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We study star formation variability, or burstiness, as a method to constrain and compare different galaxy formation models at high redshift using the Azahar simulation suite. The models range from magneto-hydrodynamics with a magneto-thermo-turbulent prescription for star formation (iMHD) to more sophisticated setups incorporating radiative transfer (RTiMHD) and cosmic ray physics (RTnsCRiMHD). Analysing a sample of galaxies at redshifts $z=4-10$, we find that the RTnsCRiMHD model exhibits more regular star formation periodicity compared to iMHD and RTiMHD, as revealed by the Lomb-Scargle periodogram. While the RTiMHD model captures a notable degree of stochasticity in star formation without cosmic rays, RTnsCRiMHD galaxies display even greater scatter in the burst intensity and in the scatter around the star-forming main sequence. To evaluate the burstiness in RTnsCRiMHD against observations, we generate a mock spectrum during a mini-quenching event at $z=7.5$. This spectrum aligns well with the low-mass quiescent galaxy JADES-GS-z7-01-QU observed at $z=7.3$, though some discrepancies attributed to stellar metallicity hint at a composite spectrum. Our findings highlight the importance of including complex physical processes like cosmic rays and radiative transfer in simulations to accurately capture the bursty nature of star formation in high-redshift galaxies. Future JWST observations, particularly regarding the scatter around the star-forming main sequence, have the potential to refine and guide the next generation of galaxy formation models., Comment: 10 pages, 4 figures, 1 table, comments welcome

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 energy packets, to synthesize the observed spectropolarimetric signal at a given viewing direction in a 3-D time-dependent radiative transfer program. Compared to the event-based technique (EBT) proposed by (Bulla et al. 2015), our algorithm significantly reduces the computation time and increases the Monte-Carlo signal-to-noise ratio. Using a 1-D spherical symmetric type Ia supernova (SN Ia) ejecta model DDC10 and its derived 3-D model, the IBT algorithm has successfully passed the verification of: (1) spherical symmetry; (2) mirror symmetry; (3) cross comparison on a 3-D SN model with direct-counting technique (DCT) and EBT. Notably, with our algorithm implemented in the 3-D Monte-Carlo radiative transfer code SEDONA, the computation time is faster than EBT by a factor of $10-30$, and the signal-to-noise (S/N) ratio is better by a factor of $5-10$, with the same number of Monte-Carlo quanta., Comment: Gesa

The wealth of high-quality observational data from the epoch of reionization that will become available in the next decade motivates further development of modeling techniques for their interpretation. Among the key challenges in modeling reionization are (1) its multi-scale nature, (2) the computational demands of solving the radiative transfer (RT) equation, and (3) the large size of reionization's parameter space. In this paper, we present and validate a new RT code designed to confront these challenges. FlexRT (Flexible Radiative Transfer) combines adaptive ray tracing with a highly flexible treatment of the intergalactic ionizing opacity. This gives the user control over how the intergalactic medium (IGM) is modeled, and provides a way to reduce the computational cost of a FlexRT simulation by orders of magnitude while still accounting for small-scale IGM physics. Alternatively, the user may increase the angular and spatial resolution of the algorithm to run a more traditional reionization simulation. FlexRT has already been used in several contexts, including simulations of the Lyman-$\alpha$ forest of high-$z$ quasars, the redshifted 21cm signal from reionization, as well as in higher resolution reionization simulations in smaller volumes. In this work, we motivate and describe the code, and validate it against a set of standard test problems from the Cosmological Radiative Transfer Comparison Project. We find that FlexRT is in broad agreement with a number of existing RT codes in all of these tests. Lastly, we compare FlexRT to an existing adaptive ray tracing code to validate FlexRT in a cosmological reionization simulation., Comment: 40+7 pages, 24 figures, submitted to JCAP. Comments welcome

This paper presents a kinetic model for the coupled evolution of radiation, electrons, and ions in a radiation plasma system. The model is solved using two methods. The gas-kinetic scheme (GKS) for electron and ion hydrodynamics and the unified gas-kinetic scheme (UGKS) for non-equilibrium radiative transfer. The UGKS accurately captures multiscale photon transport from free streaming to diffusion across varying fluid opacities. This approach enables the scheme to model equilibrium plasma with non-equilibrium radiation transport. The model is validated through several test cases, including radiative transfer in kinetic and diffusion regimes, Marshak wave, Radiative shock, 3T(three-temperature) double lax shock tube problem, two-dimensional Sedov blast wave, and two-dimensional tophat based problem. These tests demonstrate the current scheme's capability to handle diverse radiation plasma scenarios.

An asymptotic-preserving (AP) implicit-explicit PN numerical scheme is proposed for the gray model of the radiative transfer equation, where the first- and second-order numerical schemes are discussed for both the linear and nonlinear models. The AP property of this numerical scheme is proved theoretically and numerically, while the numerical stability of the linear model is verified by Fourier analysis. Several classical benchmark examples are studied to validate the efficiency of this numerical scheme.

Outflows are critical components of many astrophysical systems, including accreting compact binaries and active galactic nuclei (AGN). These outflows can significantly affect a system's evolution and alter its observational appearance by reprocessing the radiation produced by the central engine. Sirocco (Simulating Ionization and Radiation in Outflows Created by Compact Objects - or "the code formerly known as Python") is a Sobolev-based Monte Carlo ionization and radiative transfer code. It is designed to simulate the spectra produced by any system with an azimuthally-symmetric outflow, from spherical stellar winds to rotating, biconical accretion disc winds. Wind models can either be parametrized or imported, e.g. from hydrodynamical simulations. The radiation sources include an optically thick accretion disc and various central sources with flexible spectra and geometries. The code tracks the "photon packets" produced by the sources in any given simulation as they traverse and interact with the wind. The code assumes radiative near-equilibrium, so the thermal and ionization state can be determined iteratively from these interactions. Once the physical properties in the wind have converged, Sirocco can be used to generate synthetic spectra at a series of observer sightlines. Here, we describe the physical assumptions, operation, performance and limitations of the code. We validate it against tardis, cmfgen and cloudy, finding good agreement, and present illustrative synthetic spectra from disc winds in cataclysmic variables, tidal disruption events, AGN and X-ray binaries. Sirocco is publicly available on GitHub, alongside its associated data, documentation and sample input files covering a wide range of astrophysical applications., Comment: 26 pages, 16 figures. Submitted to MNRAS. This is the release paper for the SIROCCO code, which can be found at https://github.com/sirocco-rt/sirocco with links to documentation. Underlying data and figure scripts available at https://github.com/sirocco-rt/release-models -- comments on the code, paper or documentation are welcomed

