Search NASA⌕ Search

SEARCH · Search NASA

Results for “constitutive equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model

Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.

58 GEOSCIENCES↗

A Simple, Scalable Large Deformation Solid Mechanics Implementation in the MOOSE Framework

This article describes a large deformation solid mechanics solver implemented as part of the freely available and open source MOOSE finite element simulation framework. The article documents the choices made in developing the solid mechanics framework and describes novel formulations for the gradient operator and constitutive modeling framework made to simplify implementations of different coordinate systems, stabilized gradient operators, and different constitutive model inputs and outputs. In the process, the article describes a new formulation that casts objective integration of the Cauchy stress as a linear transformation of the small stress rate. Finally, the article presents key implementation details and examines the parallel efficiency of the solid mechanics solver implemented in MOOSE. The implementation retains a good weak scaling efficiency beyond 1,000 parallel processes. The article includes a discussion of the factors limiting the parallel efficiency of implicit, large deformation solid mechanics codes on current high-performance computers, with the main current limitation being the scalability of the algebraic multigrid methods used to solve the linearized equilibrium equations.

Applied computing → Computer-aided design↗

Methods for Assessing Opportunities for Ring Dam Pumped Storage Hydropower

There is growing interest in new pumped storage hydropower (PSH) deployment to provide a range of grid flexibility, reliability, and resiliency services under an evolving and uncertain future power sector. The National Laboratory of the Rockies develops open PSH resource assessment and cost modeling tools to help evaluate PSH deployment opportunities, and this report describes expansions to those tools to consider an additional PSH system configuration - ring-dam reservoirs built on flat topographical features that are constructed from roller-compacted concrete material. This reservoir type is common among current PSH proposals and requires new methods to identify sites with this reservoir geometry throughout the United States and characterize the associated dam cost. Cost characterization for ring dam reservoirs required collecting historical dam cost data for earthen, rockfill, and roller-compacted concrete dams and regressing equations that relate costs between alternative materials. The ring dam site identification algorithm follows a 5-step procedure to identify circular geometry reservoirs. Once ring dam reservoirs are identified, they are then paired with potential dry-gully reservoirs, and the full set of potential paired reservoirs is cost-optimized to produce a least-cost set of potential PSH sites with no overlapping reservoirs. The resulting analysis found 1,663 ring-dam to dry-gully systems in the contiguous United States that are lower cost than any overlapping dry-gully to dry-gully systems, 29 in Alaska, and none in Hawaii or Puerto Rico. These systems constitute 1.5 TW of capacity in the contiguous United States and nearly 29 GW in Alaska, demonstrating that under suitable topography and head, ring-dam systems can provide cost-effective PSH opportunities. The greatest density of these opportunities are found in the intermountain west where there are mesas and flat land at bases of mountain ranges, but continued work could incorporate additional site characteristics or consider more complex reservoir shapes to find additional PSH deployment opportunities.

13 HYDRO ENERGY↗

Modeling and Analysis of Wind Turbine Wake Vortex Evolution Due to Time-Constant Spatial Variations in Atmospheric Flow

Modern utility-scale wind turbines are evolving toward larger, lighter, and more flexible designs to meet the growing demand for renewable energy while minimizing logistical costs. However, these advancements in lightweight design result in heightened aeroelastic sensitivity, leading to complex interactions which affect the rotor’s capacity to withstand aerodynamic loading and the cascading effects that manifest in the wake’s vortex-structure evolution under variable atmospheric conditions. In this paper, we analyze the influence of stream-wise fluctuating atmospheric flow conditions on wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex–wake interactions for a range of conditions with spatially variant atmospheric flow. CODEF solutions for turbine operation in wind conditions featuring only one parameter fluctuation are compared to wind conditions with several wind parameter variations in combination. By isolating individual inflow variations and comparing them to multi-parameter scenarios, we determine the contributions of each atmospheric factor to rotor dynamics, wake evolution, and downstream wind farm interactions. The purpose of this paper is to analyze the effects of spatial variations in atmospheric flow on the topological evolution of wind turbine vortex wakes, which constitutes a gap in the current understanding of wind turbine wake dynamics. The insights gained from this study are particularly valuable for the development of wind farm control strategies aimed at mitigating the adverse effects of wake interactions, enhancing energy capture, and improving the overall stability of wind farm operations. With these insights, we aim to contribute to the development of modeling and simulation tools to optimize utility-scale wind power plants operating in diverse atmospheric environments.

