Radiative Equilibrium Research Articles

Neutrino Photoproduction on the Electron of a Hydrogen-Like Atom

The process of interaction of a photon with the bound electron of a hydrogen-like atom with creation of a neutrino pair $$ \upgamma +{(Ze)}^{\ast \ast}\to \overline{\upnu \upnu}+{(Ze)}^{\ast } $$ is considered here for the first time. This process can take place with and without a change in the energy of the pair relative to the energy of the “initial” photon due to atomic transitions. It is shown that in the case when the system of atoms is located in an equilibrium radiation field with temperature T << m e this process can be neglected in comparison with spontaneous emission of the hydrogen-like atom $$ {(Ze)}^{\ast}\to (Ze)+\upnu \overline{\upnu} $$ , despite the smaller power of the expansion parameter (Zα) < < 1, α = e 2/ℏc ≈ 1/137 in the expressions for the cross sections and probabilities. Calculations have been performed for the first time using the density matrix, introduced in the previous paper, of the electron in the field of the nucleus in the leading approximation in (Zα).

Measurement and simulation of the temperature evolution of a short pulse laser heated buried layer target

Short pulse laser heated buried layers experiments have been performed on the Orion laser facility to study the time-resolved emission characteristics of plasmas with mass densities ≥ 1 g/cc and electron temperatures > 500 eV. Our streak camera measurements focused on the K-shell emission lines of He-like and H-like aluminum from a buried aluminum layer. The data were analyzed by comparison to synthetic spectra generated with the non-local thermodynamic equilibrium (NLTE) radiation transfer code Cretin, which yielded maximum temperatures of nearly 800 eV at near solid density. The time precise history of the temperature evolution was reproduced with a 1-D radiation hydrodynamic code; however, the known effect of lateral transport of energy out of the focal spot made exacting agree with theory difficult. Thus, we have observed densities of ≥ 1 g/cc and temperatures of > 500 eV using the 1-D analysis, which supports the idea that the aluminum plasma is locally hotter than inferred from our spatially integrating measurements and that modeling requires the inclusion of 2-dimensional effects.

Enhancing the radiative heat dissipation from high-temperature SF6 gas plasma by using selective absorbers

Radiative cooling accomplished by tailoring the properties of spectral thermal emission is an interesting method for energy harvesting and high-efficiency passive cooling of terrestrial structures. This strategy, however, has not been extended to cool enclosed heat sources, common in engineering applications, and heat sources in high-temperature environments where radiative transfer plays a dominant role. Here we show a radiative cooling scheme for a high-temperature gaseous medium, using radiative heat extraction with selective absorbers matched to the gas-selective emission properties. We used SF6 gas plasma as a model, because this gas is used in gas circuit breakers, which require effective cooling of the hot insulating gas. Our theoretical analysis confirms that a copper photonic absorber, matched to the ultraviolet-to-near-infrared-selective emission properties of the gas, effectively extracts heat from the high-temperature gas plasma and lowers the radiative equilibrium gas temperature by up to 1270 K, exceeding both blackbody-like and metallic surfaces in practical operating conditions.

An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits

AbstractThis paper is about the construction of a unified gas-kinetic scheme (UGKS) for a coupled system of radiative transport and material heat conduction with different diffusive limits. Different from the previous approach, instead of including absorption/emission only, the current method takes both scattering and absorption/emission mechanism into account in the radiative transport process. As a result, two asymptotic limiting solutions will appear in the diffusive regime. In the strong absorption/emission case, an equilibrium diffusion limit is obtained, where the system is mainly driven by a nonlinear diffusion equation for the equilibrium radiation and material temperature. However, in the strong scattering case, a non-equilibrium limit can be obtained, where coupled nonlinear diffusion system with different radiation and material temperature is obtained. In addition to including the scattering term in the transport equation, an implicit UGKS (IUGKS) will be developed in this paper as well. In the IUGKS, the numerical flux for the radiation intensity is constructed implicitly. Therefore, the conventional CFL constraint for the time step is released. With the use of a large time step for the radiative transport, it becomes possible to couple the IUGKS with the gas dynamic equations to develop an efficient numerical method for radiative hydrodynamics. The IUGKS is a valid method for all radiative transfer regimes. A few numerical examples will be presented to validate the current implicit method for both optical thin to optical thick cases.