We conducted systematic radiative transfer (RT) modeling of the Mg II doublet line profiles for 33 low-redshift Lyman continuum (LyC) leakers, and Ly$\alpha$ modeling for a subset of six objects, using a multiphase, clumpy circumgalactic medium (CGM) model. Our RT models successfully reproduced the Mg II line profiles for all 33 galaxies, revealing a necessary condition for strong LyC leakage: high maximum clump outflow velocity ($v_{\rm MgII,\,max} \gtrsim 390\,\rm km\,s^{-1}$) and low total Mg II column density ($N_{\rm MgII,\,tot} \lesssim 10^{14.3}\,\rm cm^{-2}$). We found that the clump outflow velocity and total Mg II column density have the most significant impact on Mg II spectra and emphasized the need for full RT modeling to accurately extract the CGM gas properties. In addition, using archival HST COS/G160M data, we modeled Ly$\alpha$ profiles for six objects and found that their spectral properties do not fully align with the conventional LyC leakage criteria, yet no clear correlation was identified between the modeled parameters and observed LyC escape fractions. We inferred LyC escape fractions based on HI properties from Ly$\alpha$ RT modeling and found that LyC leakage is primarily governed by the number of optically thick HI clumps per sightline ($f_{\rm cl}$). Intriguingly, two galaxies with relatively low observed LyC leakage exhibited the highest RT-inferred LyC escape fractions due to their lowest $f_{\rm cl}$ values, driven by the strong blue peaks of their Ly$\alpha$ emission. Future high-resolution, spatially resolved observations are crucial for resolving this puzzle. Overall, our results support a "picket fence" geometry over a "density-bounded" scenario for the CGM, where a combination of high Mg II outflow velocities and low Mg II column densities may be correlated with the presence of more low-density HI channels that facilitate LyC escape., Comment: 22 pages, 16 figures, comments are welcome

Parametric radiative transfer equation (RTE) occurs in multi-query applications such as uncertainty quantification, inverse problems, and sensitivity analysis, which require solving RTE multiple times for a range of parameters. Consequently, efficient iterative solvers are highly desired. Classical Synthetic Acceleration (SA) preconditioners for RTE build on low order approximations to an ideal kinetic correction equation such as its diffusion limit in Diffusion Synthetic Acceleration (DSA). Their performance depends on the effectiveness of the underlying low order approximation. In addition, they do not leverage low rank structures with respect to the parameters of the parametric problem. To address these issues, we proposed a ROM-enhanced SA strategy, called ROMSAD, under the Source Iteration framework in Peng (2024). In this paper, we further extend the ROMSAD preconditioner to flexible general minimal residual method (FGMRES). The main new advancement is twofold. First, after identifying the ideal kinetic correction equation within the FGMRES framework, we reformulate it into an equivalent form, allowing us to develop an iterative procedure to construct a ROM for this ideal correction equation without directly solving it. Second, we introduce a greedy algorithm to build the underlying ROM for the ROMSAD preconditioner more efficiently. Our numerical examples demonstrate that FGMRES with the ROMSAD preconditioner (FGMRES-ROMSAD) is more efficient than GMRES with the right DSA preconditioner. Furthermore, when the underlying ROM in ROMSAD is not highly accurate, FGMRES-ROMSAD exhibits greater robustness compared to Source Iteration accelerated by ROMSAD.

FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) was selected in 2019 as the ninth Earth Explorer mission by the European Space Agency (ESA). Its primary objective is to collect interferometric measurements in the Far-InfraRed (FIR) spectral range, which accounts for 50\% of Earth's outgoing longwave radiation emitted into space, and will be observed from space for the first time. Accurate measurements of the FIR at the top of the atmosphere are crucial for improving climate models. Current instruments are insufficient, necessitating the development of advanced computational techniques. To ensure the quality of the mission data, an End-to-End Simulator (E2ES) was developed to simulate the measurement process and evaluate the effects of instrument characteristics and environmental factors. The core challenge of the mission is solving the retrieval problem, which involves estimating atmospheric properties from the radiance spectra observed by the satellite. This problem is ill-posed and regularization techniques are necessary. In this work, we present a novel and fast data-driven approach to approximate the inverse mapping. In the first phase, we generate an initial approximation of the inverse mapping using only simulated FORUM data. In the second phase, we improve this approximation by introducing climatological data as a priori information and using a neural network to estimate the optimal regularization parameters. While our approach does not match the precision of full-physics retrieval methods, its key advantage is the ability to deliver results almost instantaneously, making it highly suitable for real-time applications. Furthermore, the proposed method can provide more accurate a priori estimates for full-physics methods, thereby improving the overall accuracy of the retrieved atmospheric profiles.