Farrell, Alayna (ORCID:000000023555720X)↗

Ab initio quantum scattering calculations for the CO–O 2 system and a new CO–O 2 potential energy surface: O 2 and air broadening of the R(0) line in CO

We present ab initio calculations of the collisional broadening of the R(0) pure rotational line in CO (at 115 GHz) perturbed by O 2 . Our calculations are done in a fully quantum way by solving close-coupling quantum-scattering equations without any approximations. We also report a new, highly accurate CO–O 2 potential energy surface on which we did the quantum-scattering calculations. The calculated collisional broadening agrees with the available experimental data in a wide temperature range. The calculated collisional shift is negligible compared to the broadening, which is also consistent with the experimental data. We combine this result with our previous calculations for the same line in CO perturbed by N 2 [Józwiak et al., J. Chem. Phys. 154, 054314 (2021)]; the obtained air-perturbed broadening of the R(0) pure rotational line in CO and its temperature dependence perfectly agree with the HITRAN database. This result constitutes an important step toward developing a methodology for providing accurate ab initio reference data on spectroscopic collisional line-shape parameters for molecular systems relevant to the Earth’s atmosphere and for populating spectroscopic line-by-line databases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Crystal structure of calcium-ferrite type NaAlSiO4 up to 45 GPa

Abstract Alkali-rich aluminous high-pressure phases including calcium-ferrite (CF) type NaAlSiO4 are thought to constitute ~20% by volume of subducted mid-ocean ridge basalt (MORB) under lower mantle conditions. As a potentially significant host for incompatible elements in the deep mantle, knowledge of the crystal structure and physical properties of CF-type phases is therefore important to understanding the crystal chemistry of alkali storage and recycling in the Earth’s mantle. We determined the evolution of the crystal structure of pure CF-NaAlSiO4 and Fe-bearing CF-NaAlSiO4 at pressures up to ~45 GPa using synchrotron-based, single-crystal X-ray diffraction. Using the high-pressure lattice parameters, we also determined a third-order Birch-Murnaghan equation of state, with V0 = 241.6(1) Å3, KT0 = 220(4) GPa, and KT0′ = 2.6(3) for Fe-free CF, and V0 = 244.2(2) Å3, KT0 = 211(6) GPa, and KT0′ = 2.6(3) for Fe-bearing CF. The addition of Fe into CF-NaAlSiO4 resulted in a 10 ± 5% decrease in the stiffest direction of linear compressibility along the c-axis, leading to stronger elastic anisotropy compared with the Fe-free CF phase. The NaO8 polyhedra volume is 2.6 times larger and about 60% more compressible than the octahedral (Al,Si)O6 sites, with K0NaO8 = 127 GPa and K0(Al,Si)O6 ~304 GPa. Raman spectra of the pure CF-type NaAlSiO4 sample shows that the pressure coefficient of the mean vibrational mode, 1.60(7) cm–1/GPa, is slightly higher than 1.36(6) cm−1/GPa obtained for the Fe-bearing CF-NaAlSiO4 sample. The ability of CF-type phases to contain incompatible elements such as Na beyond the stability field of jadeite requires larger and less-compressible NaO8 polyhedra. Detailed high-pressure crystallographic information for the CF phases provides knowledge on how large alkali metals are hosted in alumina framework structures with stability well into the lowermost mantle.

Geochemistry & Geophysics↗

Can the Solar Atmosphere Generate Very-High-Energy Cosmic Rays?

The origin and acceleration of high-energy particles, constituting cosmic rays, is likely to remain an important topic in modern astrophysics. Among the two categories galactic and solar cosmic rays, the latter are much less investigated. The primary source of solar cosmic ray particles are impulsive explosions of the magnetized plasma, known as solar flares and coronal mass ejections. These particles, however, are characterized by relatively low energies compared to their galactic counterparts. In this work, we explore the resonance wave–wave (RWW) interaction between the polarized electromagnetic radiation emitted by the solar active regions and the quantum waves associated with high-energy, relativistic electrons generated during solar flares. Mathematically, the RWW interaction problem boils down to analyzing a Klein–Gordon Equation (spinless electrons) embedded in the electromagnetic field. We find that RWW could accelerate the relativistic electrons to enormous energies even comparable to energies in the galactic cosmic rays.

