Radiative Equilibrium Research Articles

Low-Frequency Asymptotics of the Spectral Energy Distribution of Equilibrium Radiation in an Electron Plasma

It has been shown that a logarithmic singularity in low-frequency asymptotics of the spectral energy distribution of equilibrium radiation in an electron plasma may occur in the case of arbitrary degeneracy of electrons in the ideal gas approximation for transverse permittivity.

Additive‐Manufactured Ordered Porous Structures Made of Ceria for Concentrating Solar Applications

Porous structures made of redox active ceria are attractive for high‐temperature concentrating solar applications and particularly for the thermochemical splitting of H2O and CO2 as their enhanced heat and mass transport properties lead to fast reaction rates, especially with regard to the absorption of concentrated solar radiation during the endothermic reduction step. Hierarchically ordered porous structures, fabricated by the Schwartzwald replica method on 3D‐printed polymer scaffolds, are experimentally assessed for their ability to volumetrically absorb high‐flux irradiation of up to 670 suns. Temperature distributions across the porosity‐gradient path are measured (peak 1724 K) and compared with that obtained for a reticulated porous ceramic (RPC) structure with a uniform porosity. To assist the analysis, a Monte Carlo ray‐tracing model is developed for pore‐level numerical simulations of the ordered geometries and applied to analyze the absorbing–emitting–scattering exchange and determine the radiation attenuation and the temperature distribution at a radiative equilibrium. In contrast to the Bouguer's law exponential‐decay attenuation of incident radiation observed for the RPC, the ordered structures with a porosity gradient exhibit a step‐wise radiative attenuation that leads to a more uniform temperature distribution across the structure. This in turn predicts a superior redox performance.

Development of a Rapid Determination Method for Strontium-90 in Foods Using a Strontium Extraction Column for Use during Emergency Events

To ensure food safety during emergency events such as nuclear disasters, we developed a practical rapid determination method for strontium-90 (Sr-90) in foods. Purification of Sr from foods was simplified using a commercial Sr-extraction column. We also reduced the waiting time to achieve radiative equilibrium between Sr-90 and Y-90. Finally, we developed a rapid determination method for Sr-90 that can be completed in about a week. Using the new method, stable Sr recoveries exceeded 85%. The trueness of the method ranged from 109 to 115% and the detection limit of Sr-90 was estimated to be 0.07 Bq/kg fresh weight according to a performance evaluation using standard materials. Sr-90 radioactivity concentrations in food samples determined by the new method were highly correlated and nearly equal to concentrations determined by the conventional method. The present study suggests that the new method offers highly sensitive and rapid detection of Sr-90 which are necessary attributes for food tests during emergency events.

Convective Self‐Aggregation As a Cold Pool‐Driven Critical Phenomenon

AbstractConvective self‐aggregation is when thunderstorm clouds cluster over a constant temperature surface in radiative convective equilibrium. Self‐aggregation was implicated in the Madden‐Julian Oscillation and hurricanes. Yet, numerical simulations succeed or fail at producing self‐aggregation, depending on modeling choices. Common explanations for self‐aggregation invoke radiative effects, acting to concentrate moisture in a subdomain. Interaction between cold pools, caused by rain evaporation, drives reorganization of boundary layer moisture and triggers new updrafts. We propose a simple model for aggregation by cold pool interaction, assuming a local number density ρ(r) of precipitation cells, and that interaction scales quadratically with ρ(r). Our model mimics global energy constraints by limiting further cell production when many cells are present. The phase diagram shows a continuous phase transition between a continuum and an aggregated state. Strong cold pool‐cold pool interaction gives a uniform convective phase, while weak interaction yields few and independent cells. Segregation results for intermediate interaction strength.