The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to handle numerically, they often fail to accurately describe the radiation field inside complex geometries. For these cases, it is necessary to directly solve numerically the radiative transfer equation. We investigate the accuracy of a discontinuous Galerkin finite element method (DGFEM hereafter) applied to the frequency-dependent two dimensional radiative transfer equation, coupled with the radiative equilibrium equation, inside axis-symmetric circumstellar envelopes. The DGFEM is a variant of finite element methods. It employs discontinuous elements and flux integrals along their boundaries, ensuring local conservation. However, as opposed to the classical finite-element methods, the solution is discontinuous across element edges. We implemented the method in a code and tested its accuracy by comparing our results with the benchmarks from the literature. For all the tested cases, the temperature profile agrees within one percent. Additionally, the emerging spectral energy distributions (SEDs) and images, obtained subsequently by ray-tracing techniques from the DGFEM solution, agree on average within $5~\mathrm{\%}$ and $10~\mathrm{\%}$, respectively. We show that the DGFEM can accurately describe the temperature profile inside axis-symmetric circumstellar envelopes. Consecutively the emerging SEDs and images are also well reproduced. The discontinuous Galerkin finite element method provides an alternative method (other than Monte Carlo methods for instance) for solving the radiative transfer equation, and could be used in cases that are more difficult to handle with the other methods., Comment: 14 pages, 13 figures, 1 table

Non-LTE radiative transfer is a key tool for modern astrophysics: it is the means by which many key synthetic observables are produced, thus connecting simulations and observations. Radiative transfer models also inform our understanding of the primary formation layers and parameters of different spectral lines, and serve as the basis of inversion tools used to infer the structure of the solar atmosphere from observations. The default approach for computing the radiation field in multidimensional solar radiative transfer models has long remained the same: a short characteristics, discrete ordinates method, formal solver. In situations with complex atmospheric structure and multiple transitions between optically-thick and -thin regimes these solvers require prohibitively high angular resolution to correctly resolve the radiation field. Here, we present the theory of radiance cascades, a technique designed to exploit structure inherent to the radiation field, allowing for efficient reuse of calculated samples, thus providing a very high-resolution result at a fraction of the computational cost of existing methods. We additionally describe our implementation of this method in the DexRT code, and present initial results of the synthesis of a snapshot of a magnetohydrodynamic model of a solar prominence formed via levitation-condensation. The approach presented here provides a credible route for routinely performing multidimensional radiative transfer calculations free from so-called ray effects, and scaling high-quality non-LTE models to next-generation high-performance computing systems with GPU accelerators., Comment: 21 pages, 14 figures, ancillary videos. To be submitted to RASTI

Radiative transfer (RT) modelling is a necessary tool in the interpretation of observations of the thermal emission of interstellar dust. It is also often part of multi-physics modelling. In this context, the efficiency of radiative transfer calculations is important, even for one-dimensional models. We investigate the use of the so-called immediate re-emission (IRE) method for fast calculation of one-dimensional spherical cloud models. We wish to determine whether weighting methods similar to those used in traditional Monte Carlo simulations can speed up the estimation of dust temperature. We present the program DIES, a parallel implementation of the IRE method, which makes it possible to do the calculations also on graphics processing units (GPUs). We tested the program with externally and internally heated cloud models, and examined the potential improvements from the use of different weighted sampling schemes. The execution times of the program compare favourably with previous programs, especially when run on GPUs. On the other hand, weighting schemes produce only limited improvements. In the case of an internal radiation source, the basic IRE method samples the re-emission well, while traditional Monte Carlo requires the use of spatial importance sampling. Some noise reduction could be achieved for externally heated models by weighting the initial photon directions. Only in optically very thin models does weighting - such as the proposed method of forced first interaction - result in noise reduction by a factor of several. The IRE method performs well for both internally and externally heated models, typically without the need for any additional weighting schemes. With run times of the order of one second for our test models, the DIES program is suitable even for larger parameter studies., Comment: Accepted for publication in A&A

Context. 3D numerical simulations of radiative transfer are crucial for understanding complex astrophysical objects. For Monte Carlo radiative transfer, the spatial grid design is critical yet complex. Common grids include hierarchical octree and unstructured Voronoi grids, each with its own strengths and weaknesses. Tetrahedral grids, widely used in ray-tracing graphics, are a potential alternative. Aims. We explore the possibilities, advantages, and limitations of tetrahedral grids for Monte Carlo radiative transfer, comparing their performance with other grid structures. Method. We integrated a tetrahedral grid structure, using the TetGen library, into the SKIRT Monte Carlo radiative transfer code. Tetrahedral grids can be imported or adaptively constructed and refined within SKIRT. We implemented an efficient grid traversal method using Pl\"ucker coordinates and Pl\"ucker products. Results. We validated the tetrahedral grid construction and traversal algorithm with 2D radiative transfer benchmarks. In a simple 3D model, we compared the performance of tetrahedral, octree, and Voronoi grids. The octree grid outperformed the others in traversal speed, while the tetrahedral grid had the lowest grid quality. Overall, tetrahedral grids performed worse than octree and Voronoi grids. Conclusion. While tetrahedral grids may not be ideal for most astrophysical simulations, they offer a viable unstructured alternative to Voronoi grids for specific applications, such as post-processing hydrodynamical simulations on tetrahedral or unstructured grids., Comment: 10 pages, 8 figures, abstract was shortened to fit the arxiv abstract requirements, article is accepted to Astronomy & Astrophysics (in production)

General relativistic radiative transfer calculations are essential for comparing theoretical models of black hole accretion flows and jets with observational data. In this work, we introduce Coport, a novel public code specifically designed for covariant polarized ray-tracing radiative transfer computations in any spacetime. Written in Julia, Coport includes an interface for visualizing numerical results obtained from HARM, a publicly available implementation of the general relativistic magnetohydrodynamics code. We validate the precision of our code by comparing its outputs with the results from a variety of established methodologies. This includes the verification against analytical solutions, the validation through thin-disk assessments, and the evaluation via thick-disk analyses. Notably, our code employs a methodology that eliminates the need for separating the computations of spacetime propagation and plasma propagation. Instead, it directly solves the coupled, covariant, polarized radiative transfer equation in curved spacetime, seamlessly integrating the effects of gravity with plasma influences. This approach sets our code apart from the existing alternatives and enhances its accuracy and efficiency., Comment: 27 pages, 6 figures

