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DOE OSTI2025

Angular-spatial hp -adaptivity for radiative transfer with discontinuous Galerkin spectral element methods

Radiative transfer is important for many science and engineering applications, and numerical simulations of radiative transfer can be challenging. For instance, the radiation field is seven-dimensional – three spatial, two angular, one wavelength, and one temporal – and often features steep gradients. Therefore, memory usage is a key issue. To reduce memory, some past work has investigated the use of adaptive mesh refinement (AMR), typically for either the spatial or angular coordinate, and typically for only h -adaptivity. Here, we propose the use of AMR for the spatial and angular coordinates together, and the use of h - and p -adaptivity together as hp -AMR for the potential for further memory savings. We implemented the proposed method for several test cases in two spatial and one angular dimension, with the discontinuous Galerkin spectral element method. These test cases featured highly anisotropic angular radiation, with or without steep spatial gradients. Our primary findings from these test cases were: (1) Angular hp -adaptivity can deliver the radiation solution with the same accuracy as, and with much less computational memory than, uniform angular h - or p -refinements, or angular h -adaptivity alone. This is most obvious when the incoming radiation is highly anisotropic, in which case the savings can be orders of magnitude. (2) Full spatial-angular hp -adaptivity is more efficient in solution representation, compared to solely spatial or solely angular -adaptivity. This is most evident when steep gradients are present in both the spatial and angular distribution. These results suggest that adaptive spatial- hp angular-refinement may perform well in large-scale seven-dimensional applications.

Adaptive refinement↗

DOE OSTI2025

An Integral-based Technique to Accelerate the Monte Carlo Radiative Transfer Computation for Supernovae

We present an integral-based technique (IBT) algorithm to accelerate supernova (SN) radiative transfer calculations. The algorithm utilizes “integral packets,” which are calculated by the path integral of the Monte Carlo (MC) energy packets, to synthesize the observed spectropolarimetric signal at a given viewing direction in a 3D time-dependent radiative transfer program. Compared to the event-based technique (EBT) proposed by M. Bulla et al., our algorithm significantly reduces the computation time and increases the MC signal-to-noise ratio (S/N). Using a 1D spherical symmetric Type Ia SN ejecta model DDC10 and its derived 3D model, the IBT algorithm has successfully passed the verification of spherical symmetry and cross comparison on a 3D SN model with the direct-counting technique and EBT. Notably, with our algorithm implemented in the 3D MC radiative transfer code SEDONA, the computation time is faster than EBT by a factor of 10−30, and the S/N is better by a factor of 1.5−3, with the same number of MC quanta.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Mahakala: A Python-based Modular Ray-tracing and Radiative Transfer Algorithm for Curved Spacetimes

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved spacetimes. We employ Google's JAX framework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr spacetimes. JAX also enables Mahakala to run in parallel on both CPUs and GPUs. Mahakala natively uses the Cartesian Kerr–Schild coordinate system, which avoids numerical issues caused by the pole in spherical coordinate systems. We demonstrate Mahakala's capabilities by simulating 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature of Mahakala allows us to quantitatively explore how different regions of the flow influence different image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole and peaks near the photon orbit. We also quantify the relative contribution of the disk, forward jet, and counterjet to 1.3 mm images.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Second Order Closures for the Radiative Transfer Equation: Some Are Unstable

The largest existing simulations of cosmic reionization model radiative transfer with moment methods that require a closure relation. The two most commonly used closure relations are M1 and OTVET; both close the moment hierarchy at the first moment. We explore the properties of a higher, second-order closure. We show that direct generalizations of M1 and OTVET to one higher order are physically unstable - i.e., the closure equations themselves result in unstable solutions, not just their numerical implementation. In fact, a generalization of OTVET to any order higher than the first one is unstable. We are also able to show that any local (i.e., depending only on the local moments of the radiation field, like M1) second-order closure that depends only on the radiation intensity and radiation flux, but does not explicitly depend on the radiation pressure, is physically unstable. This result restricts the choice of possible second-order closure relations.

Gnedin, Nickolay Y. [Fermilab; Chicago U., Astron.↗

DOE OSTI2025

Outflowing photoionized plasma in Circinus X-1 using the high-resolution X-ray spectrometer Resolve onboard XRISM and the radiative transfer code cloudy