High-resolution spectroscopy of Boyajian’s star during optical dimming events

Boyajian's star is an apparently normal main sequence F-type star with a very unusual light curve. The dipping activity of the star, discovered during the Kepler mission, presents deep, asymmetric, and aperiodic events. Here we present high resolution spectroscopic follow-up during some dimming events recorded post-Kepler observations, from ground-based telescopes. We analise data from the HERMES, HARPS-N and FIES spectrographs to characterise the stellar atmosphere and to put some constraints on the hypotheses that have appeared in the literature concerning the occulting elements. The star's magnetism, if existing, is not extreme. The spots on the surface, if present, would occupy 0.02% of the area, at most. The chromosphere, irrespective of the epoch of observation, is hotter than the values expected from radiative equilibrium, meaning that the star has some degree of activity. We find no clear evidence of the interstellar medium nor exocoments being responsible for the dimmings of the light curve. However, we detect at 1-2 sigma level, a decrease of the radial velocity of the star during the first dip recorded after the \emph{\emph{Kepler}} observations. We claim the presence of an optically thick object with likely inclined and high impact parameter orbits that produces the observed Rossiter-McLaughlin effect.

The TORUS radiation transfer code

Abstract We present a review of the torus radiation transfer and hydrodynamics code. torus uses a 1-D, 2-D or 3-D adaptive mesh refinement scheme to store and manipulate the state variables, and solves the equation of radiative transfer using Monte Carlo techniques. A framework of microphysics modules is described, including atomic and molecular line transport in moving media, dust radiative equilibrium, photoionisation equilibrium, and time-dependent radiative transfer. These modules provide a flexible scheme for producing synthetic observations, either from analytical models or as post-processing of hydrodynamical simulations (both grid-based and Lagrangian). A hydrodynamics module is also presented, which may be used in combination with the radiation-transport modules to perform radiation-hydrodynamics simulations. Benchmarking and validation tests of each major mode of operation are detailed, along with descriptions and performance/scaling tests of the various parallelisation schemes. We give examples on the uses of the code in the literature, including applications to low- and high-mass star formation, cluster feedback, and stellar winds, along with an Appendix listing the refereed papers that have used torus .

Atmospheric Structure and Radiation Pattern for Neutron-star Polar Caps Heated by Magnetospheric Return Currents

Abstract The Neutron-star Interior Composition ExploreR (NICER) is collecting data to measure the radii of neutron stars by observing the pulsed emission from their surfaces. The primary targets are isolated, rotation-powered pulsars, in which the surface polar caps are heated by bombardment from magnetospheric currents of electrons and positrons. We investigate various stopping mechanisms for the beams of particles that bombard the atmosphere and calculate the heat deposition, the atmospheric temperature profiles, and the energy spectra and beaming of the emerging radiation. We find that low-energy particles with γ ∼ 2–10 deposit most of their energy in the upper regions of the atmosphere, at low optical depth, resulting in beaming patterns that are substantially different from those of deep-heated, radiative equilibrium models. Only particles with energies γ ≳ 50 penetrate to high optical depths and fulfill the conditions necessary for a deep-heating approximation. We discuss the implications of our work for modeling the pulse profiles from rotation-powered pulsars and for the inference of their radii with NICER observations.

Fluctuation Dissipation Theorem and Electrical Noise Revisited

The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter. By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the linear-response regime, the theorem interrelates the macroscopic spontaneous fluctuations of an observable with the kinetic coefficients that are responsible for energy dissipation in the linear response to an applied perturbation. In the quantum form provided by Callen and Welton in their pioneering paper of 1951 for the case of conductors [H. B. Callen and T. A. Welton, Irreversibility and generalized noise, Phys. Rev. 83 (1951) 34], electrical noise in terms of the spectral density of voltage fluctuations, [Formula: see text], detected at the terminals of a conductor was related to the real part of its impedance, [Formula: see text], by the simple relation [Formula: see text] where [Formula: see text] is the Boltzmann constant, [Formula: see text] is the absolute temperature, [Formula: see text] is the reduced Planck constant and [Formula: see text] is the angular frequency. The drawbacks of this relation concern with: (i) the appearance of a zero-point contribution which implies a divergence of the spectrum at increasing frequencies; (ii) the lack of detailing the appropriate equivalent-circuit of the impedance, (iii) the neglect of the Casimir effect associated with the quantum interaction between zero-point energy and boundaries of the considered physical system; (iv) the lack of identification of the microscopic noise sources beyond the temperature model. These drawbacks do not allow to validate the relation with experiments, apart from the limiting conditions when [Formula: see text]. By revisiting the FDT within a brief historical survey of its formulation, since the announcement of Stefan–Boltzmann law dated in the period 1879–1884, we shed new light on the existing drawbacks by providing further properties of the theorem with particular attention to problems related with the electrical noise of a two-terminals sample under equilibrium conditions. Accordingly, among others, we will discuss the duality and reciprocity properties of the theorem, the role played by different statistical ensembles, its applications to the ballistic transport-regime, to the case of vacuum and to the case of a photon gas.