This work introduces an approach to enhancing the computational efficiency of 3D atmospheric simulations by integrating a machine-learned surrogate model into the OASIS global circulation model (GCM). Traditional GCMs, which are based on repeatedly numerically integrating physical equations governing atmospheric processes across a series of time-steps, are time-intensive, leading to compromises in spatial and temporal resolution of simulations. This research improves upon this limitation, enabling higher resolution simulations within practical timeframes. Speeding up 3D simulations holds significant implications in multiple domains. Firstly, it facilitates the integration of 3D models into exoplanet inference pipelines, allowing for robust characterisation of exoplanets from a previously unseen wealth of data anticipated from JWST and post-JWST instruments. Secondly, acceleration of 3D models will enable higher resolution atmospheric simulations of Earth and Solar System planets, enabling more detailed insights into their atmospheric physics and chemistry. Our method replaces the radiative transfer module in OASIS with a recurrent neural network-based model trained on simulation inputs and outputs. Radiative transfer is typically one of the slowest components of a GCM, thus providing the largest scope for overall model speed-up. The surrogate model was trained and tested on the specific test case of the Venusian atmosphere, to benchmark the utility of this approach in the case of non-terrestrial atmospheres. This approach yields promising results, with the surrogate-integrated GCM demonstrating above 99.0% accuracy and 101 factor GPU speed-up of the entire simulation compared to using the matched original GCM under Venus-like conditions., Comment: 17 pages, 11 figures

Much interest surrounds the nature of the compact remnant formed in core collapse supernovae (SNe). One means to constrain its nature is to search for signatures of power injection from the remnant in the SN observables years after explosion. In this work, we conduct a large grid of 1D nonlocal thermodynamic equilibrium radiative transfer calculations of He-star explosions under the influence of magnetar-power injection from post-explosion age of about one to ten years. Our results for SN observables vary with He-star mass, SN age, injected power, or ejecta clumping. At high mass, the ejecta coolants are primarily O and Ne, with [OI]6330A, [OII]7325A, and [OIII]5000A dominating in the optical, and with strong [NeII]12.81micron in the infrared -- this line may carry more than half the total SN luminosity. For lower He-star masses, a greater diversity of coolants appear, in particular Fe, S, Ar, or Ni from the Si- and Fe-rich regions. All models tend to rise in ionization in time, with twice-ionized species (i.e., OIII, NeIII, SIII, or FeIII) dominating at ~10yr, although this ionization is significantly reduced if clumping is introduced. Our treatment of magnetar power in the form of high-energy electrons or X-ray irradiation yields similar results -- no X-rays emerge from our ejecta even at ten years because of high-optical depth in the keV range. An uncertainty of our work concerns the power deposition profile, which is not known from first principles, although this profile could be constrained from observations. Our magnetar-powered model he8p00 with moderate clumping yields a good match to the optical and near-infrared observations of Type Ib SN2012au at both ~300d (power of 1-2x10^41erg/s) and 2269d (power of 10^40erg/s). Unless overly ionized, we find that all massive magnetar-powered ejecta should be infrared luminous at 5-10yr through strong [NeII]12.81micron line emission., Comment: submitted to A&A

When dealing with the steady-state multiscale radiative transfer equation (RTE) with heterogeneous coefficients, spatially localized low-rank structures are present in the angular space. This paper introduces an adaptive tailored finite point scheme (TFPS) for RTEs in heterogeneous media, which can adaptively compress the angular space. It does so by selecting reduced TFPS basis functions based on the local optical properties of the background media. These reduced basis functions capture the important local modes in the velocity domain. A detailed a posteriori error analysis is performed to quantify the discrepancy between the reduced and full TFPS solutions. Additionally, numerical experiments demonstrate the efficiency and accuracy of the adaptive TFPS in solving multiscale RTEs, especially in scenarios involving boundary and interface layers.

The vast majority of star-forming galaxies are surrounded by large reservoirs of gas ejected from the interstellar medium. Ultraviolet absorption and emission lines represent powerful diagnostics to constrain the cool phase of these outflows, through resonant transitions of hydrogen and metal ions. The interpretation of these observations is often remarkably difficult as it requires detailed modelling of the propagation of the continuum and emission lines in the gas. To this aim, we present a large public grid of about 20000 simulated spectra which includes HI Lyman-alpha (Lya) and five metal transitions associated with MgII, CII, SiII, and FeII that is accessible online at https://rascas.univ-lyon1.fr/app/idealised_models_grid/. The spectra have been computed with the RASCAS radiative transfer code for 5760 idealised spherical configurations surrounding a central point source emission, and characterised by their column density, Doppler parameter, dust opacity, wind velocity, as well as various density/velocity gradients. Designed to interpret Lya and metal line profiles, our grid exhibits a wide diversity of resonant absorption and emission features, as well as fluorescent lines. We illustrate how it can help better constrain wind properties by performing a joint modelling of observed Lya, CII, and SiII spectra. Using CLOUDY simulations and virial scaling relations, we show that Lya is expected to be a faithful tracer of the gas at T=10^4-10^5 K, even if the medium is highly-ionised. While CII is found to probe the same range of temperatures as Lya, other metal lines merely trace cooler phases (T=10^4 K). As their gas opacity strongly depends on gas temperature, incident radiation field, metallicity and dust depletion, we caution that optically thin metal lines do not necessarily originate from low HI column densities and may not accurately probe Lyman continuum leakage., Comment: 18 pages, 13 figures

We consider the iterative solution of anisotropic radiative transfer problems using residual minimization over suitable subspaces. We show convergence of the resulting iteration using Hilbert space norms, which allows us to obtain algorithms that are robust with respect to finite dimensional realizations via Galerkin projections. We investigate in particular the behavior of the iterative scheme for discontinuous Galerkin discretizations in the angular variable in combination with subspaces that are derived from related diffusion problems. The performance of the resulting schemes is investigated in numerical examples for highly anisotropic scattering problems with heterogeneous parameters., Comment: 20 pages, 5 figures

In this paper we study the distribution of the temperature within a body where the heat is transported only by radiation. Specifically, we consider the situation where both emission-absorption and scattering processes take place. We study the initial boundary value problem given by the coupling of the radiative transfer equation with the energy balance equation on a convex domain $ \Omega \subset \mathbb{R}^3 $ in the diffusion approximation regime, i.e. when the mean free path of the photons tends to zero. Using the method of matched asymptotic expansions we will derive the limit initial boundary value problems for all different possible scaling limit regimes and we will classify them as equilibrium or non-equilibrium diffusion approximation. Moreover, we will observe the formation of boundary and initial layers for which suitable equations are obtained. We will consider both stationary and time dependent problems as well as different situations in which the light is assumed to propagate either instantaneously or with finite speed., Comment: 1 Figure, 1 table