acceleration of particles↗

Interacting quantum and classical waves: Resonant and non-resonant energy transfer to electrons immersed in an intense electromagnetic wave

Dynamics of electrons subjected to a constant amplitude classical electromagnetic (EM) wave is investigated as a fundamental, representative problem in the physics of interacting quantum and classical waves. In the nonrelativistic regime (electrons as Schrödinger waves), the electron energy acquires a constant and a time dependent part. Driven by EM waves, both parts scale strongly with the amplitude, but we expect no resonant enhancement since the parallel electron “speed” of nonrelativistic electrons could never match the wave phase velocity. In the relativistic regime (electron as a Klein–Gordon wave), however, a class of electron waves (with parallel speed matching the EM phase speed) are resonantly excited to extremely high energies. Such a direct resonant energy transfer from intense electromagnetic waves constitutes a mechanism that could, in principle, power the most energetic of cosmic rays (this mechanism will work on protons just as well). Some predictions of the theory will, hopefully, be tested in laboratory laser experiments. In conclusion, the nonrelativistic calculations will also be examined in the context of recent experiments using photon-induced near-field electron microscopy in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗

Equation of state and strength of diamond in high-pressure ramp loading

Diamond is used extensively as a component in high-energy-density experiments, but existing equation of state (EOS) models do not capture its observed response to dynamic loading. In particular, in contrast with first-principles theoretical models of equilibrium multiphase EOS, no solid-solid phase changes have been detected, and no general-purpose EOS models match the measured ambient isotherm. We have performed density functional theory (DFT) calculations of the diamond phase to ~10 TPa, well beyond its predicted range of thermodynamic stability, and used these results as the basis of a Mie-Grüneisen EOS. We also performed DFT calculations of the elastic moduli, and calibrated an algebraic elasticity model for use in simulations. We then estimated the flow stress of diamond by comparison with the stress-density relation measured experimentally in ramp-loading experiments. Furthermore, the resulting constitutive model allows us to place a constraint on the Taylor-Quinney factor (the fraction of plastic work converted to heat) from the observation that diamond does not melt on ramp compression.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Partially averaged Navier-Stokes closure modeling for variable-density turbulent flow

We report this work extends the framework of the partially averaged Navier-Stokes (PANS) equations to variable-density flow, i.e., multimaterial and/or compressible mixing problems with density variations and production of turbulence kinetic energy by both shear and buoyancy mechanisms. The proposed methodology is utilized to derive the PANS BHR-LEVM closure. This includes a priori testing to analyze and develop guidelines toward the efficient selection of the parameters controlling the physical resolution and, consequently, the range of resolved scales of PANS. Two archetypal test-cases involving transient turbulence, hydrodynamic instabilities, and coherent structures are used to illustrate the accuracy and potential of the method: the Taylor-Green vortex at Reynolds number Re = 3000, and the Rayleigh-Taylor flow at Atwood number 0.5 and (Re) max ≈ 500. These representative problems, for which turbulence is generated by shear and buoyancy processes, constitute the initial validation space of the new model, and their results are comprehensively discussed in two subsequent studies. The computations indicate that PANS can accurately predict the selected flow problems, resolving only a fraction of the scales of large-eddy simulation and direct numerical simulation strategies. The results also reiterate that the physical resolution of the PANS model must guarantee that the key instabilities and coherent structures of the flow are resolved. The remaining scales can be modeled through an adequate turbulence scale-dependent closure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging: Theory, algorithms, and applications

Plug-and-play (PnP) priors constitute one of the most widely used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly successful applications of PnP algorithms include biomicroscopy, computerized tomography (CT), magnetic resonance imaging (MRI), and joint ptychotomography. This article presents a unified and principled review of PnP by tracing its roots, describing its major variations, summarizing main results, and discussing applications in computational imaging. Additionally, we also point the way toward further developments by discussing recent results on equilibrium equations that formulate the problem associated with PnP algorithms.

