Planck Mean Research Articles

Simulations of Early Kilonova Emission from Neutron Star Mergers

Abstract We present radiative transfer simulations for blue kilonovae hours after neutron star (NS) mergers by performing detailed opacity calculations for the first time. We calculate atomic structures and opacities of highly ionized elements (up to the 10th ionization) with atomic number Z = 20–56. We find that the bound–bound transitions of heavy elements are the dominant source of the opacities in the early phase (t < 1 day after the merger) and that the ions with a half-closed electron shell provide the highest contributions. The Planck mean opacity for lanthanide-free ejecta (with electron fraction of Y e = 0.30–0.40) can only reach around at t = 0.1 days, whereas that increases up to at t = 1 day. The spherical ejecta model with an ejecta mass of M ej = 0.05 M ⊙ gives the bolometric luminosity of at t ∼ 0.1 days. We confirm that the existing bolometric and multicolor data of GW170817 can be naturally explained by the purely radioactive model. The expected early UV signals reach 20.5 mag at t ∼ 4.3 hr for sources even at 200 Mpc, which is detectable by the facilities such as Swift and the Ultraviolet Transient Astronomy Satellite (ULTRASAT). The early-phase luminosity is sensitive to the structure of the outer ejecta, as also pointed out by Kasen et al. Therefore, the early UV observations give strong constraints on the structure of the outer ejecta and the presence of a heating source besides r-process nuclei.

Transient combustion of a multi-component fuel droplet with gas radiation

The transient modeling of radiation effects on combustion of an isolated nonane and hexanol droplet in standard atmospheric conditions with finite rate chemistry has been performed. Transient effects have been included in a comprehensive manner by including initial droplet heating, variable liquid and gas phase properties and non-luminous gas radiations. Results show that gas radiations are important for determining various parameters in droplet combustion. Estimation of Planck's mean absorption coefficient is critical for non-luminous gas radiation modeling. Gas radiation suppresses gas, liquid and flame temperatures. The burning rate decreases in the presence of radiative losses with increasing initial droplet diameter.

Development of full spectrum correlated k-model for spectral radiation penetration within liquid fuels

In this paper, full spectrum correlated k-distribution (FSCK) models are developed for several liquid fuels including decane, ethanol, ethylene glycol, heptane, and toluene. The models were built using high-resolution absorption spectra, collected from the literature. To validate the novel FSCK models, they were used to solve radiative heat transfer within liquid pools assuming three temperature profiles (i.e. constant temperature, linear and nonlinear temperature profiles) and the calculated transmissivity and radiative heat source of FSCK were compared with those of using high resolution absorption spectra and the gray models implementing Planck mean absorption coefficient. The sensitivity analysis was performed for the accuracy of the FSCK results with number of quadrature points for different fuels. Using seven quadrature points for FSCK model has been found to be sufficient for providing good accuracy of spectral radiative heat transfer within the liquid fuels with a reasonable computational cost. Moreover, we studied the effect of the reference temperature used in FSCK model and found out that for the pool fire scenario, the FSCK provides its best accuracy if an equivalent temperature representing the radiation feedback from the flame is used as the reference temperature. Comparison of computational costs of high-resolution spectral radiation calculations and FSCK method revealed a significant computational gain by use of FSCK model.