Clustering of Lyman-$\alpha$ (Ly$\alpha$) emitting galaxies (LAEs) is a useful probe of cosmology. However, Ly$\alpha$ radiative transfer (RT) effects, such as absorption, line shift, and line broadening, and their dependence on the large-scale density and velocity fields can modify the measured LAE clustering and line intensity mapping (LIM) statistics. We explore the effect of RT on the Ly$\alpha$ LIM power spectrum in two ways: using an analytic description based on linear approximations and using lognormal mocks. The qualitative effect of intergalactic Ly$\alpha$ absorption on the LIM auto- and cross-power spectrum is a scale-dependent, reduced effective bias, reduced mean intensity, and modified redshift-space distortions. The linear absorption model does not describe the results of the lognormal simulations well. The random line shift suppresses the redshift-space power spectrum similar to the Fingers-of-God effect. In cross-correlation of LAEs or Ly$\alpha$ intensity with a non-Ly$\alpha$ tracer, the Ly$\alpha$ line shift leads to a phase shift of the complex power spectrum, i.e. a cosine damping of the real part. Line broadening from RT suppresses the LIM power spectra in the same way as limited spectral resolution. We study the impact of Ly$\alpha$ RT effects on the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) LAE and LIM power spectra using lognormal mocks. We find that even small amounts of IGM absorption will significantly change the measured LAE auto-power spectrum and the LAE-intensity cross-power spectrum. Therefore, HETDEX will be able to constrain Ly$\alpha$ RT effects., Comment: 12 pages, 6 figures, comments are welcome

The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependency of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the Non-Local Thermodynamical Equilibrium (NLTE) problem. In this study we have developed a Jacobian-Free Newton-Krylov method (JFNK) to solve multi-level NLTE radiative transfer problems. Using the Rybicki & Hummer (1992) method as a reference (Rybicki, G. B. & Hummer, D. G. 1992, A&A, 262, 209), our results show that our JFNK solver can achieve up to a factor two speed up when using local approximate operators / preconditioners, while also achieving a lower residual error in the statistical equilibrium equations. Another advantage of this method is that the addition of charge conservation and partial redistribution effects should be straight forward. Our method can help accelerating the calculation of the emerging spectra from numerical models and also the reconstruction of chromospheric datasets through NLTE inversions., Comment: A&A accepted version

We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo method with four pseudo-random number generators and five Quasi-Monte Carlo implementations using different low-discrepancy sequences and the Hammersley set. For the comparison, we study different test matter geometries and problems. We present comparison results for single scatterings of radiation from a point source, multiple scatterings of radiation from a point source, and single scatterings of radiation from a spherical star. In all cases, Quasi-Monte Carlo shows better convergence than Monte Carlo. In several test cases, the gain in computation time to achieve a fixed error value reached 40 times. We obtained ten times speed up in many of the considered tests., Comment: 57 pages, 10 figures, 3 tables; Submitted to Astronomy and Computing

We study the anisotropy of centroid and integrated intensity maps with synthetic observations. We perform post-process radiative transfer including the optically thick regime that was not covered in Hern\'andez-Padilla et al. (2020). We consider the emission in various CO molecular lines, that range from optically thin to optically thick ($\mathrm{^{12}CO}$, $\mathrm{^{13}CO}$, $\mathrm{C^{18}O}$, and $\mathrm{C^{17}O}$). The results for the velocity centroids are similar to those in the optically thin case. For instance, the anisotropy observed can be attributed to the Alfv\'en mode, which dominates over the slow and fast modes when the line of sight is at a high inclination with respect to the mean magnetic field. A few differences arise in the models with higher opacity, where some dependence on the sonic Mach number becomes evident. In contrast to the optically thin case, maps of integrated intensity become more anisotropic in optically thick lines. In this situation the scales probed are restricted, due to absorption, to smaller scales which are known to be more anisotropic. We discuss how the sonic Mach number can affect the latter results, with highly supersonic cases exhibiting a lower degree of anisotropy.

Carbon monoxide (CO) emission has been observed in a number of core-collapse supernovae (SNe) and is known to be an important coolant at late times. We have implemented a chemical reaction network in the radiative-transfer code CMFGEN to investigate the formation of CO and its impact on SN ejecta. We calculate two 1D SN models with and without CO: a BSG explosion model at one nebular epoch and a full time sequence (50 to 300 days) for a RSG explosion. In both models, CO forms at nebular times in the dense, inner regions at velocities $<2000 \mathrm{km/s}$ where line emission from CO can dominate the cooling and reduce the local temperature by as much as a factor of two, weakening emission lines and causing the optical light curve to fade faster. That energy is instead emitted in CO bands, primarily the fundamental band at $\sim 4.5\mathrm{\mu m}$, which accounts for up to 20% of the total luminosity at late times. However, the non-monotonic nature of the CO cooling function can cause numerical difficulties and introduce multiple temperature solutions. This issue is compounded by the sensitivity of the CO abundance to a few reaction rates, many of which have large uncertainties or disparate values across literature sources. Our results also suggest that, in many SNe, CO level populations are far from their LTE values. Unfortunately, accurate collisional data, necessary to compute NLTE populations, are limited to a few transitions., Comment: 15 pages, 12 figures. Accepted for publication in MNRAS