High-resolution X-ray spectroscopy is a key to understanding the mass inflow and outflow of compact objects. Spectral lines carry information about the ionization, density, and velocity structures through their intensity ratios and profiles. They are formed in non-local thermodynamic equilibrium conditions under the intense radiation field from the compact objects; thus radiative transfer (RT) calculation is a requisite for proper interpretations. We present such a study for a low-mass X-ray binary, Circinus X-1, from which the P Cygni profile was discovered using the X-ray grating spectrometer onboard Chandra. We observed the source using the X-ray microcalorimeter onboard XRISM at an orbital phase of 0.93–0.97 and revealed many spectral features unidentified before: the higher series transitions ($n{\rightarrow }1$; $n>2$) of highly ionized (H- and He-like) S, Ca, Ar, and Fe in emission and absorption, the Fe K$\alpha$ and K$\beta$ inner-shell excitation absorption of mildly ionized (O- to Li-like) Fe, and resolved fine-structure level transitions in the Fe Ly$\alpha$ and He$\alpha$ complexes. They blend with each other at different velocity shifts on top of apparently variable continuum emission that changed its flux by an order of magnitude within a 70 ks telescope time. Despite such complexity in the observed spectra, most of them can be explained by a simple model consisting of the photoionized plasma outflowing at $\sim$300 km s$^{-1}$ and the variable blocking material in the line of sight of the incident continuum emission from the accretion disk. We demonstrate this with the aid of the RT code cloudy for the line ratio diagnostics and spectral fitting. We further constrain the physical parameters of the outflow and argue that the outflow is launched close to the outer edge of the accretion disk and can be driven radiatively by being assisted by the line force calculated using the RT simulation.

X-rays: binaries↗

DOE OSTI2025

Monte Carlo Simulations of Polarized Radiative Transfer in Neutron Star Atmospheres

Soft X-ray emission from neutron stars affords powerful diagnostic tools for uncovering their surface and interior properties, as well as their geometric configurations. In the atmospheres of neutron stars, the presence of magnetic fields alters the photon-electron scattering cross sections, resulting in nontrivial angular dependence of intensity and polarization of the emergent signals. This paper presents recent developments of our Monte Carlo simulation, MAGTHOMSCATT, which tracks the complex electric field vector for each photon during its transport. Our analysis encompasses the anisotropy and polarization characteristics of X-ray emission for field strengths ranging from nonmagnetic to extremely magnetized regimes that are germane to magnetars. In the very low field domain, we reproduced the numerical solution to the radiative transfer equation for nonmagnetic Thomson scattering, and provided analytical fits for the angular dependence of the intensity and the polarization degree. These fits can be useful for studies of millisecond pulsars and magnetic white dwarfs. By implementing a refined injection protocol, we show that, in the magnetar regime, the simulated intensity and polarization pulse profiles of emission from extended surface regions becomes invariant with respect to the ratio of photon (ω) and electron cyclotron (ω B ) frequencies once ω/ω B ≲ 0.01. This circumvents the need for simulations pertinent to really high magnetic field strengths, which are inherently slower. Our approach will be employed elsewhere to model observational data to constrain neutron star geometric parameters and properties of emitting hot spots on their surfaces.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Uncovering the truth about M101, NGC 3938, and their significant others through radiative transfer

ABSTRACT Solving the inverse problem in spiral galaxies, that allows the derivation of the spatial distribution of dust, gas, and stars, together with their associated physical properties, directly from panchromatic imaging observations, is one of the main goals of this work. To this end, we used radiative transfer models to decode the spatial and spectral distributions of the nearby face-on galaxies M101 and NGC 3938. In both cases, we provide excellent fits to the surface-brightness distributions derived from GALEX, SDSS, 2MASS, Spitzer, and Herschel imaging observations. Together with previous results from M33, NGC 628, M51, and the Milky Way, we obtain a small statistical sample of modelled nearby galaxies that we analyse in this work. We find that in all cases Milky Way-type dust with Draine-like optical properties provide consistent and successful solutions. We do not find any ‘submm excess’, and no need for modified dust-grain properties. Intrinsic fundamental quantities like star-formation rates (SFR), specific SFR (sSFR), dust opacities, and attenuations are derived as a function of position in the galaxy and overall trends are discussed. In the SFR surface density versus stellar mass surface density space, we find a structurally resolved relation (SRR) for the morphological components of our galaxies, that is steeper than the main sequence (MS). Exception to this is for NGC 628, where the SRR is parallel to the MS.

Pricopi, D.↗

DOE OSTI2025

Jipole: A Differentiable ipole-based Code for Radiative Transfer in Curved Spacetimes

Recent imaging of supermassive black holes by the Event Horizon Telescope has relied on exhaustive parameter-space searches, matching observations to large, precomputed libraries of theoretical models. As observational data become increasingly precise, the limitations of this computationally expensive approach grow more acute, creating a pressing need for more efficient methods. In this work, we present Jipole, an automatically differentiable (AD), ipole-based code for radiative transfer in curved spacetimes, designed to compute image gradients with respect to underlying model parameters. These gradients quantify how parameter changes—such as the black hole’s spin or the observer’s inclination—affect the image, enabling more efficient parameter estimation and reducing the number of required images. We validate Jipole against ipole in two analytical tests and then compare pixelwise intensity derivatives from AD with those from finite-difference methods. We then demonstrate the utility of these gradients by performing parameter recovery for an analytical model in three increasingly complex cases for the injected image: ideal, blurred, and blurred with added noise. In most cases, high-accuracy fits are obtained in only a few optimization steps, failing only in cases with extremely low signal-to-noise ratios. These results highlight the potential of AD-based methods to accelerate robust, high-fidelity model-data comparisons in current and future black hole imaging efforts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗

DOE OSTI2026