arXiv subjects

Patrick D. Mullen

Publications and source records attributed to Patrick D. Mullen.

10 recordsLinked to original sources

arXiv2026

Multigroup Thermal Radiation Transport with Tensor Trains

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than $100 \times$ and speedups exceeding $2 \times$. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as $7$. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.

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arXiv2026

Radiation GRMHD Models of Accretion onto Stellar-Mass Black Holes: II. Super-Eddington Accretion

We present a comprehensive analysis of super-Eddington black hole accretion simulations that solve the GRMHD equations coupled with angle-discretized radiation transport. The simulations span a range of accretion rates, two black hole spins, and two magnetic field topologies, and include resolution studies as well as comparisons with non-radiative models. Super-Eddington accretion flows consistently develop geometrically thick disks supported by radiation pressure, regardless of magnetic field configuration. Radiation generated in the inner disk drives substantial outflows, forming conical funnel regions that limit photon escape and result in very low radiation efficiency. The accretion flows are highly turbulent with thermal energy transport dominated by radiation advection rather than diffusion. Angular momentum is primarily carried outward by Maxwell stress, with turbulent Reynolds stress playing a subdominant role. Both strong and weak jets are produced. Strong jets arise from sufficient net vertical magnetic flux and rapid black hole spin and can effectively evacuate the funnel, enabling radiation to escape through strong geometric beaming. In contrast, weak jets fail to clear the funnel, which becomes obscured by radiation-driven outflows and leads to distinct observational signatures. Spiral structures are observed in the plunging region, behaving like density waves. These super-Eddington models are applicable to a variety of astronomical systems, including ultraluminous X-ray sources, little red dots, and black hole transients.

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arXiv2026

Radiation GRMHD Models of Accretion onto Stellar-Mass Black Holes: III. Near-Eddington Accretion

We present a comprehensive analysis of four near-Eddington black hole accretion models from GRMHD simulations with full radiation transport. This study investigates the dynamical effects of magnetic field topology and black hole spin using two representative choices of each. Two stable near-Eddington solutions emerge in these models: a thin thermal disk embedded within a magnetic envelope when sufficient net vertical magnetic flux is present (e.g., vertical field $\gtrsim 5\times10^5$ G at $20r_g$), and a magnetically elevated disk when the net vertical flux is weak or absent. One model initialized without net vertical flux evolves into the thin disk solution, as strong, anisotropic radiation feedback at high accretion rates promotes the accumulation of vertical magnetic flux in the inner disk. In the thin thermal disk, accretion is driven primarily by mean-field Maxwell stress and proceeds largely within the magnetic envelope, while heat dissipation is spatially decoupled and concentrated near the midplane. However, in the magnetically elevated disk, accretion occurs throughout the disk body and is comparably driven by mean-field and turbulent stresses; heat dissipation therefore occurs locally through turbulence. Radiation transport is diffusion-dominated, enabling efficient radiative cooling ($\sim$4-10%). An optically thin wind is launched from the disk surface by combined radiative and magnetic forces, with stronger winds found in models with larger vertical magnetic flux and higher spin. Both strong and weak jets are produced: strong jets are persistent, highly relativistic, and magnetically driven, while weak jets are intermittent, mildly relativistic, and powered by a combination of magnetic and radiative forces.

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arXiv2025

Radiation GRMHD Models of Accretion onto Stellar-Mass Black Holes: I. Survey of Eddington Ratios

We summarize results from a survey of radiation-dominated black hole accretion flows across a wide range of mass accretion rates, as well as two values of black hole spin and initial magnetic field geometry. These models apply an algorithm targeting direct solutions to the radiation transport equation in full general relativity and have been enabled by access to modern exascale computing systems. Super-Eddington accretion flows form geometrically thick radiation pressure supported disks that drive powerful equatorial outflows. A narrow funnel-shaped photosphere in the inner region results in very low radiative efficiencies in this regime. The structure of near- and sub-Eddington accretion depends on whether there is net vertical magnetic flux at the midplane of the disk. With net flux, the disk forms a thin, dense layer at the midplane surrounded by a magnetically-dominated corona, whereas without net flux the disk remains magnetically dominated everywhere. Although none of our models achieve the magnetically arrested disk (MAD) regime, those with net vertical flux and a rapidly spinning black hole still produce powerful relativistic jets. Our calculations adopt simple opacity models (with scalings appropriate to stellar-mass black hole accretion). We discuss the application of our results to observations of X-ray binaries and ultraluminous X-ray sources such as Cyg X-3 and SS433. We also speculate on the application of our super-Eddington models to the interpretation of little red dots (LRDs) recently discovered by JWST.