In this paper we present the publicly available open-source spectral energy distribution (SED) fitting code SMART (Spectral energy distributions Markov chain Analysis with Radiative Transfer models). Implementing a Bayesian Markov chain Monte Carlo (MCMC) method, SMART fits the ultraviolet to millimetre SEDs of galaxies exclusively with radiative transfer models that currently constitute four types of pre-computed libraries, which describe the starburst, active galactic nucleus (AGN) torus, host galaxy and polar dust components. An important novelty of SMART is that, although it fits SEDs exclusively with radiative transfer models, it takes comparable time to popular energy balance methods to run. Here we describe the key features of SMART and test it by fitting the multi-wavelength SEDs of the 42 local ultraluminous infrared galaxies (ULIRGs) that constitute the HERschel Ultraluminous Infrared Galaxy Survey (HERUS) sample. The Spitzer spectroscopy data of the HERUS ULIRGs are included in the fitting at a spectral resolution, which is matched to that of the radiative transfer models. We also present other results that highlight the performance and versatility of SMART. SMART promises to be a useful tool for studying galaxy evolution in the JWST era. SMART is developed in PYTHON and is available at https://github.com/ch-var/SMART.git., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society

The optical depth parameterisation is typically used to study the 21-cm signals associated with the properties of the neutral hydrogen (HI) gas and the ionisation morphology during the Epoch of Reionisation (EoR), without solving the radiative transfer equation. To assess the uncertainties resulting from this simplification, we conduct explicit radiative transfer calculations using the cosmological 21-cm radiative transfer (C21LRT) code and examine the imprints of ionisation structures on the 21-cm spectrum. We consider a globally averaged reionisation history and implement fully ionised cavities (HII bubbles) of diameters $d$ ranging from 0.01 Mpc to 10 Mpc at epochs within the emission and the absorption regimes of the 21-cm global signal. The single-ray C21LRT calculations show that the shape of the imprinted spectral features are primarily determined by $d$ and the 21-cm line profile, which is parametrised by the turbulent velocity of the HI gas. It reveals the spectral features tied to the transition from ionised to neutral regions that calculations based on the optical depth parametrisation were unable to capture. We also present analytical approximations of the calculated spectral features of the HII bubbles. The multiple-ray calculations show that the apparent shape of a HII bubble (of $d=5$ Mpc at $z=8$), because of the finite speed of light, differs depending on whether the bubble's ionisation front is stationary or expanding. Our study shows the necessity of properly accounting for the effects of line-continuum interaction, line broadening and cosmological expansion to correctly predict the EoR 21-cm signals., Comment: 15 pages, 11 figures, 1 table

Our understanding of how exoplanets form and evolve relies on analyses of both the mineralogy of protoplanetary disks and their detailed structures; however, these key complementary aspects of disks are usually studied separately. We present initial results from a hybrid model that combines the empirical characterization of the mineralogy of a disk, as determined from its mid-infrared spectral features, with the MCFOST radiative transfer disk model, a combination we call the EaRTH Disk Model. With the results of the mineralogy detection serving as input to the radiative transfer model, we generate mid-infrared spectral energy distributions (SEDs) that reflect both the mineralogical and structural parameters of the corresponding disk. Initial fits of the SED output by the resulting integrated model to Spitzer Space T elescope mid-infrared (IRS) spectra of the protoplanetary disk orbiting the nearby T Tauri star MP Mus demonstrate the potential advantages of this approach by revealing details like the dominance of micron-sized olivine and micron-sized forsterite in this dusty disk. The simultaneous insight into disk composition and structure provided by the EaRTH Disk methodology should be directly applicable to the interpretation of mid-infrared spectra of protoplanetary disks that will be produced by the James Webb Space Telescope., Comment: Accepted for publication in ApJ, 38 pages, 11 figures, 6 tables

The 21-cm hyperfine line of neutral hydrogen is a useful tool to probe the conditions of the Universe during the Dark Ages, Cosmic Dawn, and the Epoch of Reionisation. In most of the current calculations, the 21-cm line signals at given frequencies are computed, using an integrated line-of-sight line opacity, with the correction for cosmological expansion. These calculations have not fully captured the line and continuum interactions in the radiative transfer, in response to evolution of the radiation field and the variations of thermal and dynamic properties of the line-of-sight medium. We construct a covariant formulation for the radiative transfer of the 21-cm line and derive the cosmological 21-cm line radiative transfer (C21LRT) equation. The formulation properly accounts for local emission and absorption processes and the interaction between the line and continuum when the radiation propagates across the expanding Universe to the present observer. Our C21LRT calculations show that methods simply summing the line optical depth could lead to error of $5\%$ in the 21-cm signals for redshift $z \sim 12-35$ and of $>10\%$ for redshift $z \lesssim 8$. Proper covariant radiative transfer is therefore necessary for producing correct theoretical templates for extracting information of the structural evolution of the Universe through the Epoch of Reionisation from the 21-cm tomographic data., Comment: 16 pages, 11 figures, 3 tables

The polarization characteristics of atmospheric scattering are important and should not be ignored in radiative transfer simulations. In this study, a new vector radiative transfer model called the polarized adding method of discrete ordinate approximation (POLDDA) is proposed for use in remote sensing applications for ultraviolet-visible and near-infrared spectra. The single-layer radiative transfer process and inhomogeneous multi-layer connection are solved using the discrete ordinate method (DOM) and adding methods, respectively. By combining the advantages of DOM and the adding method, the Stokes vector (including the I-, Q-, U-, and V-components) calculated using the new method conforms to the results of PolRadtran/RT3, whether in a Rayleigh scattering atmosphere or the water cloud case. Moreover, the relative root-mean-square error (RMSE) values of the Stokes vector for the test cases between MYSTIC and the new method or RT3 prove the accuracy of the proposed method. Meanwhile, the new method has a higher computational efficiency than RT3, particularly for an atmosphere with a large scattering optical depth. Unlike RT3, the computation time of the proposed method does not increase with the optical depth of each layer.

