Radiative Equilibrium Research Articles

Heating of the solar chromosphere through current dissipation

Context.The solar chromosphere is heated to temperatures higher than predicted by radiative equilibrium. This excess heating is greater in active regions where the magnetic field is stronger.Aims.We aim to investigate the magnetic topology associated with an area of enhanced millimeter (mm) brightness temperatures in a solar active region mapped by the Atacama Large Millimeter/submillimeter Array (ALMA) using spectropolarimetric co-observations with the 1-m Swedish Solar Telescope (SST).Methods.We used Milne–Eddington inversions, nonlocal thermodynamic equilibrium (non-LTE) inversions, and a magnetohydrostatic extrapolation to obtain constraints on the three-dimensional (3D) stratification of temperature, magnetic field, and radiative energy losses. We compared the observations to a snapshot of a magnetohydrodynamics simulation and investigate the formation of the thermal continuum at 3 mm using contribution functions.Results.We find enhanced heating rates in the upper chromosphere of up to ∼5 kW m−2, where small-scale emerging loops interact with the overlying magnetic canopy leading to current sheets as shown by the magnetic field extrapolation. Our estimates are about a factor of two higher than canonical values, but they are limited by the ALMA spatial resolution (∼1.2″). Band 3 brightness temperatures reach about ∼104K in the region, and the transverse magnetic field strength inferred from the non-LTE inversions is on the order of ∼500 G in the chromosphere.Conclusions.We are able to quantitatively reproduce many of the observed features including the integrated radiative losses in our numerical simulation. We conclude that the heating is caused by dissipation in current sheets. However, the simulation shows a complex stratification in the flux emergence region where distinct layers may contribute significantly to the emission in the mm continuum.

Sensitivity of the Horizontal Scale of Convective Self‐Aggregation to Sea Surface Temperature in Radiative Convective Equilibrium Experiments Using a Global Nonhydrostatic Model

AbstractWe conduct radiative convection equilibrium experiments using a global nonhydrostatic model to investigate the dependence of convective self‐aggregation (CSA) on domain size and sea surface temperature (SST). We use a spherical domain with radii varying from 1 to 1/16 of Earth's radius, as well as SSTs between 290 and 310 K. A single aggregation occurs at small domain sizes, whereas multiple aggregations emerge at sufficiently large domain sizes. Domain‐averaged atmospheric temperature and humidity gradually increase with domain size until they reach convergence in cases of multiple aggregations. As domain size increases, surface wind speed increases, and the boundary layer becomes more humid. Because the radiative cooling in the free atmosphere also converges in cases of multiple aggregations, the surface evaporation must be limited due to the constraint of the energy balance. Thus, the convective region shifts from single to multiple aggregations to avoid increasing the surface wind speed. Our results show that the dependence of the horizontal scale of CSA on SST is not monotonic. This dependency is closely related to changes in the structure of the detrainment from the convective region at the melting level, resulting in enhanced radiative cooling at the top of the boundary layer near the convective region for cooler and warmer SSTs. This change in the circulation structure leads to increased surface wind speed with increasing domain size. This process affects the non‐monotonic dependence of the horizontal scale of CSA on SST.

Equilibrium Equation of Thermal Radiation of Earth and Solution

The Earth is isolate on its orbit motion around the Sun. The thermal radiation on Earth determines climate warmer or colder. By Kirchhoff’s law, the thermal radian on Earth must be in an equilibrium state. Which equivalents to an optimum problem. This paper establishes an equilibrium equation of thermal radiation of Earth, transmits it to an optimum problem, and proves that the equilibrium of thermal radiation of Earth is an indifferent equilibrium, neither stable, nor un-stable, based on the Stefan-Boltzmann law and the emissivity formula. The result means that the climate neither getting warmer and warmer, nor getting colder and colder.