97 MATHEMATICS AND COMPUTING↗

SAM-ML: Integrating data-driven closure with nuclear system code SAM for improved modeling capability

Advanced reactors often involve complicated thermal-fluid (T-F) phenomena. Modeling such phenomena with the traditional one-dimensional (1-D) system code is a challenging task. The System Analysis Module (SAM), a modern nuclear system code, has developed a coarse mesh multi-dimensional (multi-D) flow model to capture the spatial effect of T-F phenomena in advanced reactors. As a coarse mesh solver, constitutive relations are required for SAM's multi-D model for unresolved fine-scale physics, such as turbulence. Here this work presents a novel approach that integrates neural networks as data-driven closure for SAM's multi-D flow model. The data-driven closure is trained with fine-resolution data to ensure its accuracy while maintaining a coarse mesh setup to ensure its efficiency and consistency with SAM. We demonstrate the applicability of this SAM-ML capability in an open volume thermal stratification problem, where a neural network model serves as the eddy viscosity closure. A customized interface between the neural network and SAM is developed to ensure flexible and efficient data exchange. The SAM-ML results demonstrate superior performance compared to SAM's built-in zero-equation eddy viscosity closure. The case study shows that although the generalization capability of the data-driven closure still needs to be improved for different transient case or different geometric setup, SAM -ML demonstrates good potential for challenging simulation problems with improved accuracy and computational efficiency.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. Additionally, we analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

42 ENGINEERING↗

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

97 MATHEMATICS AND COMPUTING↗

Exploring the NΛ–NΣ coupled system with high precision correlation techniques at the LHC

The interaction of Λ and Σ hyperons (Y) with nucleons (N) is strongly influenced by the coupled-channel dynamics. Due to the small mass difference of the NΛ and NΣ systems, the sizable coupling strength of the NΣ↔NΛ processes constitutes a crucial element in the determination of the NΛ interaction. In this letter we present the most precise measurements on the interaction of pΛ pairs, from zero relative momentum up to the opening of the NΣ channel. The correlation function in the relative momentum space for pΛ ⊕$\bar{p}$$\bar{Λ}$ pairs measured in high-multiplicity triggered pp collisions at $\sqrt{s}$=13 TeV at the LHC is reported. The opening of the inelastic NΣ channels is visible in the extracted correlation function as a cusp-like structure occurring at relative momentum k*=289 MeV/c. This represents the first direct experimental observation of the NΣ↔NΛ coupled channel in the pΛ system. The correlation function is compared with recent chiral effective field theory calculations, based on different strengths of the NΣ↔NΛ transition potential. A weaker coupling, as possibly supported by the present measurement, would require a more repulsive three-body NNΛ interaction for a proper description of the Λ in-medium properties, which has implications on the nuclear equation of state and for the presence of hyperons inside neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Magnetars and axion-like particles: probes with the hard X-ray spectrum

Quiescent hard X-ray and soft gamma-ray emission from neutron stars constitute a promising frontier to explore axion-like-particles (ALPs). ALP production in the core peaks at energies of a few keV to a few hundreds of keV; subsequently, the ALPs escape and convert to photons in the magnetosphere. The emissivity goes as ~T 6 while the conversion probability is enhanced for large magnetic fields, making magnetars, with their high core temperatures and strong magnetic fields, ideal targets for probing ALPs. We compute the energy spectrum of photons resulting from conversion of ALPs in the magnetosphere and then compare it against hard X-ray data from NuSTAR, INTEGRAL, and XMM-Newton, for a set of eight magnetars for which such data exists. Upper limits are placed on the product of the ALP-nucleon and ALP-photon couplings. For the production in the core, we perform a calculation of the ALP emissivity in degenerate nuclear matter modeled by a relativistic mean field theory. The reduction of the emissivity due to improvements to the one-pion exchange approximation is incorporated, as is the suppression of the emissivity due to proton superfluidity in the neutron star core. A range of core temperatures is considered, corresponding to different models of the steady heat transfer from the core to the stellar surface. For the subsequent conversion, we solve the coupled differential equations mixing ALPs and photons in the magnetosphere. The conversion occurs due to a competition between the dipolar magnetic field and the photon refractive index induced by the external magnetic field. Semi-analytic expressions are provided alongside the full numerical results. Furthermore, we also present an analysis of the uncertainty on the axion limits we derive due to the uncertainties in the magnetar masses, nuclear matter equation of state, and the proton superfluid critical temperature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