Comparison of the blocked-off and embedded boundary methods in radiative heat transfer problems in 2D complex enclosures at radiative equilibrium

Radiative heat transfer in participating media at radiative equilibrium in two-dimensional complex geometries will be investigated using two Cartesian boundary treatments, i.e. the blocked-off method and the embedded boundary method. The main advantages of Cartesian formulation are to simplify grid generation and using efficient Cartesian solvers for complicated problems. Angular and spatial discretization of the radiative transfer equation are performed using the discrete ordinates method and the finite volume method, respectively. The accuracy of both methods in solution of radiative heat transfer problems in irregular geometries are verified by comparison with benchmark solutions from literatures. Then, in order to investigate all features of the blocked-off and embedded boundary methods, two radiative problems with complex enclosures that contain gray absorbing and emitting medium at radiative equilibrium are examined. The results obtained from the two methods are compared with each other as well as with results obtained by body-fitted grid system. It has been shown that for a medium at radiative equilibrium with Cartesian formulation, the embedded boundary method is the method of choice, especially for calculations near the complex boundaries. It should be noted that for optically thick media, both blocked-off and embedded boundary methods show poor performance.

The tropical precipitation pickup threshold and clouds in a radiative convective equilibrium model: 2. Two‐layer moisture

AbstractThis paper complements Part 1 in which cloud processes of aggregated convection are examined in a large‐domain radiative convective equilibrium simulation in order to uncover those responsible for a consistently observed, abrupt increase in mean precipitation at a column relative humidity value of approximately 77%. In Part 2, the focus is on how the transition is affected independently by total moisture above and below the base of the melting layer. When mean precipitation rates are examined as simultaneous functions of these two moisture layers, four distinct behaviors are observed. These four behaviors suggest unique, yet familiar, physical regimes in which (i) little rain is produced by infrequent clouds, (ii) shallow convection produces increasing warm rain with increasing low‐level moisture, (iii) deep convection produces progressively heavier rain above the transition point with increasing total moisture, and (iv) deep stratiform cloud produces increasingly intense precipitation from melting for increasing upper level moisture. The independent thresholds separating regimes in upper and lower layer humidity are shown to result in the value of total column humidity at which a transition between clear air and deep convection, and therefore a pickup in precipitation, is possible. All four regimes force atmospheric columns toward the pickup value at 77% column humidity, but each does so through a unique set of physical processes. Layer moisture and microphysical budgets are analyzed and contrasted with column budgets.

The tropical precipitation pickup threshold and clouds in a radiative convective equilibrium model: 1. Column moisture

AbstractA survey of published results indicates that a column relative humidity near 77% is consistently observed to separate raining and nonraining columns in a time and space mean in the tropics, but why this approximate value of humidity should initiate such a statistical state transition is not readily apparent. An investigation is conducted of the submesoscale cloud processes that link column relative humidity to this abrupt pickup in heavy precipitation and of the magnitude of humidity at which this transition occurs. A cloud system resolving model in radiative convective equilibrium is used. Precipitation statistics from this simulation indicate a switch in mean precipitation state at 77% relative humidity with infrequent heavy rainfall at lower humidity. These statistics are broadly insensitive to spatial scaling. Low‐level cloud fraction and convergent flux of moisture are shown to be sensitive to column humidity near 77%, while upper level cloud fraction is markedly less sensitive. Mean updraft mass flux increases with increasing humidity but only at values of humidity well above the pickup. Both warm rain processes and melting are shown to depend strongly on column humidity near the pickup but in different circumstances. No single process is determined to result in a pickup in precipitation. It is suggested that column humidity temporally leads precipitation and therefore causes its intensity.

Radiative entropy generation in a gray absorbing, emitting, and scattering planar medium at radiative equilibrium

Radiative entropy generation through a gray absorbing, emitting, and scattering planar medium at radiative equilibrium with diffuse-gray walls is investigated. The radiative transfer equation and radiative entropy generation equations are solved using discrete ordinates method. Components of the radiative entropy generation are considered for two different boundary conditions: two walls are at a prescribed temperature and mixed boundary conditions, which one wall is at a prescribed temperature and the other is at a prescribed heat flux. The effect of wall emissivities, optical thickness, single scattering albedo, and anisotropic-scattering factor on the entropy generation is attentively investigated. The results reveal that entropy generation in the system mainly arises from irreversible radiative transfer at wall with lower temperature. Total entropy generation rate for the system with prescribed temperature at walls remarkably increases as wall emissivity increases; conversely, for system with mixed boundary conditions, total entropy generation rate slightly decreases. Furthermore, as the optical thickness increases, total entropy generation rate remarkably decreases for the system with prescribed temperature at walls; nevertheless, for the system with mixed boundary conditions, total entropy generation rate increases. The variation of single scattering albedo does not considerably affect total entropy generation rate. This parametric analysis demonstrates that the optical thickness and wall emissivities have a significant effect on the entropy generation in the system at radiative equilibrium. Considering the parameters affecting radiative entropy generation significantly, provides an opportunity to optimally design or increase overall performance and efficiency by applying entropy minimization techniques for the systems at radiative equilibrium.