Chemical diversity of the atmospheres and interiors of sub-Neptunes: a case study of GJ 436 b

ABSTRACT The atmospheres of sub-Neptunes are expected to exhibit considerable chemical diversity, beyond what is anticipated for gas-giant exoplanets. In the current study, we construct self-consistent radiative transfer and equilibrium chemistry models to explore this chemical diversity. We use GJ 436 b as a case study to further study joint atmosphere-interior models. In particular, we constrain the properties of the interior and atmosphere of the planet based on the available Spitzer measurements. While it is possible to fit the emission spectrum of GJ 436 b using a high-metallicity model, we demonstrate that such an atmosphere is inconsistent with physically plausible interior structures. It remains the case that no existing study can adequately fit the 4.5-$\mu$m Spitzer secondary eclipse measurement, which is probably caused by chemical disequilibrium. Finally, an information content analysis reveals that emission and transmission spectra constrain the carbon-to-oxygen ratio and metallicity at different wavelengths, but the former are less susceptible to flat spectra stemming from highly metal-enriched atmospheres. With the recently launched James Webb Space Telescope, we recommend that future analysis of emission and transmission spectra of sub-Neptune planets are carried out self-consistently using both the atmospheric and interior structure models.

Thermal-Neutron capture cross-section measurements of Neptunium-237 with graphite thermal column in KUR

ABSTRACT In terms of nuclear transmutation studies of minor actinides in nuclear wastes, the present work selected 237Np among them and aimed to measure the thermal-neutron capture cross-section of 237Np using a well-thermalized neutron field by a neutron activation method because there have been discrepancies among reported cross-section data. A 237Np standard solution was used for irradiation samples. The thermal-neutron flux at an irradiation position was measured with flux monitors: 45Sc, 59Co, 98Mo, 181Ta, and 197Au. The 237Np sample was irradiated together with the flux monitors for 30 minutes in the graphite thermal column equipped in the Kyoto University Research Reactor. The similar irradiation was repeated once more to confirm the reproducibility of the results. After irradiation, the 237Np samples were quantified using 312-keV gamma-ray emitted from 233Pa in radiation equilibrium with 237Np. The reaction rates of 237Np were obtained from the peak net counts of gamma-rays emitted from generated 238Np, and then the thermal-neutron capture cross-section of 237Np was found to be 173.8 ± 4.7 barn by averaging the results obtained by the two irradiations. The present result was in agreement with the reported data given by a time-of-flight method within a limit of uncertainty.

Studies on effects of wall temperature variation on heat transfer in hypersonic laminar boundary layer

The effects of wall temperature variation on heat transfer in the hypersonic laminar boundary layer are investigated using a typical blunt-headed cone under isothermal and radiation equilibrium wall boundary conditions, respectively. It is found that, under the isothermal wall boundary condition, the wall heat flux is strongly linearly related to the wall temperature for perfect gas flow, while linearly related to the wall enthalpy for chemical nonequilibrium flow. Under the radiation equilibrium wall condition, even for the same wall point with the same wall temperature, the heat flux may show significant difference from the result of the isothermal wall due to the spatial variation of wall temperature on the upstream flow filed. Consequently, using the heat flux under the isothermal condition to estimate the heat flux under the radiation equilibrium condition by linear interpolation based on the local wall temperature would introduce considerable errors. Further, the analysis of the heat transfer for the radiation equilibrium wall with different emissivity reveals that the heat flux has a strong linear relationship with the local wall temperature (for perfect gas flow) or wall enthalpy (for chemical nonequilibrium flow). Finally, a new method using the heat flux results obtained under known wall parameters to estimate the heat flux under new wall parameters based on the local wall enthalpy linear interpolation is proposed, and the numerical experiments show that the relative errors are basically below 5% for the isothermal wall and the radiation equilibrium wall cases studied in this paper.

High-frequency spectral density of equilibrium radiation and zero oscillations in the presence of electron gas

Based on the general expression for the spectral density of equilibrium radiation in a nonrelativistic plasma medium, the high-frequency asymptotics is found for an electron gas accounting for the spatial dispersion of the transverse dielectric permittivity. The necessity of modifying zero oscillations in the presence of a collisionless plasma medium is shown.

