Astrophysical Applications Research Articles

Solve third order Lane-Emden-Fowler equation by Adomian decomposition method and quartic trigonometric B-spline method

In this work, we study the Lane-Emden-Fowler equation which has a wide range of applications in astrophysics, classical and quantum mechanics. Firstly, we convert this nonlinear differential equation into an equivalent integral equation. We employ the powerful Adomian decomposition method to derive an analytical solution that will also lead to numerical solutions. Moreover, we exhibit two theorems to ensure the uniqueness of the solution of the problem and to confirm the convergence of the proposed scheme. In addition, we use quartic trigonometric B-spline as a powerful numerical method to achieve numerical solutions. Finally we present a comparison between the proposed methods to show their accuracy performance. Proper graphs are also provided to illustrate the obtained solutions.

Swift: A modern highly-parallel gravity and smoothed particle hydrodynamics solver for astrophysical and cosmological applications

Abstract Numerical simulations have become one of the key tools used by theorists in all the fields of astrophysics and cosmology. The development of modern tools that target the largest existing computing systems and exploit state-of-the-art numerical methods and algorithms is thus crucial. In this paper, we introduce the fully open-source highly-parallel, versatile, and modular coupled hydrodynamics, gravity, cosmology, and galaxy-formation code Swift. The software package exploits hybrid shared- and distributed-memory task-based parallelism, asynchronous communications, and domain-decomposition algorithms based on balancing the workload, rather than the data, to efficiently exploit modern high-performance computing cluster architectures. Gravity is solved for using a fast-multipole-method, optionally coupled to a particle mesh solver in Fourier space to handle periodic volumes. For gas evolution, multiple modern flavours of Smoothed Particle Hydrodynamics are implemented. Swiftalso evolves neutrinos using a state-of-the-art particle-based method. Two complementary networks of sub-grid models for galaxy formation as well as extensions to simulate planetary physics are also released as part of the code. An extensive set of output options, including snapshots, light-cones, power spectra, and a coupling to structure finders are also included. We describe the overall code architecture, summarise the consistency and accuracy tests that were performed, and demonstrate the excellent weak-scaling performance of the code using a representative cosmological hydrodynamical problem with ≈300 billion particles. The code is released to the community alongside extensive documentation for both users and developers, a large selection of example test problems, and a suite of tools to aid in the analysis of large simulations run with Swift.

Unified Framework for Diffusion Generative Models in SO(3): Applications in Computer Vision and Astrophysics

Diffusion-based generative models represent the current state-of-the-art for image generation. However, standard diffusion models are based on Euclidean geometry and do not translate directly to manifold-valued data. In this work, we develop extensions of both score-based generative models (SGMs) and Denoising Diffusion Probabilistic Models (DDPMs) to the Lie group of 3D rotations, SO(3). SO(3) is of particular interest in many disciplines such as robotics, biochemistry and astronomy/cosmology science. Contrary to more general Riemannian manifolds, SO(3) admits a tractable solution to heat diffusion, and allows us to implement efficient training of diffusion models. We apply both SO(3) DDPMs and SGMs to synthetic densities on SO(3) and demonstrate state-of-the-art results. Additionally, we demonstrate the practicality of our model on pose estimation tasks and in predicting correlated galaxy orientations for astrophysics/cosmology.

Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body’s middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions’ extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications.

Targeted optimization in small-scale atomic structure calculations: application to Au I

The lack of reliable atomic data can be a severe limitation in astrophysical modelling, in particular of events such as kilonovae that require information on all neutron-capture elements across a wide range of ionization stages. Notably, the presence of non-orthonormalities between electron orbitals representing configurations that are close in energy can introduce significant inaccuracies in computed energies and transition probabilities. Here, we propose an explicit targeted optimization (TO) method that can effectively circumvent this concern while retaining an orthonormal orbital basis set. We illustrate this method within the framework of small-scale atomic structure models of Au I, using the Grasp2018 multiconfigurational Dirac–Hartree–Fock atomic structure code. By comparing to conventional optimization schemes we show how a TO approach improves the energy level positioning and ordering. TO also leads to better agreement with experimental data for the strongest E1 transitions. This illustrates how small-scale models can be significantly improved with minor computational costs if orbital non-orthonormalities are considered carefully. These results should prove useful to multi-element atomic structure calculations in, for example, astrophysical opacity applications involving neutron-capture elements.