Inverse Design for Radiative Heat Source in Nongray Media

An optimization technique is performed to obtain the unknown heat source distribution to produce the known temperature and heat flux distribution over the design surface. The medium is considered as nongray, absorber, emitter, and nonscatter in radiative equilibrium. The discrete ordinates method in combination with the spectral line-based weighted sum of gray gases approach is used for solving the radiative transfer equation. The inverse problem involves the minimization of an appropriate objective function, which is minimized by the conjugate gradient method. The objective function is defined as the square residuals between the desired and estimated heat flux distribution over the design surface. Some examples are presented to prove the ability of the approach for achieving the desired thermal conditions.

Inelastic Scattering of a Photon by a Hydrogen-Like Atom

Inelastic scattering of a photon by a bound electron of a hydrogen-like atom is considered. An expression for the cross section of this process, which can take place both without and with a change in the energy of the photon due to atomic transitions, is obtained. Within the framework of the standard technique of Feynman diagrams with a free electron propagator, general expressions for the amplitude and cross section of the process have been obtained. Arguments in favor of the validity of using this representation of the propagator in the calculation of the amplitude in the field of a nucleus are presented. As an accompanying result, an expression for the density matrix of an electron in the field of a nucleus is found in the leading approximation in the small “atomic” expansion parameter (Zα) << 1, α = e 2 / ћc. It is shown that in a real situation at temperatures Т << m e of the equilibrium radiation field this process can be neglected in comparison with spontaneous emission of radiation by a hydrogen-like atom despite the lower power of the parameter (Zα) in its amplitude. As far as is known, this quite important question, framed in such a way, has not been discussed in the literature.

Mathematical Assessment of Physical and Chemical Processes from the Middle B to the Early F Type Main Sequence Stars

AbstractThe middle B to the early F Main Sequence stars have some of the most quiet stellar atmospheres. In this part of the HR diagram we find stars with atmospheres in radiative equilibrium. They lack the convective circulations of the middle F and cooler stars and the massive stellar winds of hotter stars. When stars of different mass evolve off the Main Sequence in this part of the HR Diagram their evolutionary paths do not cross initially. Thus stars with the same effective temperature and surface gravity have the same luminosity and mass. By comparing their elemental abundances, we might be able to identify physical processes which cause any differences in their abundances. Here we begin with stars whose effective temperatures and surface gravities are similar, and which have been analyzed by us using spectra obtained from the Dominion Astrophysical Observatory (DAO). Improvements in our knowledge of the energy distributions of stars (for example via GAIA measurements) should lead to improved estimates of stellar effective temperatures and surface gravities.

The Role of Monsoon-like Zonally Asymmetric Heating in Interhemispheric Transport.

While the importance of the seasonal migration of the zonally averaged Hadley circulation on interhemispheric transport of trace gases has been recognized, few studies have examined the role of the zonally asymmetric monsoonal circulation. This study investigates the role of monsoon-like zonally asymmetric heating on interhemispheric transport using a dry atmospheric model that is forced by idealized Newtonian relaxation to a prescribed radiative equilibrium temperature. When only the seasonal cycle of zonally symmetric heating is considered, the mean age of air in the Southern Hemisphere since last contact with the Northern Hemisphere midlatitude boundary layer, is much larger than the observations. The introduction of monsoon-like zonally asymmetric heating not only reduces the mean age of tropospheric air to more realistic values, but also produces an upper-tropospheric cross-equatorial transport pathway in boreal summer that resembles the transport pathway simulated in the NASA Global Modeling Initiative (GMI) Chemistry Transport Model driven with MERRA meteorological fields. These results highlight the monsoon-induced eddy circulation plays an important role in the interhemispheric transport of long-lived chemical constituents.