Non-LTE radiation hydrodynamics in PLUTO

Context. Modeling the dynamics of most astrophysical structures requires an adequate description of the interaction of radiation and matter. Several numerical (magneto-) hydrodynamics codes were upgraded with a radiation module to fulfill this request. However, those that used either the flux-limited diffusion (FLD) or the M1 radiation moment approaches are restricted to local thermodynamic equilibrium (LTE). This assumption may not be valid in some astrophysical cases. Aims. We present an upgraded version of the LTE radiation-hydrodynamics (RHD) module implemented in the PLUTO code, which we have extended to handle non-LTE regimes. Methods. Starting from the general frequency-integrated comoving-frame equations of RHD, we have justified all the assumptions that were made to obtain the non-LTE equations that are implemented in the module under the FLD approximation. An operator-split method with two substeps was employed: the hydrodynamics part was solved with an explicit method by the solvers that are currently available in PLUTO, and the non-LTE radiation diffusion and energy exchange part was solved with an implicit method. The module was implemented in the PLUTO environment. It uses databases of radiative quantities that can be provided independently by the user: the radiative power loss, and the Planck and Rosseland mean opacities. In our case, these quantities were determined from a collisional-radiative steady-state model, and they are tabulated as functions of temperature and density. Results. Our implementation has been validated through different tests, in particular, radiative shock tests. The agreement with the semi-analytical solutions (when available) is good, with a maximum error of 7%. Moreover, we have proved that a non-LTE approach is of paramount importance to properly model accretion shock structures. Conclusion. Our radiation FLD module represents a step toward a general non-LTE RHD modeling.

Simultaneous X-ray and XUV absorption measurements in nickel laser-produced plasma close to LTE

We present an experiment performed in 2016 at the LULI2000 laser facility in which X-ray and XUV absorption structures of nickel hot plasmas were measured simultaneously. Such experiments may provide stringent tests of the accuracy of plasma atomic-physics codes used to the modeling of plasmas close to local thermodynamic equilibrium. The experimental set-up relies on a symmetric heating of the sample foil by two gold hohlraums in order to reduce the spatial gradients. The plasma conditions are characterized by temperatures between 10 and 20 eV and densities of the order of 10−3 g/cm3–10−2 g/cm3. For the X-ray part, we investigate the 2p-3d and 2p-4d transitions, and for the XUV part, we recorded the Δn = 0 (n = 3) transitions, which present a high sensitivity to plasma temperature. These latter transitions are of particular interest because, in mid-Z plasmas, they dominate the Planck and Rosseland mean opacities. Measured spectra are compared to calculations performed using the hybrid opacity code SCO-RCG and the Flexible Atomic Code (FAC). The influence of a spectator electron on the calculated spectra is analyzed using the latter code.

Extended Calculations of Energy Levels and Transition Rates of Nd ii-iv Ions for Application to Neutron Star Mergers

Abstract The coalescence of a binary neutron star gives rise to electromagnetic emission, known as a kilonova, that is powered by radioactive decays of r-process nuclei. Observations of a kilonova associated with GW170817 provide a unique opportunity to study heavy element synthesis in the universe. However, the atomic data of r-process elements are not yet complete enough to decipher the light curves and spectral features of kilonovae. In this paper, we perform extended atomic calculations of neodymium (Nd, Z = 60) to study the impact of the accuracy in atomic calculations on astrophysical opacities. By employing multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods, we calculate the energy levels and transition data of electric dipole transitions for Nd ii, Nd iii, and Nd iv ions. Compared with previous calculations, our new results provide better agreement with the experimental data. The energy level accuracies achieved in the present work are 10%, 3%, and 11% for Nd ii, Nd iii, and Nd iv, respectively, compared to the NIST database. We confirm that the overall properties of the opacity are not significantly affected by the accuracies of the atomic calculations. The impact on the Planck mean opacity is up to a factor of 1.5, which affects the timescale of kilonovae by at most 20%. However, we find that the wavelength-dependent features in the opacity are affected by the accuracies of the calculations. We emphasize that accurate atomic calculations, in particular for low-lying energy levels, are important to provide predictions of kilonova light curves and spectra.

Impact of Radiative Losses on Flame Acceleration and Deflagration to Detonation Transition of Lean Hydrogen-Air Mixtures in a Macro-Channel with Obstacles