The Flexible Modelling Framework for the Met Office Unified Model (Flex-UM, using UM 12.0 release)

Abstract. The Met Office Unified Model (UM) is a world-leading atmospheric weather and climate model. In addition to comprehensive simulations of the atmosphere, the UM is capable of running idealised simulations, such as the dry physics Held–Suarez test case, radiative convective equilibrium and simulating planetary atmospheres other than Earth. However, there is a disconnect between the simplicity of the idealised UM model configurations and the full complexity of the UM. This gap inhibits the broad use of climate model hierarchy approaches within the UM. To fill this gap, we have developed the Flexible Modelling Framework for the UM – Flex-UM – which broadens the climate model hierarchy capabilities within the UM. Flex-UM was designed to replicate the atmospheric physics of the Geophysical Fluid Dynamics Laboratory (GFDL) idealised moist physics aqua-planet model. New parameterisations have been implemented in Flex-UM, including simplified schemes for convection, large-scale precipitation, radiation, boundary layer and sea surface temperature (SST) boundary conditions. These idealised parameterisations have been implemented in a modular way, so that each scheme is available for use in any model configuration. This has the advantage that we can incrementally add or remove complexity within the model hierarchy. We compare Flex-UM to ERA5 and aqua-planet simulations using the Isca climate modelling framework (based on the GFDL moist physics aqua-planet model) and comprehensive simulations of the UM (using the GA7.0 configuration). We also use two SST boundary conditions to compare the models (fixed SST and a slab ocean). We find the Flex-UM climatologies are similar to both Isca and GA7.0 (though Flex-UM is generally a little cooler, with higher relative humidity and a less pronounced storm track). Flex-UM has a single Intertropical Convergence Zone (ITCZ) in the slab-ocean simulation but a double-ITCZ in the fixed-SST simulation. Further work is needed to ensure that the atmospheric energy budget closes to within 1–2 W m−2, as the current configuration of Flex-UM gains 9–11 W m−2 (the range covers the two SST boundary conditions). Flex-UM greatly extends the modelling hierarchy capabilities of the UM and offers a simplified framework for developing, testing and evaluating parameterisations within the UM.

Quantifying Energy Balance Regimes in the Modern Climate, Their Link to Lapse Rate Regimes, and Their Response to Warming

Abstract Energy balance and lapse rate regimes qualitatively characterize the low, middle, and high latitudes of Earth’s modern climate. Currently we do not have a complete quantitative understanding of the spatiotemporal structure of energy balance regimes [e.g., radiative convective equilibrium (RCE) and radiative advective equilibrium (RAE)] and their connection to lapse rate regimes (moist adiabat and surface inversion). Here we use the vertically integrated moist static energy budget to define a nondimensional number that quantifies where and when RCE and RAE are approximately satisfied in Earth’s modern climate. We find RCE exists year-round in the tropics and in the northern midlatitudes during summertime. RAE exists year-round over Antarctica and in the Arctic with the exception of early summer. We show that lapse rates in RCE and RAE are consistent with moist adiabatic and surface inversion lapse rates, respectively. We use idealized models (energy balance and aquaplanet) to test the following hypotheses: 1) RCE occurs during midlatitude summer for land-like (small heat capacity) surface conditions, and 2) sea ice is necessary for the existence of annual-mean RAE over a polar ocean, such as the Arctic. Consistent with point 1, an aquaplanet configured with a shallow mixed layer transitions to RCE in the midlatitudes during summertime whereas it does not for a deep mixed layer. Furthermore, we confirm point 2 using mechanism-denial aquaplanet experiments with and without thermodynamic sea ice. Finally, we show energy balance regimes of the modern climate provide a useful guide to the vertical structure of the warming response in the annual mean, and seasonally over the tropics and the southern high latitudes.

Temperature Dependence of the Speed of Equilibrium Radiation Propagation

Temperature Dependence of the Speed of Equilibrium Radiation Propagation

Analysis of radiative heat transfer in two-dimensional irregular geometries by developed immersed boundary–lattice Boltzmann method