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arXiv2025

Mahakala: a Python-based Modular Ray-tracing and Radiative Transfer Algorithm for Curved Space-times

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved space-times. 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 counter jet to 1.3 mm images.

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arXiv2025

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is "low-rank," the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector thereby enabling large speedups for low-rank solutions. To achieve these speedups we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar SN algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low rank structure and supplies up to $\simeq$60$\times$ speedups and $\simeq$1000$\times$ compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

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arXiv2025

Towards Higher Order Accuracy in Self-Gravitating Hydrodynamics

High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $Δx$) with only a moderate increase to computational expense. Significant effort has been placed in the development of finite volume algorithms for (magneto)hydrodynamics, however, state-of-the-art astrophysical simulations tightly couple a plenitude of physics, additionally including gravity, photon transport, cosmic ray transport, chemistry, and/or diffusion, to name a few. Algorithms frequently operator split this additional physics (often a first order error in time) and/or adopt a model wherein their evaluation is limited to second order accuracy in space. In this work, we present a fourth order accurate finite volume scheme for self-gravitating hydrodynamics on a uniform Cartesian grid. The method supplies source terms for the gravitational acceleration ($ρ{\bf g}$) and gravitational energy release ($ρ{\bf v} \cdot {\bf g}$) associated with fourth-order accurate solutions to the Poisson equation. Our scheme (1) guarantees the conservation of total linear momentum, while (2) decreasing (in proportion to $Δx^4$) the effects of spurious heating and/or cooling associated with truncation error in the gravity. We demonstrate expected convergence rates for the algorithm by measuring errors in test problems evolving self-gravity modified linear waves and 3D polytropic equilibria. We test robustness of the algorithm by integrating an induced "inside-out" adiabatic collapse. We also discuss a method to smoothly downgrade the solution to second-order spatial accuracy to avoid spurious overshoots near steep density and/or pressure gradients.

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arXiv2024

AthenaK: A Performance-Portable Version of the Athena++ AMR Framework

We describe AthenaK: a new implementation of the Athena++ block-based adaptive mesh refinement (AMR) framework using the Kokkos programming model. Finite volume methods for Newtonian, special relativistic (SR), and general relativistic (GR) hydrodynamics and magnetohydrodynamics (MHD), and GR-radiation hydrodynamics and MHD, as well as a module for evolving Lagrangian tracer or charged test particles (e.g., cosmic rays) are implemented using the framework. In two companion papers we describe (1) a new solver for the Einstein equations based on the Z4c formalism and (2) a GRMHD solver in dynamical spacetimes also implemented using the framework, enabling new applications in numerical relativity. By adopting Kokkos, the code can be run on virtually any hardware, including CPUs, GPUs from multiple vendors, and emerging ARM processors. AthenaK shows excellent performance and weak scaling, achieving over one billion cell updates per second for hydrodynamics in three-dimensions on a single NVIDIA Grace Hopper processor and with a typical parallel efficiency of 80% on 65536 AMD GPUs on the OLCF Frontier system. Such performance portability enables AthenaK to leverage modern exascale computing systems for challenging applications in astrophysical fluid dynamics, numerical relativity, and multimessenger astrophysics.

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arXiv2023

An Extension of the Athena++ Code Framework for Radiation-Magnetohydrodynamics in General Relativity Using a Finite-Solid-Angle Discretization

We extend the general-relativistic magnetohydrodynamics (GRMHD) capabilities of Athena++ to incorporate radiation. The intensity field in each finite-volume cell is discretized in angle, with explicit transport in both space and angle properly accounting for the effects of gravity on null geodesics, and with matter and radiation coupled in a locally implicit fashion. Here we describe the numerical procedure in detail, verifying its correctness with a suite of tests. Motivated in particular by black hole accretion in the high-accretion-rate, thin-disk regime, we demonstrate the application of the method to this problem. With excellent scaling on flagship computing clusters, the port of the algorithm to the GPU-enabled AthenaK code now allows the simulation of many previously intractable radiation-GRMHD systems.

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arXiv2019

X-rays Studies of the Solar System

X-ray observatories contribute fundamental advances in Solar System studies by probing Sun-object interactions, developing planet and satellite surface composition maps, probing global magnetospheric dynamics, and tracking astrochemical reactions. Despite these crucial results, the technological limitations of current X-ray instruments hinder the overall scope and impact for broader scientific application of X-ray observations both now and in the coming decade. Implementation of modern advances in X-ray optics will provide improvements in effective area, spatial resolution, and spectral resolution for future instruments. These improvements will usher in a truly transformative era of Solar System science through the study of X-ray emission.

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