FORKLENS: Accurate weak-lensing shear measurement with deep learning

Context. Weak gravitational lensing is one of the most important probes of the nature of dark matter and dark energy. In order to extract cosmological information from next-generation weak lensing surveys (e.g., Euclid, Roman, LSST, and CSST) as much as possible, accurate measurements of weak lensing shear are required. Aims. There are existing algorithms to measure the weak lensing shear on imaging data, which have been successfully applied in previous surveys. In the meantime, machine learning (ML) has been widely recognized in various astrophysics applications in modeling and observations. In this work, we present a fully deep-learning-based approach to measuring weak lensing shear accurately. Methods. Our approach comprises two modules. The first one contains a convolutional neural network (CNN) with two branches for taking galaxy images and point spread function (PSF) simultaneously, and the output of this module includes the galaxy’s magnitude, size, and shape. The second module includes a multiple-layer neural network (NN) to calibrate weak-lensing shear measurements. We name the program FORKLENS and make it publicly available online. Results. Applying FORKLENS to CSST-like mock images, we achieve consistent accuracy with traditional approaches (such as moment-based measurement and forward model fitting) on the sources with high signal-to-noise ratios (S/N > 20). For the sources with S/N < 10, FORKLENS exhibits an ~36% higher Pearson coefficient on galaxy ellipticity measurements. Conclusions. After adopting galaxy weighting, the shear measurements with FORKLENS deliver accuracy levels to 0.2%. The whole procedure of FORKLENS is automated and costs about 0.7 milliseconds per galaxy, which is appropriate for adequately taking advantage of the sky coverage and depth of the upcoming weak lensing surveys.

Theories of Relativistic Dissipative Fluid Dynamics.

Relativistic dissipative fluid dynamics finds widespread applications in high-energy nuclear physics and astrophysics. However, formulating a causal and stable theory of relativistic dissipative fluid dynamics is far from trivial; efforts to accomplish this reach back more than 50 years. In this review, we give an overview of the field and attempt a comparative assessment of (at least most of) the theories for relativistic dissipative fluid dynamics proposed until today and used in applications.

Calculations of energy levels, transition rates, lifetimes and Landé g factors for silicon-like Kr XXIII

The multiconfiguration Dirac–Hartree–Fock (MCDHF) method is employed to calculate excitation energies, transition rates, lifetimes and Landé g factors for the lowest 700 levels belonging to the 22 configurations 3s23p{3l,4l′}, 3s3p2{3l,4l′}, 3s23d{3d,4s,4p}, 3s{3p3d2,3d3}, 3p{3p3,3p23d,3p3d2,3d3}, 3d4 with l = 1, 2 and l′ = 0, 1, 2, 3 in Kr XXIII. The present excitation energies are compared with available experimental and theoretical values. The mean relative difference between our results and the values provided by the National Institute of Standards and Technology (NIST) is only 0.05%, which suggests a good agreement. The uncertainties of the transition rates are estimated based on quantitative and qualitative evaluation method which analyzes the dependencies of the line strength S on the gauge parameter G. It is observed that 49.6% of E1 S values have uncertainties of ≤ 1% (AA) and over 82% have uncertainties of ≤ 3% (A). The present wavelengths and transition rates are compared with the experimental values and generally good agreements have been achieved. For lifetime, the present MCDHF values fall well within the range of experimental error. Comparison of the computed Landé g factors is also made with the Landé g factors in pure LS-coupling. These accurate data can be useful for fusion plasma research and astrophysical applications.

New acetylene line list near 3.8-μm - Part III - 12C13CH2 and 12C2HD

The intensities of minor acetylene isotopologues 12C13CH2 and 12C2HD have been studied from Fourier transform spectra of acetylene in natural abundance using high optical path length. This study completes the work performed in the two first paper of the series (JQSRT 2023;295:108,413 and JQSRT 2023;311:108,771) where 71 bands of 12C2H2 were studied in the ΔP = 4 spectral region (∼2400–2900 cm−1). In this work, 692 measured line intensities allowed to derive vibrational transition dipole moment squared (and sometimes Herman-Wallis coefficients) for 11 bands of 12C13CH2 and 6 bands of 12C2HD. Using line positions and broadening parameters from literature, a line list has been generated for atmospheric and astrophysical applications.

Harnessing the Power of Quantum: Applications in Astrophysics and Cosmology

Harnessing the Power of Quantum: Applications in Astrophysics and Cosmology

A quintic B-spline technique for a system of Lane-Emden equations arising in theoretical physical applications

<abstract> <p>In the present study, we introduce a collocation approach utilizing quintic B-spline functions as bases for solving systems of Lane Emden equations which have various applications in theoretical physics and astrophysics. The method derives a solution for the provided system by converting it into a set of algebraic equations with unknown coefficients, which can be easily solved to determine these coefficients. Examining the convergence theory of the proposed method reveals that it yields a fourth-order convergent approximation. It is confirmed that the outcomes are consistent with the theoretical investigation. Tables and graphs illustrate the proficiency and consistency of the proposed method. Findings validate that the newly employed method is more accurate and effective than other approaches found in the literature. All calculations have been performed using Mathematica software.</p> </abstract>