While there has been some recognition regarding the impact of thermal boundary conditions (adiabatic versus isothermal) on premixed flame propagation mechanisms in micro-channels (hydraulic diameters <10 mm), their impact in macro-channels has often been overlooked due to small surface-area-to-volume ratios of the propagating combustion wave. Further, the impact of radiative losses has also been neglected due to its anticipated insignificance based on scaling analysis and the high computational cost associated with resolving it’s spatial, temporal, directional, and wavelength dependencies. However, when channel conditions promote flame acceleration and deflagration-to-detonation transitions (DDT), large pressures are encountered in the vicinity of the combustion wave, thereby increasing the magnitude of radiative losses which in turn can impact the strength and velocity of the combustion wave. This is demonstrated for the first time through simulations of lean (equivalence ratio: 0.5) hydrogen-air mixtures in a macro-channel (hydraulic diameter: 174 mm) with obstacles (Blockage ratio: 0.51). By employing Planck mean absorption coefficients in conjunction with the P-1 radiation model, radiative losses are shown to affect the run-up distances to DDT in a long channel (length: 11.878 m). As anticipated, the differences in run-up distances resulting from radiative losses only increased with system pressure.

A full spectrum k-distribution based non-gray radiative property model for unburnt char

By using the concept of weighted sum of four gray particles and spectrum k-distribution (WSGP-SK), a non-gray radiative property model for unburnt char particles is developed. Based on the carbon burnout kinetic model for structure during oxidation, and the linear mixed approximation theory for complex index of refraction, spectral radiative properties of unburnt char particles are first calculated as function of the burnout ratio by Mie theory. Referring to the full spectrum k-distribution model, k-distribution is applied to reorder absorption and scattering efficiencies of particles. Then, weighting factors and efficiency factors of the non-gray radiative property model are directly obtained from Gaussian integral points of k-distribution. The model is validated against the benchmark solutions of line-by-line (LBL) model. Maximum relative errors of this model are 3% and 15% for radiative heat fluxes and source terms in non-isothermal inhomogeneous particulate media, respectively. The assumption of linearly varying radiative properties with burnout ratio (Lockwood et al. 1986) will result in a predicted deviation of 53% for radiative source terms. Results also show that this non-gray model is remarkably better than the Planck mean method. Moreover, a satisfactory comparison with LBL solutions is achieved in the gas and particle mixture by combining the non-gray WSGG-SK model (Guo et al. 2015). As a radiation sub-model, this non-gray radiative property model can significantly improve prediction accuracy of radiative heat transfer in oxy-fuel combustion.

A full spectrum k-distribution based non-gray radiative property model for fly ash particles

Particle radiation characteristics have a strong wavelength-dependence. However, the gray particle assumption is widely used for coal combustion simulations, which cannot reflect the non-gray radiative property of the particles. In this study, based on the measured complex index of refraction from literatures (Gupta and Wall, 1985, Goodwin and Mitchner, 1989, and Lohi et al., 1992), a new non-gray particle radiative property model for fly ash is proposed by combining the features of full-spectrum k-distribution (FSK) model with the weighted sum of gray gases (WSGG) model. Four gray particles with different absorption and scattering efficiencies are used to replace the non-gray particles, for which absorption efficiency, scattering efficiency and weighting factor are directly obtained from the k-distribution, with model parameters obtained based on rational polynomials. Simultaneously, a gray particle model based on the Planck’s law is also obtained for comparison. The new model is systematically validated by comparing the radiative source terms and radiative heat fluxes, with those predicted by the line-by-line (LBL) integration of Mie-data in a one-dimensional plane-parallel slab system. The maximum relative error of radiative source term is 8% for the new non-gray radiative property model, 13% for Planck mean coefficients, 14% for modified Johansson model (Johansson, 2017), and 18% for empirical-constant model in non-isothermal inhomogeneous particle media, respectively. Combining the new non-gray radiative property model with the non-gray formulation of WSGG-SK model (Guo et al., 2015), the prediction accuracy is further validated by LBL solutions in the gas and particle mixture. Moreover, the contribution of gases and particles to radiative heat transfer is discussed at different path lengths, which shows the accuracy of the particle radiative property model determines the prediction accuracy of the radiative heat transfer in large-scale furnace.