Quantitative evaluation of the computational accuracy for the Monte Carlo calculation of radiative heat transfer

Generally, there is no common method for directly and quantitatively evaluating computational errors in the calculation of radiative transfer. A method for quantitatively evaluating the accuracy in calculation of radiative transfer using the Monte Carlo method (MCM) is proposed, which is based on setting a radiative transfer enclosure in an isothermal and radiative equilibrium state, i.e. a state that equates exactly to a blackbody. For a gray emitting, absorbing, isotropically scattering, cubic enclosure bounded with diffusely emitting and reflecting surfaces, the computational accuracy and efficiency of the MCM are examined under fixed, constant surface emissivity of 0.5 and medium scattering albedo of 0.5. The concept of Mean Optical Thickness per Element (MOTE), that is the product of the absorption coefficient and the average length of three coordinate directions of the discrete space elements, is proposed to serve as a key scaling parameter to evaluate the calculation errors. When the MOTE is less than around 0.1, the errors for the surface elements reach a minimum level, even if the mesh density continues to increase. Scaling laws have been set up to relate the minimum errors for both the surface elements and space elements with the variation in the number of energy bundles (NEB). A desirable calculation error level is set as 1.0% for radiative heat transfer with an acceptable cost, for which the minimum NEBs are 3000 and 750 for the surface and space elements, respectively. For the surface elements, a scaling law relating the NEB and the maximum MOTE has been obtained that will enable the desirable error not to be exceeded; for the space elements, achieving the desirable error is dominated by the NEB, not the MOTE. It is stated that the cases studied in the paper have many limitations, and additional research should be done in the future to address the real cases of interest.

The stellar atmosphere physical system II. An operative sequential algorithm to solve the stellar atmosphere problem

In this paper, the second and the last of the series, we present a sequential algorithm to solve the stellar atmosphere problem that may serve as a paradigm for the solution of more general non-linear and non-local problems. The Iteration Factors (IF) Method is applied to achieve a solution of the radiative transfer equations, consistent with the radiative equilibrium constraint.

Памяти А.А. Рухадзе и В.П. Силина Низкочастотная асимптотика спектрального распределения энергии равновесного излучения в электронной плазме

It is shown that a logarithmic feature in the low-frequency asymptotics of the spectral energy distribution of the equilibrium radiation in an electron plasma occurs with arbitrary degeneration of electrons within the framework of the ideal gas approximation for the transverse dielectric permittivity.

Radiative transfer in a semi-transparent medium enclosed in a spherical annulus with specularly reflecting surfaces

The behaviour of the radiative field inside an emitting-absorbing gray semi-transparent medium at radiative equilibrium, enclosed in a spherical annular cavity bounded by specularly reflecting hot surfaces, is described in an exact analytical way. In this approach, the incident radiation and the radiative flux are expressed as a linear combination of the internal temperatures power 4 at each point of the medium, whatever the reflection on the boundary surfaces is, the coefficients of the combination being the weighting coefficients determined from an analytical way. Some examples show that the proposed method gives perfectly smooth results of high accuracy for both the temperature and flux fields inside the medium.

Application of metaheuristic algorithms for solving inverse radiative boundary design problems with discrete power levels

In this study, an analysis for solving inverse radiative boundary design problem with discrete design variables is developed and presented when radiation is the dominant mode of heat transfer. An absorbing, emitting, and participating medium is considered in radiative equilibrium. The discrete ordinate method (DOM) is implemented to solve the radiative transfer equation (RTE). The goal of the design problem is to find the optimum power of heaters from a discrete set of powers in such a way that they produce the desired temperature and heat flux profile over the design surface. Therefore, several metaheuristic optimization methods including the genetic algorithm (GA), particle swarm optimization (PSO), and its modified forms such as PSO with Constriction Factor (PSO-CF), PSO with repulsion factor (PSO-RF) and PSO with adaptive inertia weight (PSO-W) are explored to solve the inverse problem. The accuracy of the direct solution of radiative heat transfer is examined by comparison of the present results with findings from the literature. Then the efficiency and accuracy of the optimization methods are assessed by their ability of finding and reconstructing of the results from the direct solution. Finally, the effects of some thermos-physical properties including the absorption coefficient, emissivity of the heater surface and design surface, on the optimum solutions are examined. The comparison of the results revealed that the genetic optimization algorithm converged faster and with fewer calculations of the objective function compared to other optimization techniques.