Scalable stellar evolution forecasting

Many astrophysical applications require efficient yet reliable forecasts of stellar evolution tracks. One example is population synthesis, which generates forward predictions of models for comparison with observations. The majority of state-of-the-art rapid population synthesis methods are based on analytic fitting formulae to stellar evolution tracks that are computationally cheap to sample statistically over a continuous parameter range. The computational costs of running detailed stellar evolution codes, such as MESA, over wide and densely sampled parameter grids are prohibitive, while stellar-age based interpolation in-between sparsely sampled grid points leads to intolerably large systematic prediction errors. In this work, we provide two solutions for automated interpolation methods that offer satisfactory trade-off points between cost-efficiency and accuracy. We construct a timescale-adapted evolutionary coordinate and use it in a two-step interpolation scheme that traces the evolution of stars from zero age main sequence all the way to the end of core helium burning while covering a mass range from 0.65 to 300 M⊙. The feedforward neural network regression model (first solution) that we train to predict stellar surface variables can make millions of predictions, sufficiently accurate over the entire parameter space, within tens of seconds on a 4-core CPU. The hierarchical nearest-neighbor interpolation algorithm (second solution) that we hard-code to the same end achieves even higher predictive accuracy, the same algorithm remains applicable to all stellar variables evolved over time, but it is two orders of magnitude slower. Our methodological framework is demonstrated to work on the MESA ISOCHRONES AND STELLAR TRACKS (Choi et al. 2016) data set, but is independent of the input stellar catalog. Finally, we discuss the prospective applications of these methods and provide guidelines for generalizing them to higher dimensional parameter spaces.

Mechanics of geodesics in information geometry and black hole thermodynamics

In this paper, we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers–Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner–Nordström black holes.

Investigation of the valence-shell excitations of molecular carbon disulfide by high-energy electron scattering

Absolute generalized oscillator strengths of the valence-shell excitations of carbon disulfide have been determined by a joint investigation of a fast electron impact experiment and equation of motion coupled cluster with singles and doubles (EOM-CCSD) calculations. Based on the present experimental and theoretical results, the transition nature of the excitations are elucidated, and some controversies about the transition assignments are resolved. By extrapolating the generalized oscillator strengths to zero momentum transfer, the corresponding optical oscillator strengths were determined, which provide a cross-check to the previous experimental and theoretical results. Moreover, the integral cross sections of the valence-shell excitations from their excitation thresholds to 5000 eV have been obtained by means of the BE-scaling method. The oscillator strengths and integral cross-sections complement the fundamental data of carbon disulfide and supply important applications in astrophysics and atmospheric physics.

Waveform systematics in identifying strongly gravitationally lensed gravitational waves: posterior overlap method

Gravitational lensing has been extensively observed for electromagnetic signals, but not yet for gravitational waves (GWs). Detecting lensed GWs will have many astrophysical and cosmological applications, and becomes more feasible as the sensitivity of the ground-based detectors improves. One of the missing ingredients to robustly identify lensed GWs is to ensure that the statistical tests used are robust under the choice of underlying waveform models. We present the first systematic study of possible waveform systematics in identifying candidates for strongly lensed GW event pairs, focusing on the posterior overlap method. To this end, we compare Bayes factors from all posteriors using different waveforms included in GWTC data releases from the first three observing runs (O1–O3). We find that waveform choice yields a wide spread of Bayes factors in some cases. However, it is likely that no event pairs from O1 to O3 were missed due to waveform choice. We also perform parameter estimation with additional waveforms for interesting cases, to understand the observed differences. We also briefly explore if computing the overlap from different runs for the same event can be a useful metric for waveform systematics or sampler issues, independent of the lensing scenario.

Flow morphology of a supersonic gravitating sphere

ABSTRACT Stars and planets move supersonically in a gaseous medium during planetary engulfment, stellar interactions, and within protoplanetary discs. For a nearly uniform medium, the relevant parameters are the Mach number and the size of the body, R, relative to its accretion radius, RA. Over many decades, numerical and analytical work has characterized the flow, the drag on the body, and the possible suite of instabilities. Only a limited amount of work has treated the stellar boundary as it is in many of these astrophysical settings, a hard sphere at R. Thus, we present new 3D athena++  hydrodynamic calculations for a large range of parameters. For RA ≪ R, the results are as expected for pure hydrodynamics with minimal impact from gravity, which we verify by comparing to experimental wind tunnel data in air. When RA ≈ R, a hydrostatically supported separation bubble forms behind the gravitating body, exerting significant pressure on the sphere and driving a recompression shock, which intersects with the bow shock. For RA ≫ R, the bubble transitions into an isentropic, spherically symmetric halo, as seen in earlier works. These two distinct regimes of flow morphology may be treated separately in terms of their shock stand-off distance and drag coefficients. Most importantly for astrophysical applications, we propose a new formula for the dynamical friction, which depends on the ratio of the shock stand-off distance to RA. That exploration also reveals the minimum size of the simulation domain needed to accurately capture the deflection of incoming streamlines due to gravity.