The Scaled SLW model of gas radiation in non-uniform media based on Planck-weighted moments of gas absorption cross-section

The Scaled SLW model for prediction of radiation transfer in non-uniform gaseous media is presented. The paper considers a new approach for construction of a Scaled SLW model. In order to maintain the SLW method as a simple and computationally efficient engineering method special attention is paid to explicit non-iterative methods of calculation of the scaling coefficient. The moments of gas absorption cross-section weighted by the Planck blackbody emissive power (in particular, the first moment – Planck mean, and first inverse moment – Rosseland mean) are used as the total characteristics of the absorption spectrum to be preserved by scaling. Generalized SLW modelling using these moments including both discrete gray gases and the continuous formulation is presented. Application of line-by-line look-up table for corresponding ALBDF and inverse ALBDF distribution functions (such that no solution of implicit equations is needed) ensures that the method is flexible and efficient. Predictions for radiative transfer using the Scaled SLW model are compared to line-by-line benchmark solutions, and predictions using the Rank Correlated SLW model and SLW Reference Approach. Conclusions and recommendations regarding application of the Scaled SLW model are made.

Numerically optimized band boundaries of Planck mean absorption coefficients in air plasma

Radiation heat transfer plays an important role in the energy balance of plasma in an electric arc and its accurate prediction is essential for the development of new electrical devices. Unfortunately, a very complex spectrum of the absorption coefficient makes accurate radiation heat transfer calculations a very challenging task, especially with complex geometries. Numerical approximation of the absorption coefficient is therefore commonly used to reduce computing demands. This paper presents our contribution to the topic of computing requirements reduction, namely the problem of frequency band selection for mean absorption coefficients (MACs). We show that, with the proper band distribution and averaging method, even a very low number of bands can be sufficient for an accurate approximation of the real radiation heat transfer. The band selection process is based upon numerical optimization with a mean value of each band being calculated as a line limited Planck MAC. Both the line limiting factor and associated characteristic plasma absorption length are investigated in detail and an optimal value equal to the three plasma radii is proposed. Tables for three bands mean absorption coefficients in air at the pressure of 1 bar and temperature range spanning from 300 K to 30 kK are included in this paper. These tables serve as input parameters for a fast evaluation of radiation transfer using either the P1 or discrete ordinates method (DOM) approximation with satisfactory accuracy.

Benchmarking grey particle approximations against nongrey particle radiation in circulating fluidized bed combustors

ABSTRACTInvestigation of the effect of grey/nongrey particle property models on radiative heat fluxes and source terms is performed in the dilute zone of the lignite-fired 150 kW Middle East Technical University circulating fluidized bed combustor test rig. Predictive accuracy and computational economy of several grey particle models, geometric optics approximation (GOA) with average particle reflectivity (GOA2), GOA with Fresnel solution for particle reflectivity (GOA3), and Planck mean particle properties from spectral Mie solution are tested by benchmarking their predictions against spectrally banded solution of radiative transfer equation (RTE). Comparisons reveal that all grey models lead to accurate and CPU efficient radiative heat flux predictions. On the other hand, only GOA3 and Planck mean properties are in favorable agreement with the benchmark solution for both incident fluxes and source terms. These findings indicate that grey particle approximation with GOA3 is a more practical choice in solution of RTE as it eliminates the need for spectral calculations.

Influence of atomic kinetics in the simulation of plasma microscopic properties and thermal instabilities for radiative bow shock experiments.

Numerical simulations of laboratory astrophysics experiments on plasma flows require plasma microscopic properties that are obtained by means of an atomic kinetic model. This fact implies a careful choice of the most suitable model for the experiment under analysis. Otherwise, the calculations could lead to inaccurate results and inappropriate conclusions. First, a study of the validity of the local thermodynamic equilibrium in the calculation of the average ionization, mean radiative properties, and cooling times of argon plasmas in a range of plasma conditions of interest in laboratory astrophysics experiments on radiative shocks is performed in this work. In the second part, we have made an analysis of the influence of the atomic kinetic model used to calculate plasma microscopic properties of experiments carried out on magpie on radiative bow shocks propagating in argon. The models considered were developed assuming both local and nonlocal thermodynamic equilibrium and, for the latter situation, we have considered in the kinetic model different effects such as external radiation field and plasma mixture. The microscopic properties studied were the average ionization, the charge state distributions, the monochromatic opacities and emissivities, the Planck mean opacity, and the radiative power loss. The microscopic study was made as a postprocess of a radiative-hydrodynamic simulation of the experiment. We have also performed a theoretical analysis of the influence of these atomic kinetic models in the criteria for the onset possibility of thermal instabilities due to radiative cooling in those experiments in which small structures were experimentally observed in the bow shock that could be due to this kind of instability.