The discovery of protoplanets and circumplanetary disks provides a unique opportunity to characterize planet formation through observations. Massive protoplanets shape the physical and chemical structure of their host circumstellar disk by accretion, localized emission, and disk depletion. In this work, we study the thermal changes induced within the disk by protoplanet accretion and synthetic predictions through hydrodynamical simulations with post-processed radiative transfer with an emphasis on radio millimeter emission. We explored distinct growth conditions and varied both planetary accretion rates and the local dust-to-gas mass ratios for a protoplanet at 1200 K. The radiative transfer models show that beyond the effect of disk gaps, in most cases, the CPD and the planet's emission locally increase the disk temperature. Moreover, depending on the local dust-to-gas depletion and accretion rate, the CPD presence may have detectable signatures in millimeter emission. It also has the power to generate azimuthal asymmetries important for continuum subtraction. Thus, if other means of detection of protoplanets are proven, the lack of corresponding evidence at other wavelengths can set limits on their growth timescales through a combined analysis of the local dust-to-gas ratio and the accretion rate., Comment: 17 pages, 10 figures. Accepted for publication in ApJ

Type Iax supernovae (SNe Iax) are proposed to arise from deflagrations of Chandrasekhar mass white dwarfs (WDs). Previous deflagration simulations have achieved good agreement with the light curves and spectra of intermediate-luminosity and bright SNe Iax. However, the model light curves decline too quickly after peak, particularly in red optical and near-infrared (NIR) bands. Deflagration models with a variety of ignition configurations do not fully unbind the WD, leaving a remnant polluted with $^{56}\mathrm{Ni}$. Emission from such a remnant may contribute to the luminosity of SNe Iax. Here we investigate the impact of adding a central energy source, assuming instantaneous powering by $^{56}\mathrm{Ni}$ decay in the remnant, in radiative transfer calculations of deflagration models. Including the remnant contribution improves agreement with the light curves of SNe Iax, particularly due to the slower post-maximum decline of the models. Spectroscopic agreement is also improved, with intermediate-luminosity and faint models showing greatest improvement. We adopt the full remnant $^{56}\mathrm{Ni}$ mass predicted for bright models, but good agreement with intermediate-luminosity and faint SNe Iax is only possible for remnant $^{56}\mathrm{Ni}$ masses significantly lower than those predicted. This may indicate that some of the $^{56}\mathrm{Ni}$ decay energy in the remnant does not contribute to the radiative luminosity but instead drives mass ejection, or that escape of energy from the remnant is significantly delayed. Future work should investigate the structure of remnants predicted by deflagration models and the potential roles of winds and delayed energy escape, as well as extend radiative transfer simulations to late times., Comment: 17 pages, 6 figures. Lightcurves and spectra available at https://hesma.h-its.org

The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption and scattering in many relevant societal applications, and requires numerical approximations. However, classical numerical algorithms scale unfavorably with respect to the dimensionality of such radiative transfer problems, where solutions depend on physical as well as angular variables. In this paper we address this dimensionality issue by developing a low-rank tensor product framework for the RTE in plane-parallel geometry. We exploit the tensor product nature of the phase space to recover an operator equation where the operator is given by a short sum of Kronecker products. This equation is solved by a preconditioned and rank-controlled Richardson iteration in Hilbert spaces. Using exponential sums approximations we construct a preconditioner that is compatible with the low-rank tensor product framework. The use of suitable preconditioning techniques yields a transformation of the operator equation in Hilbert space into a sequence space with Euclidean inner product, enabling rigorous error and rank control in the Euclidean metric., Comment: 22 pages, 4 Figures, submitted to SIAM Journal on Numerical Analysis

The Mg II resonance doublet at 2796 {\AA} and 2803 {\AA} is an increasingly important tool to study cold, $T \sim 10^{4}\,$K, gas -- an observational driven development requiring theoretical support. We develop a new Monte Carlo radiative transfer code to systematically study the joined Mg II and Ly$\alpha$ escape through homogeneous and `clumpy' multiphase gas with dust in arbitrary 3D geometries. Our main findings are: (i) The Mg II spectrum differs from Ly$\alpha$ due to the large difference in column densities, even though the atomic physics of the two lines are similar. (ii) the Mg II escape fraction is generally higher than that of Ly$\alpha$ because of lower dust optical depths and path lengths -- but large variations due to differences in dust models and the clumpiness of the cold medium exist. (iii) Clumpy media possess a `critical covering factor' above which Mg II radiative transfer matches a homogeneous medium. The critical covering factors for Mg II and Ly$\alpha$ differ, allowing constraints on the cold gas structure. (iv) The Mg II doublet ratio $R_{\rm MgII}$ varies for strong outflows/inflows ($\gtrsim 700 \mathrm{km\,s}^{-1}$), in particular, $R_{\rm MgII}<1$ being an unambiguous tracer for powerful galactic winds. (v) Scattering of stellar continuum photons can decrease $R_{\rm MgII}$ from two to one, allowing constraints on the scattering medium. Notably, we introduce a novel probe of the cold gas column density -- the halo doublet ratio -- which we show to be a powerful indicator of ionizing photon escape. We discuss our results in the context of interpreting and modeling observations as well as their implications for other resonant doublets., Comment: 32 pages, 30 figures, submitted to MNRAS

Young stellar objects (YSOs) accrete up to half of their material in short periods of enhanced mass accretion. For massive YSOs (MYSOs with more than 8 solar masses), accretion outbursts are of special importance, as they serve as diagnostics in highly obscured regions. Within this work, two outbursting MYSOs within different evolutionary stages, the young source G358.93-0.03 MM1 (G358) and the more evolved one G323.46-0.08 (G323), are investigated, and the major burst parameters are derived. For both sources, follow-up observations with the airborne SOFIA observatory were performed to detect the FIR afterglows. All together, we took three burst-/post-observations in the far infrared. The burst parameters are needed to understand the accretion physics and to conclude on the possible triggering mechanisms behind it. Up to today, G323s burst is the most energetic one ever observed for a MYSO. G358s burst was about two orders of magnitude weaker and shorter (2 months instead of 8 years). We suggest that G358s burst was caused by the accretion of a spiral fragment (or a small planet), where G323 accreted a heavy object (a planet or even a potential companion). To model those sources, we use radiative transfer (RT) simulations (static and time-dependent). G323s accretion burst is the first astrophysical science case, that is modeled with time-dependent RT (TDRT). We incorporate a small TDRT parameter-study and develop a time-depending fitting tool (the TFitter) for future modeling., Comment: PhD Thesis