Monte Carlo simulation of radiative transfer in a medium with varying refractive index specified at discrete points

• Monte Carlo simulation for radiative transfer in refractive media is presented. • Discrete ray tracing using scattered discrete refractive indices is developed. • Refractive-index values and gradients are retreived by a moving least square method. • Ray-tracing results for various irregularly-spaced refractive indices are examined. A Monte Carlo method with discrete ray tracing is developed to simulate radiative transfer in a medium with a spatially varying refractive-index distribution available merely at a set of arbitrary discrete points. We solve the ray equation by a Runge−Kutta Dormand−Prince method to carry out the numerical ray tracing. To retrieve the refractive-index values and gradients needed in the discrete ray tracing, we apply cubic spline interpolation for one-dimensional simulation and a moving least square (MLS) method for two-dimensional simulation. The influence of the basis vectors and the numbers of sampled data used by the MLS method on ray tracing based on the retrieved refractive-index values and gradients has been examined. The results of radiative equilibrium in a planar medium and radiative transfer in two-dimensional media with different geometries and conditions obtained by the present methods are compared with those obtained by solving the integral equations of radiative transfer and the discrete ordinates method. The comparisons show that the present methods generate accurate results for radiative transfer with various geometries, parameters and refractive-index distributions specified at discrete points.

Photoionization Models for the Inner Gaseous Disks of Herbig Be Stars: Evidence against Magnetospheric Accretion?*

Abstract We investigate the physical properties of the inner gaseous disks of three hot Herbig B2e stars, HD 76534, HD 114981, and HD 216629, by modeling CFHT-ESPaDOns spectra using non-LTE radiative transfer codes. We assume that the emission lines are produced in a circumstellar disk heated solely by photospheric radiation from the central star in order to test whether the optical and near-infrared emission lines can be reproduced without invoking magnetospheric accretion. The inner gaseous disk density was assumed to follow a simple power-law in the equatorial plane, and we searched for models that could reproduce observed lines of H i (Hα and Hβ), He i, Ca ii, and Fe ii. For the three stars, good matches were found for all emission line profiles individually; however, no density model based on a single power-law was able to reproduce all of the observed emission lines. Among the single power-law models, the one with the gas density varying as ∼10−10(R */R)3 g cm−3 in the equatorial plane of a 25 R * (0.78 au) disk did the best overall job of representing the optical emission lines of the three stars. This model implies a mass for the Hα-emitting portion of the inner gaseous disk of ∼10−9 M *. We conclude that the optical emission line spectra of these HBe stars can be qualitatively reproduced by a ≈1 au, geometrically thin, circumstellar disk of negligible mass compared to the central star in Keplerian rotation and radiative equilibrium.

Irradiation of astrophysical objects – SED and flux effects on thermally driven winds

We develop a general method for the self consistent calculation of the hydrodynamics of an astrophysical object irradiated by a radiation field with an arbitrary strength and spectral energy distribution (SED). Using the XSTAR photoionization code, we calculate heating and cooling rates as a function of gas photoionization parameter and temperature for several examples of SEDs: bremsstrahlung, blackbody, hard and soft state XRBs, Type 1 and Type 2 AGN. As an application of our method we study the hydrodynamics of 1-dimensional spherical winds heated by a uniform radiation field using the code Athena++. We find that in all cases explored a wind settles into a transonic, steady state. The wind evolves along the radiative heating equilibrium curve until adiabatic cooling effects become important and the flow departs from radiative equilibrium. If the flow is heated very rapidly, for example as in a thermally unstable regime, the corresponding column density of gas is low. Perhaps one of the most intriguing results of our work is the two stage acceleration of the wind that happens when there are two thermally unstable regions and the flux is relatively high. The efficiency with which the radiation field transfers energy to the wind is dependent on the SED of the external source, particularly the relative flux of soft X-rays. These results suggest that detailed photoionization calculations are essential not only to predict spectra but also to properly capture the flow dynamics.

Spatial redistribution of radiation in flip-chip photodiodes based on InAsSbP/InAs double heterostructures

The spatial distribution of equilibrium and nonequilibrium (including luminescent) IR (infrared) radiation in flip-chip photodiodes based on InAsSbP/InAs double heterostructures (λmax = 3.4 μm) is measured and analyzed; the structural features of the photodiodes, including the reflective properties of the ohmic contacts, are taken into account. Optical area enhancement due to multiple internal reflection in photodiodes with different geometric characteristics is estimated.