An analysis of the symmetry issue in the ℓ-distribution method of gas radiation in non-uniform gaseous media

The recently proposed ℓ-distribution/ICE (Iterative Copula Evaluation) method of gas radiation suffers from symmetry issues when applied in highly non-isothermal and non-homogeneous gaseous media. This problem is studied in a detailed theoretical way. The objective of the present paper is: 1/to provide a mathematical analysis of this problem of symmetry and, 2/to suggest a decisive factor, defined in terms of the ratio between the narrow band Planck and Rosseland mean absorption coefficients, to handle this issue. Comparisons of model predictions with reference LBL calculations show that the proposed criterion improves the accuracy of the intuitive ICE method for applications in highly non-uniform gases at high temperatures.

Influence of turbulent fluctuations on radiation heat transfer, NO and soot formation under ECN Spray A conditions

This paper investigates the influence of unresolved turbulent fluctuations on radiation heat transfer and formation of NO and soot in an n-dodecane spray flame (known as Spray A) under diesel engine conditions. The transported probability density function (TPDF) model – including the effect of turbulent fluctuations in temperature and composition – has been compared with the well-mixed (WM) model – neglecting these fluctuations – to separate and quantify the relative influence of turbulence-chemistry interactions (TCI), radiation heat transfer and turbulence-radiation interaction (TRI). Radiation is solved with the discrete ordinate method (DOM) including grey radiative properties from soot and gaseous species in the Reynolds-averaged Navier–Stokes (RANS) framework. At Spray A conditions (60bar), the contribution to the Planck mean absorption coefficient from gas-phase species (mainly CO2 and H2O) was found to be comparable to the one of soot, this plays an important role for the radiation reabsorption in the periphery of the jet. Radiation was found to reduce the flame temperature by 10–20K with a consequent reduction of the total NO mass by approximately 5–10%, with these reductions being comparable for both combustion models. However, neglecting turbulent fluctuations results in an increase of the NO mass by a factor of two. The effect of TRI on the emitted radiation was found to be modest (10% at most). The effect of radiation on soot formation was seen to be minor. Overall, it is concluded that under Spray A conditions the effect of radiation heat transfer does influence the NO formation but the effect of the combustion model is more important and needs further attention.

Computationally Efficient Assessments of the Effects of Radiative Transfer, Turbulence Radiation Interactions, and Finite Rate Chemistry in the Mach 20 Reentry F Flight Vehicle

Effects of finite rate chemistry, radiative heat transfer, and turbulence radiation interactions (TRI) are assessed in a fully coupled manner in simulations of the Mach 20 Reentry F flight vehicle. Add-on functions were employed to compute a Planck mean absorption coefficient and the temperature self-correlation term (for TRI effects) in the optically thin shock layer. Transition onset was induced by specifying a wall roughness height at the experimentally observed transition location. The chemistry was modeled employing eight elementary reactions and an equilibrium approach allowing species to relax towards their chemical equilibrium values over the process characteristic time scale. The wall heat fluxes in the turbulent region, density, and velocity profiles compared reasonably well against measurements as well as similar calculations reported previously. The density predictions were more sensitive to the choice of modeling options than the velocities. The radiative source term magnitude agreed closely with its measurements deduced from shock tube experiments. The TRI model predicted a 60% enhancement in emission due to temperature fluctuations in the turbulent boundary layer. While the variations in density and velocity predictions among the models diminished along the length of the body, the O and NO prediction variations extended well into the turbulent boundary layer.