Simulating Jupiter’s weather layer. Part I: Jet spin-up in a dry atmosphere

We investigate the dynamics of Jupiter’s upper troposphere and lower stratosphere using a General Circulation Model that includes two-stream radiation and optional heating from below. Based on the MITgcm dynamical core, this is a new generation of Oxford's Jupiter General Circulation Model [Zuchowski, L.C. et al., 2009. Plan. Space Sci., 57, 1525–1537, doi:10.1016/j.pss.2009.05.008]. We simulate Jupiter’s atmosphere at up to 0.7° horizontal resolution with 33 vertical levels down to a pressure of 18 bar, in configurations with and without a 5.7Wm−2 interior heat flux. Simulations ran for 130000–150000 d to allow the deep atmosphere to come into radiative equilibrium. Baroclinic instability generates alternating, eddy-driven, midlatitude jets in both cases. With interior heating the zonal jets migrate towards the equator and become barotropically unstable. This generates Rossby waves that radiate away from the equator, depositing westerly momentum there via eddy angular momentum flux convergence and spinning up a super-rotating 20ms−1 equatorial jet throughout the troposphere. There are 30–35 zonal jets with latitudinal separation comparable with the real planet, and there is strong eddy activity throughout. Without interior heating the jets do not migrate and a divergent eddy angular momentum flux at the equator spins up a broad, 50ms−1 sub-rotating equatorial jet with weak eddy activity at low latitudes.

Low-Frequency Behavior of the Spectral Energy Distribution Function of Equilibrium Radiation in a Degenerate Electron Gas

The low-frequency asymptotic behavior of the spectral energy distribution density of equilibrium radiation in a collisionless degenerate electron gas is studied. It is shown that the spatial dispersion in the electron gas permittivity leads to a logarithmic singularity in the spectral density distribution at low frequencies, similar to that we previously obtained for a Maxwellian plasma. In this case, the contribution of low frequencies to the total radiation energy remains finite. The results of the analytical consideration coincide with the numerical calculation.

Systematic study of magnetar-powered hydrogen-rich supernovae

Context. It has been suggested that some supernovae (SNe) may be powered by a magnetar formed at the moment of the explosion. While this scenario has mostly been applied to hydrogen-free events, it may also be possible for hydrogen-rich objects. Aims. We aim to explore the effect of including a magnetar on the light curves of supernovae with H-rich progenitors. Methods. We have applied a version of our one-dimensional local thermodynamic equilibrium radiation hydrodynamics code that takes into account the relativistic motion of the ejecta caused by the extra energy provided by the magnetar. For a fixed red supergiant (RSG) progenitor, we have obtained a set of light curves that corresponds to different values of the magnetar initial rotation energy and the spin-down timescale. The model is applied to SN 2004em and OGLE-2014-SN-073, two peculiar Type II SNe with long-rising SN 1987A-like light curves, although with much larger luminosities. Results. The presence of a plateau phase in either normal or superluminous supernovae is one possible outcome, even if a magnetar is continuously injecting energy into the ejecta. In other cases, the light curve shows a peak but not a plateau. Also, there are intermediate events with a first peak followed by a slow decline and a late break of the declining slope. Our models show that bright and long rising morphologies are possible even assuming RSG structures. Conclusions. A large number of supernova discoveries per year reveal unexpected new types of explosions. According to our results, SLSNe II-P are to be expected, as well as a variety of light curve morphologies that can all be possible signs of a newly born magnetar.