The Immersed Boundary–lattice Boltzmann method (IB-LBM) is developed to analyze radiative heat transfer in two-dimensional (2D) irregular geometries. Lattice Boltzmann method (LBM) has been adopted to discretize the radiative heat transfer equation in an absorbing and emitting media, and the immersed boundary method (IBM) is used to model the boundaries of irregular geometries. Due to the mismatch between boundary and computational nodes in the Immersed Boundary method, a radiative density term based on the difference of radiation intensity is added to the lattice Boltzmann equation to satisfy the boundary condition. Radiative heat flux distribution is obtained for several irregular geometries which are maintained at an isothermal media or radiative equilibrium condition in the enclosure. The results are successfully validated by comparing the results obtained from other methods of irregular geometries analysis, such as the blocked-off domain, embedded boundary, and body-fitted grid method. According to the obtained results, their accuracy, and numerical cost, the combined IB-LBM benefits from the unique and worthy advantages of both IBM and LBM in solving the complicated analysis of 2D radiative heat transfer problems. Compared to the traditional methods used for the radiative analysis of irregular geometries, the immersed boundary method can solve the complexities of modeling curved boundaries effortlessly. It should be pointed that for optically thin media, the proposed model shows poor performance.

Джинсовская неустойчивость астрофизической самогравитирующей среды при наличии высокого радиационного давления и диффузионного переноса излучения

Within the framework of the problem of modeling the evolution of a protostellar disk, the influence of radiation on the Jeans gravitational instability for a self-gravitating optically thick (for intrinsic infrared radiation) gas-dust medium is discussed, taking into account the influence of radiation pressure and diffusion transfer of radiation on the critical wavelength of the perturbing wave. Two approximations of radiative diffusion are considered: 1. the case of ideal radiative equilibrium, when the temperatures of matter and radiation are the same; 2. the case of the time dependence of the radiation field, when there is an energy decoupling between radiation and matter. Using the analysis of the normal regime, dispersion relations are derived that allow one to obtain modifications of the Jeans gravitational instability criterion under the influence of radiation pressure and radiation diffusion. In particular, it is shown that, in contrast to local radiation equilibrium, when the acoustic velocity of the gas coincides with the isothermal speed of sound, in the case of a difference in the temperatures of radiation and gas, the perturbing wave propagates with the adiabatic speed of sound in the gas. The results obtained are aimed at solving the problem of gravitational instability of individual massive protostellar disks or self-gravitating radiation media characterized by large optical depths for their own infrared radiation transformed by dust.

Radiative Equilibrium in a Square Cavity Containing a Square Inner Centred Obstacle, Both with Reflecting Surfaces, and an Absorbing-Emitting Medium

Radiative Equilibrium in a Square Cavity Containing a Square Inner Centred Obstacle, Both with Reflecting Surfaces, and an Absorbing-Emitting Medium

High-frequency asymptotics of one integral in the theory of equilibrium radiation of electron gas

It is considered an improper integral that determines the high-frequency asymptotics of the spectral energy distribution of equilibrium radiation in an ideal electron gas. It has been established that in the "high-frequency" limit the asymptotics of this integral has a power-law character, and its value is proportional to the density of the electron gas as a function of temperature and chemical potential for arbitrary degeneracy of electrons. Keywords: equilibrium radiation, spectral energy distribution, electron gas.

Non-Gaussian effects of the Saha\u2019s ionization in the early universe

Tsallis’ thermostatistical has received increasing attention due to its success in describing phenomena that manifest unusual thermodynamic properties. In this context, the generalized Saha equation must follow a condition of generalized thermal equilibrium of matter and radiation. The present work aims to explore the non-Gaussian effects on Saha’s ionization via Tsallis statistics. To accomplish this, we generalized the number density taking into account a non-Gaussian Fermi-Dirac distribution and then set out the Saha equation for the cosmological recombination. As a result, we highlight two new non-Gaussian effects: (i) two generalized chemical equilibrium conditions, one for the relativistic regime and the other for the non-relativistic one; and (ii) the hydrogen binding q-energy. We demonstrated that to yield smooth shifts in the binding energy, the a-parameter must be very small. We also showed that binding q-energy exhibits symmetrical behavior around the value of the standard binding energy. Besides, we used the q-energy in order to access other hydrogen energy levels, and we ascertained the values of the a-parameter that access those levels and their relationship to temperature. Finally, we employed these results to examine the non-Gaussian effects of the deuterium bottleneck, recombination, and the particle anti-particle excess.