The Generalized SLW Model

The Generalized SLW Method is presented, formulating the SLW method with the help of both the ALBDF and the Inverse ALBDF. The result is two equivalent symmetric models: the SLW Model and the Inverse SLW Model. The advantage of the unified dual formulation and of application of the ALBDF and the Inverse ALBDF is in more efficient implementation of the model and the elimination of the solution of the implicit equations for the absorption cross-sections in the construction of the spectral model in the case of nonisothermal media. The generalized approach explores all possibilities of the SLW method under both direct and inverse formulations including its limiting cases: the minimal one clear gas-one gray gas SLW-1 model, and the case when the number of gray gases approaches infinity termed the Exact SLW model. The present work outlines the steps in a unified construction of the generalized SLW model in isothermal and non-isothermal media, and compares different forms of the modelled radiative quantities in plane parallel media: directional total radiative flux, total emissivity, Planck mean and Rosseland mean absorption coefficients.

Ionization competition effects on population distribution and radiative opacity of mixture plasmas

Ionization competition arising from the electronic shell structures of various atomic species in the mixture plasmas was investigated, taking SiO2 as an example. Using a detailed-level-accounting approximation, we studied the competition effects on the charge state population distribution and spectrally resolved and Planck and Rosseland mean radiative opacities of mixture plasmas. A set of coupled equations for ionization equilibria that include all components of the mixture plasmas are solved to determine the population distributions. For a given plasma density, competition effects are found at three distinct temperature ranges, corresponding to the ionization of M-, L-, and K-shell electrons of Si. Taking the effects into account, the spectrally resolved and Planck and Rosseland mean opacities are systematically investigated over a wide range of plasma densities and temperatures. For a given mass density, the Rosseland mean decreases monotonically with plasma temperature, whereas Planck mean does not. Although the overall trend is a decrease, the Planck mean increases over a finite intermediate temperature regime. A comparison with the available experimental and theoretical results is made.

Microscopic properties of xenon plasmas for density and temperature regimes of laboratory astrophysics experiments on radiative shocks.

This work is divided into two parts. In the first one, a study of radiative properties (such as monochromatic and the Rosseland and Planck mean opacities, monochromatic emissivities, and radiative power loss) and of the average ionization and charge state distribution of xenon plasmas in a range of plasma conditions of interest in laboratory astrophysics and extreme ultraviolet lithography is performed. We have made a particular emphasis in the analysis of the validity of the assumption of local thermodynamic equilibrium and the influence of the atomic description in the calculation of the radiative properties. Using the results obtained in this study, in the second part of the work we have analyzed a radiative shock that propagated in xenon generated in an experiment carried out at the Prague Asterix Laser System. In particular, we have addressed the effect of plasma self-absorption in the radiative precursor, the influence of the radiation emitted from the shocked shell and the plasma self-emission in the radiative precursor, the cooling time in the cooling layer, and the possibility of thermal instabilities in the postshock region.

Effects of radiative heat transfer on the turbulence structure in inert and reacting mixing layers

We use large-eddy simulation to study the interaction between turbulence and radiative heat transfer in low-speed inert and reacting plane temporal mixing layers. An explicit filtering scheme based on approximate deconvolution is applied to treat the closure problem arising from quadratic nonlinearities of the filtered transport equations. In the reacting case, the working fluid is a mixture of ideal gases where the low-speed stream consists of hydrogen and nitrogen and the high-speed stream consists of oxygen and nitrogen. Both streams are premixed in a way that the free-stream densities are the same and the stoichiometric mixture fraction is 0.3. The filtered heat release term is modelled using equilibrium chemistry. In the inert case, the low-speed stream consists of nitrogen at a temperature of 1000 K and the highspeed stream is pure water vapour of 2000 K, when radiation is turned off. Simulations assuming the gas mixtures as gray gases with artificially increased Planck mean absorption coefficients are performed in which the large-eddy simulation code and the radiation code PRISSMA are fully coupled. In both cases, radiative heat transfer is found to clearly affect fluctuations of thermodynamic variables, Reynolds stresses, and Reynolds stress budget terms like pressure-strain correlations. Source terms in the transport equation for the variance of temperature are used to explain the decrease of this variance in the reacting case and its increase in the inert case.