Equilibrium for classical zero-point radiation: detailed balance under scattering by a classical charged harmonic oscillator

It has been shown repeatedly over a period of 50 years that the use of relativistic classical physics and the inclusion of classical electromagnetic zero-point radiation leads to the Planck blackbody spectrum for classical radiation equilibrium. However, none of this work involves scattering calculations. In contrast to this work, currently accepted physical theory connects classical physics to only the Rayleigh-Jeans spectrum. Indeed, in the past, it has been shown that a nonlinear classical oscillator (which is necessarily a nonrelativistic scattering system) achieves equilibrium only for the Rayleigh-Jeans spectrum where the random radiation present at the frequency of the second harmonic of the oscillator motion has the same energy per normal mode as the radiation present at the fundamental frequency. Here we continue work emphasizing the importance of relativistic versus nonrelativistic analysis. We consider the scattering of random classical radiation by a charged harmonic oscillator of small but non-zero oscillatory amplitude (which can be considered as a relativistic scattering system) and show that detailed radiation balance holds not only at the fundamental frequency of the oscillator but through the first harmonic corresponding to quadrupole scattering, provided that the radiation energy per normal mode at the first harmonic is double the radiation energy per normal mode at the fundamental frequency. This condition corresponds exactly to the zero-point radiation spectrum which is linear in frequency. It is suggested that for this relativistic scattering system, the detailed balance for zero-point radiation holds not only for the fundamental and first harmonic but extends to all harmonics. Here we have the first example of an explicit relativistic classical scattering calculation; equilibrium corresponds not to the Rayleigh-Jeans spectrum, but rather corresponds to the Lorentz-invariant zero-point radiation spectrum.

Bright GFP with subnanosecond fluorescence lifetime

Fluorescence lifetime imaging microscopy (FLIM) measures fluorescence decay rate at every pixel of an image. FLIM can separate probes of the same color but different fluorescence lifetimes (FL), thus it is a promising approach for multiparameter imaging. However, available GFP-like fluorescent proteins (FP) possess a narrow range of FLs (commonly, 2.3–3.5 ns) which limits their applicability for multiparameter FLIM. Here we report a new FP probe showing both subnanosecond fluorescence lifetime and exceptional fluorescence brightness (80% of EGFP). To design this probe we applied semi-rational amino acid substitutions selection. Critical positions (Thr65, Tyr145, Phe165) were altered based on previously reported effect on FL or excited state electron transfer. The resulting EGFP triple mutant, BrUSLEE (Bright Ultimately Short Lifetime Enhanced Emitter), allows for both reliable detection of the probe and recording FL signal clearly distinguishable from that of the spectrally similar commonly used GFPs. We demonstrated high performance of this probe in multiparameter FLIM experiment. We suggest that amino acid substitutions described here lead to a significant shift in radiative and non-radiative excited state processes equilibrium.

Radiative heat transfer in an absorbing-emitting semi-transparent medium enclosed in a two-dimensional parallelogram cavity with diffuse reflecting boundaries

An exact analytical description of the internal radiative field inside an emitting-absorbing gray semi-transparent medium at radiative equilibrium, enclosed in a two-dimensional parallelogram cavity bounded by diffuse reflecting surfaces is proposed. The exact expressions of the incident radiation and the radiative flux field are angularly and spatially discretized with a double Gauss quadrature, and the temperature field is obtained in an iterative way. Some examples show that the proposed method gives perfectly smooth results of good accuracy for both the temperature and flux fields inside the medium.

Wildfire-driven thunderstorms cause a volcano-like stratospheric injection of smoke

Intense heating by wildfires can generate deep, smoke-infused thunderstorms, known as pyrocumulonimbus (pyroCb), which can release a large quantity of smoke particles above jet aircraft cruising altitudes. Injections of pyroCb smoke into the lower stratosphere have gained increasing attention over the past 15 years due to the rapid proliferation of satellite remote sensing tools. Impacts from volcanic eruptions and other troposphere-to-stratosphere exchange processes on stratospheric radiative and chemical equilibrium are well recognized and monitored. However, the role of pyroCb smoke in the climate system has yet to be acknowledged. Here, we show that the mass of smoke aerosol particles injected into the lower stratosphere from five near-simultaneous intense pyroCbs occurring in western North America on 12 August 2017 was comparable to that of a moderate volcanic eruption, and an order of magnitude larger than previous benchmarks for extreme pyroCb activity. The resulting stratospheric plume encircled the Northern Hemisphere over several months. By characterizing this event, we conclude that pyroCb activity, considered as either large singular events, or a full fire season inventory, significantly perturb the lower stratosphere in a manner comparable with infrequent volcanic intrusions.