Evolution of MHD torus and mass outflow around spinning AGNs

ABSTRACT We perform axisymmetric, 2D magnetohydrodynamic simulations to investigate accretion flows around spinning active galactic nuclei. To mimic the space–time geometry of spinning black holes, we consider effective Kerr potential, and the mass of the black holes is 108 M⊙. We initialize the accretion disc with a magnetized torus by adopting the toroidal component of the magnetic vector potential. The initial magnetic field strength is set by using the plasma beta parameter (β0). We observe self-consistent turbulence generated by magneto rotational instability (MRI) in the disc. The MRI turbulence transports angular momentum in the disc, resulting in an angular momentum distribution that approaches a Keplerian distribution. We investigate the effect of the magnetic field on the dynamics of the torus and associated mass outflow from the disc around a maximally spinning black hole (ak = 0.99). For the purpose of our analysis, we investigate the magnetic state of our simulation model. The model β0 = 10 indicates the behaviour similar to the ‘magnetically arrested disc’ state, and all the other low magnetic model remains in the SANE state. We observe that mass outflow rates are significantly enhanced with the increased magnetic field in the disc. We find a positive correlation between the magnetic field and mass outflow rates. We also investigate the effect of black hole spin on the magnetized torus evolution. However, we have not found any significant effect of black hole spin on mass outflows in our model. Finally, we discuss the possible astrophysical applications of our simulation results.

Collisional excitation of PO+ by para-H2: potential energy surface, scattering calculations, and astrophysical applications

ABSTRACT We report the derivation of rate coefficients for the rotational (de-)excitation of PO+ induced by collisions with H2. The calculations were performed on a 4D potential energy surface, obtained on top of highly accurate ab initio energy points. Preliminary tests pointed out the low influence of the coupling between j = 0 and the higher rotational levels of H2 on the cross-sections values, thus allowing to neglect the rotational structure of H2. On this basis, state-to-state collisional rate coefficients were derived for temperatures ranging from 5 to 200 K. Radiative transfer calculations have been used to model the recent observation of PO+ in the G+0.693–0.027 molecular cloud, in order to evaluate the possible impact of non-LTE models on the determination of its physical conditions. The derived column density was found to be approximately ∼ 3.7 × 1011 cm−2, which is 60% (a factor of ∼ 1.7) smaller than the previously LTE-derived value. Extensive simulations show that PO+ low-j rotational lines exhibit maser behaviour at densities between 104 and 106 cm−3, thus highlighting the importance of a proper treatment of the molecular collisions to accurately model PO+ emissions in the interstellar medium.

High-order implicit shock tracking boundary conditions for flows with parametrized shocks

High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with non-smooth features. This ensures the non-smooth features are perfectly represented by inter-element jumps and high-order basis functions approximate smooth regions of the solution without nonlinear stabilization, which leads to accurate approximations on traditionally coarse meshes. In this work, we introduce a robust implicit shock tracking framework specialized for problems with parameter-dependent lead shocks (i.e., shocks separating a farfield condition from the downstream flow), which commonly arise in high-speed aerodynamics and astrophysics applications. After a shock-aligned mesh is produced at one parameter configuration, all elements upstream of the lead shock are removed and the nodes on the lead shock are positioned for new parameter configurations using the implicit shock tracking solver. The proposed framework can be used for most many-query applications involving parametrized lead shocks such as optimization, uncertainty quantification, parameter sweeps, “what-if” scenarios, or parameter-based continuation. We demonstrate the robustness and flexibility of the framework using a one-dimensional space-time Riemann problem, and two- and three-dimensional supersonic and hypersonic benchmark problems.

Unsteady 3D MHD Boundary Layer Stream for Non-Newtonian Power-Law Fluid Near Stagnation Point of Moving Surfaces

An unsteady three-dimensional MHD boundary layer is a fluid flow region near a surface where magnetic fields are present and interact with the fluid flow, causing it to become unsteady. This type of flow is commonly found in various astrophysical and technological applications, such as in plasmas and fusion reactors. The 3D nature of the flow introduces additional complexities to the flow dynamics, making the study and modeling of unsteady MHD boundary layers a challenging and active area of research. The unsteady boundary layer flow of fluid over a moving stagnation surface is theoretically examined in the current work with the impression of a magnetic field. The exact outcomes of the governing equations for the flow domain are obtained by utilizing the shooting phenomena. The specified analytical outcomes are also obtained for some cases. Detailed discussions of the parameters involved are confirmed both physically and graphically. Numerical results for both profiles are presented graphically. The study and modeling of unsteady 3D MHD boundary layers is imperative for a thorough understanding of various physical phenomena, improving the performance of technological systems, and advancing our knowledge of fluid dynamics.