HELIOS: AN OPEN-SOURCE, GPU-ACCELERATED RADIATIVE TRANSFER CODE FOR SELF-CONSISTENT EXOPLANETARY ATMOSPHERES

We present the open-source radiative transfer code named HELIOS, which is constructed for studying exoplanetary atmospheres. In its initial version, the model atmospheres of HELIOS are one-dimensional and plane-parallel, and the equation of radiative transfer is solved in the two-stream approximation with non-isotropic scattering. A small set of the main infrared absorbers is employed, computed with the opacity calculator HELIOS-K and combined using a correlated-$k$ approximation. The molecular abundances originate from validated analytical formulae for equilibrium chemistry. We compare HELIOS with the work of Miller-Ricci & Fortney using a model of GJ 1214b, and perform several tests, where we find: model atmospheres with single-temperature layers struggle to converge to radiative equilibrium; $k$-distribution tables constructed with $\gtrsim 0.01$ cm$^{-1}$ resolution in the opacity function ($ \lesssim 10^3$ points per wavenumber bin) may result in errors $\gtrsim 1$-10 % in the synthetic spectra; and a diffusivity factor of 2 approximates well the exact radiative transfer solution in the limit of pure absorption. We construct "null-hypothesis" models (chemical equilibrium, radiative equilibrium and solar element abundances) for 6 hot Jupiters. We find that the dayside emission spectra of HD 189733b and WASP-43b are consistent with the null hypothesis, while it consistently under-predicts the observed fluxes of WASP-8b, WASP-12b, WASP-14b and WASP-33b. We demonstrate that our results are somewhat insensitive to the choice of stellar models (blackbody, Kurucz or PHOENIX) and metallicity, but are strongly affected by higher carbon-to-oxygen ratios. The code is publicly available as part of the Exoclimes Simulation Platform (ESP; exoclime.net).

Version of Accelerating Expansion Is in Contradistinction to a Lot of Facts of Observations

The term “accelerating expansion” is contradicted to follow observation facts: Accelerating expansion means repulsive force account for 70% and the universal space will be open. However, the observation facts indicate that the cosmetic space is flat and cosmos microwave background radiation is blackbody radiation. That is to say, it is equilibrium radiation. The cosmos is a gravitationally bound system. Obviously, open space cannot form bound system. A lot of observation facts and the Hubble relation support that the cosmos is always in reduction expansion. The term is also contradicted to the warped and closed space demanded by cosmetic principle.

The radii and limb darkenings of α Centauri A and B

The photospheric radius is one of the fundamental parameters governing the radiative equilibrium of a star. We report new observations of the nearest solar-type stars α Centauri A (G2V) and B (K1V) with the VLTI/PIONIER optical interferometer. The combination of four configurations of the VLTI enable us to measure simultaneously the limb darkened angular diameter θLD and the limb darkening parameters of the two solar-type stars in the near-infrared H band (λ = 1.65 μm). We obtain photospheric angular diameters of θLD(A) = 8.502 ± 0.038 mas (0.43%) and θLD(B) = 5.999 ± 0.025 mas (0.42%), through the adjustment of a power law limb darkening model. We find H band power law exponents of α(A) = 0.1404 ± 0.0050 (3.6%) and α(B) = 0.1545 ± 0.0044 (2.8%), which closely bracket the observed solar value (α⊙ = 0.15027). Combined with the parallax π = 747.17 ± 0.61 mas previously determined, we derive linear radii of RA = 1.2234 ± 0.0053 R⊙ (0.43%) and RB = 0.8632 ± 0.0037 R⊙ (0.43%). The power law exponents that we derive for the two stars indicate a significantly weaker limb darkening than predicted by both 1D and 3D stellar atmosphere models. As this discrepancy is also observed on the near-infrared limb darkening profile of the Sun, an improvement of the calibration of stellar atmosphere models is clearly needed. The reported PIONIER visibility measurements of α Cen A and B provide a robust basis to validate the future evolutions of these models.

The Role of Eddy Diffusivity on a Poleward Jet Shift

Abstract The authors use a quasigeostrophic (QG) two-layer model to examine how eddies modify the meridional asymmetry of a zonal jet. The initial asymmetry is introduced in the model’s “radiative equilibrium state” and is intended to mimic a radiatively forced poleward jet shift simulated by climate models. The calculations show that the initial “poleward” jet shift in the two-layer model is amplified by eddy potential vorticity fluxes. This eddy-accentuation effect is greater as the baroclinicity of the equilibrium state is reduced, suggesting that seasonal variations in baroclinicity may help explain observed and modeled jet-shift sensitivity to season. The eddy-accentuated jet shift from the corresponding radiative equilibrium state is more clearly visible in the slowly varying, eddy-free reference state of Nakamura and Zhu. This reference state formally responds only to nonadvective, nonconservative processes, but ultimately arises from the advective eddy fluxes. The implication is that fast eddies are capable of driving a slowly varying jet shift, which may be balanced by nonconservative processes such as radiative heating/cooling.