Explanations for Unusual Seasonal Variations in Chang’E-2 Microwave Radiometer Datasets of Lunar Double-Shaded Permanently Shadowed Regions

Near-surface temperatures of permanently shadowed regions (PSRs) on the Moon provide fundamental information for water ice exploration. Seasonal temperature variations of PSRs are found in both Chang’E-2 microwave radiometer data and Diviner Lunar radiometer observations. Furthermore, unusual microwave brightness temperature variations between February 2011 and May 2011 of double-shaded PSRs are shown in the Chang’E-2 observational data, i.e., that the minimum microwave brightness temperature occurs before the time when the infrared brightness temperature reaches the minimum in double-shaded PSRs. To interpret this phenomenon, the 1-D thermal model and the microwave radiation transfer model are used. In the thermal model, the reradiation energy from the illuminated area is estimated by effective solar irradiance, which is an analytic solution for the radiative equilibrium temperature in the shadowed area of a spherical bowl-shaped crater. In the simulation, an assumed internal 0.4 W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> heat flow beneath the lunar surface made a plausible fit to the unusual variations during some lunations. However, this is a huge value compared with the well-known heat flow value of about 0.018 W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Furthermore, it is difficult to obtain this extra heat energy by lateral conduction below the surface in a large impact crater due to the small thermal conductivity of the lunar regolith. Finally, the unusual microwave brightness temperature (TB) changes are concluded to be caused by a calibration problem after excluding other possible reasons. In addition, a statistical correction method is applied to revise the problematic TB data to obtain the proper variation trend of the brightness temperature.

Effects of Ellipsoidal Earth Model on Estimating the Sensitivity of Moon-Based Outgoing Longwave Radiation Measurements

The outgoing longwave radiation (OLR) at the top of the atmosphere is a key component of Earth’s radiation budget. Moon-based OLR observations take Earth as a single point, and provide an alternative to near-Earth orbital measurements. However, in the sensitivity design of a sensor, the effects of adopted Earth’s shape on the design of the sensitivity are particularly severe in the Moon-based OLR observations, which needs to be fully considered. In this study, the observational solid angle related to the ellipsoidal Earth model during OLR measurements was analyzed to improve upon previous studies conducted under the assumption of a spherical Earth. The radiative equilibrium temperature of the Earth–atmosphere system was then applied to simulate the emitted OLR according to Stephen Boltzmann’s law. The magnitude and sensitivity of the Moon-based OLR measurements were estimated by combining the observational solid angle and the simulated OLR. The results showed that the sensitivity of Moon-based OLR measurements is on the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-3}$ </tex-math></inline-formula> W m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> , and the effects of Earth’s shape on sensitivity estimates cannot be ignored. Further, quantitative estimates revealed that a more realistic (ellipsoid) shape is needed when designing the sensitivity of relevant sensors.

Высокочастотная асимптотика одного интеграла в теории равновесного излучения электронного газа

It is considered an improper integral that determines the high-frequency asymptotics of the spectral energy distribution of equilibrium radiation in an ideal electron gas. It has been established that in the "high-frequency" limit the asymptotics of this integral has a power-law character, and its value is proportional to the density of the electron gas as a function of temperature and chemical potential for arbitrary degeneracy of electrons

Assessing Middle School Students’ Understanding of Radiative Equilibrium, the Greenhouse Effect, and Global Warming Through Their Interpretation of Heat Balance Data

Assessing Middle School Students’ Understanding of Radiative Equilibrium, the Greenhouse Effect, and Global Warming Through Their Interpretation of Heat Balance Data

Shear-Convection Interactions and Orientation of Tropical Squall Lines.

Squall lines are known to be the consequence of the interaction of low‐level shear with cold pools associated with convective downdrafts. Also, as the magnitude of the shear increases beyond a critical shear, squall lines tend to orient themselves. The existing literature suggests that this orientation reduces incoming wind shear to the squall line, and maintains equilibrium between wind shear and cold pool spreading. Although this theory is widely accepted, very few quantitative studies have been conducted on supercritical regime especially. Here, we test this hypothesis with tropical squall lines obtained by imposing a vertical wind shear in cloud resolving simulations in radiative convective equilibrium. In the sub‐critical regime, squall lines are perpendicular to the shear. In the super‐critical regime, their orientation maintain the equilibrium, supporting existing theories. We also find that as shear increases, cold pools become more intense. However, this intensification has little impact on squall line orientation.