences in fitted maximum speedup.
Scope: Measured speedups are illustrative and depend on model setup, so users should determine the optimal process count for each problem.

4. Benchmarks

HYPERION is evaluated against two protoplanetary-disk radiative-transfer benchmarks spanning temperatures, SEDs, images, and polarization maps. Its results lie within the dispersion of established codes, including in the more optically thick and anisotropic-scattering benchmark.

Pascucci et al. (2004) benchmark: The Pascucci et al. benchmark covers four disk masses with radial mid-plane optical depths τV = 0.1, 1, 10, and 100, using three viewing angles.The models use a spherical polar grid with dimensions (nr, nθ, nφ) = (499, 399, 1).
Pinte et al. (2009) benchmark: The benchmark comparisons include temperature profiles, SEDs, images, and linear polarization maps against averages or results from multiple established codes.The image and polarization comparisons use cuts in both absolute and relative units, with 11-pixel widths to improve signal-to-noise.
Pascucci et al. (2004) benchmark: Hyperion temperatures for the optically thick Pascucci model are within the dispersion of results from the other codes.The comparison includes radial and polar-angle temperature profiles for τV = 100.
Pascucci et al. (2004) benchmark: Hyperion SEDs for all four Pascucci disk masses and three viewing angles are within the dispersion of results from the other codes.Figure 3 compares Hyperion with RADICAL and shows fractional differences relative to the reference code.
Pinte et al. (2009) benchmark: The Pinte benchmark tests anisotropic scattering and synthetic images and polarization maps across ten viewing angles from 18.2° to 87.1°.Images and polarization maps are computed at 1 µm on 251 × 251 pixels spanning 900 × 900 AU.

5. Case study: simulated observations of a low-mass star-forming region

HYPERION was applied to a simulated low-mass star-forming region to compute equilibrium temperatures, synthetic multi-wavelength images, and SEDs. The resulting observables illustrate how scattering, thermal emission, three-dimensional structure, viewing angle, and instrumental effects shape simulated observations.

5.1. The simulation: The simulation contains 185 M⊙ of gas and dust in a 0.65 pc box, resolving scales down to 32 AU with effective resolution 4096^3.It was computed with the ORION AMR three-dimensional gravito-radiation-hydrodynamics code and included radiative heating.
5.2. The radiative transfer model: The calculation included luminosity from forming stars and the interstellar radiation field, then computed equilibrium temperatures and images at 12 wavelengths from 1.25 to 500 µm.The bands covered JHK, Spitzer/IRAC, Herschel/PACS, and Herschel/SPIRE, assuming a distance of 300 pc.
5.2. The radiative transfer model: Near-infrared images are dominated by direct and scattered stellar light, with diffuse-cloud emission produced by scattered interstellar radiation and no thermal contribution.The reported mean colors are J-H = 0.387 ± 0.280 and H-K = −0.214 ± 0.273, where the uncertainties represent scatter.
5.2. The radiative transfer model: Three-dimensional accretion-flow and disk structure produces bipolar scattered-light features without outflows, because lower polar densities beam radiation along the rotation axis.Thus, bipolar near- and mid-infrared scattered light is not necessarily evidence for actual outflows.
5.2. The radiative transfer model: The IRAC band can show the cloud as an infrared-dark cloud against bright PAH background, while PACS traces temperature gradients and SPIRE traces most of the mass.The passage reports 10% of the shown area above Σ > 0.10 g/cm2 and 1% above Σ > 0.27 g/cm2.
5.3. Synthetic Observations: Synthetic observations were resampled to typical ground-based, Spitzer, and Herschel resolutions, convolved with instrumental PSFs, and given Gaussian noise.At degraded resolution, PACS retains mainly the brightest diffuse emission, while SPIRE confuses many protostars with the cloud.
5.4. Spectral Energy Distributions: Sources 1, 2a, and 2b have masses of roughly 0.5–2 M⊙, whereas Source 3 is around 0.06 M⊙; inferred evolutionary stages may be wrong from one viewing angle.The relative accretion rate increases from Source 1 to Source 3, consistent with the average near- to far-infrared ratio trend.

6. Future

Future development targets broader physical treatments, more flexible spatial discretizations, and improved scattered-light calculations. Planned additions include non-spherical grains, gas radiative transfer, unstructured meshes, faster raytracing, and temperature-dependent dust opacities.

6. Future: Planned grain physics includes scattering and absorption by non-spherical grains aligned with magnetic fields, producing polarization signatures that trace those fields.The planned capability extends the modeled dust interactions and polarization behavior.
6. Future: Planned radiative-transfer extensions include continuum and line gas transfer with photoionization, plus support for unstructured meshes based on irregular polyhedral cells.Unstructured meshes could sample arbitrary three-dimensional density structures more precisely for a fixed number of cells.
6. Future: Future improvements include raytracing for scattered light and temperature-dependent dust opacities, especially where dust composition changes with temperature or includes ices.Raytracing is intended to improve signal-to-noise efficiently at wavelengths dominated by scattered light.

7. Summary

Hyperion is a broadly applicable, parallelized radiative-transfer code supporting multiple three-dimensional grids. It agrees closely with published disk benchmarks, models complex star-formation observations, and is openly available.

Hyperion supports radiative transfer through Cartesian, cylindrical-polar, spherical-polar, and adaptive Cartesian three-dimensional grids.Its algorithms include photon-packet propagation, raytracing, convergence detection, and diffusion approximations.
The code scales well to hundreds or thousands of processes, with maximum speedup limited by serial work such as file input/output.
Hyperion shows excellent agreement with published Pascucci et al. and Pinte et al. circumstellar-disk benchmark results.
A low-mass star-formation simulation produced near-infrared to sub-millimeter predictions, including beamed radiation from three-dimensional accretion flows despite no simulated outflows.
Hyperion is released under an open-source license with hosted version control supporting contributions to its code and documentation.

Appendix A: The partial diffusion approximation (PDA)

The partial diffusion approximation converts diffusion transport in optically thick regions into a linear system on the computational grid. In spherical-polar coordinates, cell geometry, optical depths, and neighboring temperatures determine the system and its boundary conditions.

The diffusion approximation provides the transport equation used by Hyperion's partial diffusion approximation.
The diffusion coefficient is D = 1/3ρ χ̄_R, and the diffusion equation is written as a system of linear equations.Because Hyperion stores specific dust energy absorption rather than temperature, the PDA is solved using that stored quantity.
In spherical-polar coordinates, the diffusion equation is discretized on the computational grid.
The discrete system uses cell indices, coordinate extents, and Rosseland optical depths along each coordinate direction.Neighboring temperatures can provide boundary conditions, after which the resulting linear system is formally solved.