The mass loss rates of planets undergoing core-powered escape are usually modeled using an isothermal Parker-type wind at the equilibrium temperature, $T_\mathrm{eq}$. However, the upper atmospheres of sub-Neptunes may not be isothermal if there are significant differences between the opacity to incident visible and outgoing infrared radiation. We model bolometrically-driven escape using aiolos, a hydrodynamic radiative-transfer code that incorporates double-gray opacities, to investigate the process's dependence on the visible-to-infrared opacity ratio, $\gamma$. For a value of $\gamma \approx 1$, we find that the resulting mass loss rates are well-approximated by a Parker-type wind with an isothermal temperature $T = T_\mathrm{eq}/2^{1/4}$. However, we show that over a range of physically plausible values of $\gamma$, the mass loss rates can vary by orders of magnitude, ranging from $10^{-5} \times$ the isothermal rate for low $\gamma$ to $10^5 \times$ the isothermal rate for high $\gamma$. The differences in mass loss rates are largest for small planet radii, while for large planet radii, mass loss rates become nearly independent of $\gamma$ and approach the isothermal approximation. We incorporate these opacity-dependent mass loss rates into a self-consistent planetary mass and energy evolution model and show that lower/higher $\gamma$ values lead to more/less hydrogen being retained after core-powered mass loss. In some cases, the choice of opacities determines whether or not a planet can retain a significant primordial hydrogen atmosphere. The dependence of escape rate on the opacity ratio may allow atmospheric escape observations to directly constrain a planet's opacities and therefore its atmospheric composition., Comment: 24 pages, 10 figures. Submitted to ApJ

We introduce the RIGEL model, a novel framework to self-consistently model the effects of stellar feedback in the multiphase ISM of dwarf galaxies with radiative transfer (RT) on a star-by-star basis. The RIGEL model integrates detailed implementations of feedback from individual massive stars into the RHD code, AREPO-RT. It forms individual massive stars from the resolved multiphase ISM by sampling the IMF and tracks their evolution individually. The lifetimes, photon production rates, mass-loss rates, and wind velocities of these stars are determined by their initial masses and metallicities based on a library that incorporates a variety of stellar models. The RT equations are solved in seven spectral bins accounting for the IR to HeII ionizing bands, using an M1 RT scheme. The thermochemistry model tracks the non-equilibrium H, He chemistry and the equilibrium abundance of CI, CII, OI, OII, and CO to capture the thermodynamics of all ISM phases. We evaluated the performance of the RIGEL model using $1\,{\rm M}_\odot$ resolution simulations of isolated dwarf galaxies. We found that the SFR and ISRF show strong positive correlations to the metallicity of the galaxy. Photoionization and photoheating can reduce the SFR by an order of magnitude by removing the available cold-dense gas fuel for star formation. The ISRF also changes the thermal structure of the ISM. Radiative feedback occurs immediately after the birth of massive stars and rapidly disperses the molecular clouds within 1 Myr. As a consequence, radiative feedback reduces the age spread of star clusters to less than 2 Myr, prohibits the formation of massive star clusters, and shapes the cluster initial mass function to a steep power-law form with a slope of $\sim-2$. The mass-loading factor of the fiducial galaxy has a median of $\sim50$, while turning off radiative feedback reduces this factor by an order of magnitude., Comment: 27 pages, 18 figures; A&A in press; abstract slightly abridged; comments welcome

Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines.We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them.We focus on the CO and HCO+ isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cram{\'e}r-Rao lower bound.Column densities can be estimated with 30% accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak 12CO(1--0) is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and HCO+ isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases.Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future., Comment: Astronomy and Astrophysics - A\&A, In press

Solar prominences observed close to the limb commonly include a bright feature that, from the perspective of the observer, runs along the interface between itself and the underlying chromosphere. Despite several idealised models being proposed to explain the underlying physics, a more general approach remains outstanding. In this manuscript we demonstrate as a proof-of-concept the first steps in applying the Lightweaver radiative transfer framework's 2.5D extension to a `toy' model prominence + VAL3C chromosphere, inspired by recent 1.5D experiments that demonstrated a significant radiative chromosphere--prominence interaction. We find the radiative connection to be significant enough to enhance both the electron number density within the chromosphere, as well as its emergent intensity across a range of spectral lines in the vicinity of the filament absorption signature. Inclining the viewing angle from the vertical, we find these enhancements to become increasingly asymmetric and merge with a larger secondary enhancement sourced directly from the prominence underside. In wavelength, the enhancements are then found to be the largest in both magnitude and horizontal extent for the spectral line cores, decreasing into the line wings. Similar behaviour is found within new Chinese H$\alpha$ Solar Explorer (CHASE)/H$\alpha$ Imaging Spectrograph (HIS) observations, opening the door for subsequent statistical confirmations of the theoretical basis we develop here., Comment: 9 pages, 5 figures, accepted for publication in The Astrophysical Journal Letters (ApJL)

Advances in machine learning have boosted the use of Earth observation data for climate change research. Yet, the interpretability of machine-learned representations remains a challenge, particularly in understanding forests' biophysical reactions to climate change. Traditional methods in remote sensing that invert radiative transfer models (RTMs) to retrieve biophysical variables from spectral data often fail to account for biases inherent in the RTM, especially for complex forests. We propose to integrate RTMs into an auto-encoder architecture, creating an end-to-end learning approach. Our method not only corrects biases in RTMs but also outperforms traditional techniques for variable retrieval like neural network regression. Furthermore, our framework has potential generally for inverting biased physical models. The code is available on https://github.com/yihshe/ai-refined-rtm.git.

We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we utilize the Physics-Informed Neural Networks (PINNs) framework and design a new adaptive exponentially weighted Asymptotic-Preserving (AP) loss function, which incorporates the macroscopic auxiliary equation that is derived from the original transfer equation directly and explicitly contains the information of the diffusion limit equation. Thus, as the scale parameter tends to zero, the loss function gradually transitions from the transport state to the diffusion limit state. In addition, the initial data, boundary conditions, and conservation laws serve as the regularization terms for the loss. We present several numerical examples to demonstrate the effectiveness of MA-APNNs., Comment: 24 pages, 29 figures