Abstract Increasing interest in understanding the formation and dynamics of cool coronal condensations like solar prominences leads to complex magneto-hydrodynamical (MHD) simulations which assume a variety of physical processes responsible for energy balance. Formation of cool structures and their maintenance over the observed periods requires detailed treatment of heating/cooling processes of which the radiative ones are critically important. Most of up-to-date models use the so-called optically-thin radiative losses to account for radiative cooling. In this article, we present radiative-transfer simulations which demonstrate the importance of optically-thick line and continuum transitions. We model the process of free relaxation of prominence kinetic temperature towards the radiative equilibrium which demonstrates the formation of condensations in case where the radiative processes dominate the energy balance. We show a grid of isobaric models and how they relax to radiative equilibrium where the radiative losses are balanced by radiative gains. We also compare our results with previous works. Finally we stress the importance of realistic net radiative cooling rates for MHD modeling of cool coronal condensations.

Abstract Carbon-rich Wolf–Rayet (W-R) stars are significant contributors of carbonaceous dust to the galactic environment; however, the mechanisms and conditions for formation and subsequent evolution of dust around these stars remain open questions. Here we present JWST observations of the W-R+W-R colliding-wind binary Apep, which reveal an intricate series of nested concentric dust shells that are abundant in detailed substructure. The striking regularity in these substructures between successive shells suggests an exactly repeating formation mechanism combined with a highly stable outflow that maintains a consistent morphology even after reaching 0.6 pc (assuming a distance of 2.4 kpc) into the interstellar medium. The concentric dust shells show subtle deviations from spherical outflow, which could reflect orbital modulation along the eccentric binary orbit or nonsphericity in the stellar wind. Tracking the evolution of dust across the multitiered structure, we measure the dust temperature evolution that can broadly be described assuming an amorphous carbon composition in radiative thermal equilibrium with the central stars. The temperature profile and orbital period place new distance constraints that support Apep being at a greater distance than previously estimated, reducing the line-of-sight and sky-plane wind speed discrepancy previously thought to characterize the system.

Abstract We present measurements of the dusty torus sizes of 51 active galactic nuclei (AGNs) with a redshift of z < 0.8. Our analysis utilizes about 16 yr of optical photometric data of 146 AGNs from various time-domain surveys, including ASAS-SN, CRTS, and ZTF, along with 14 yr of infrared data in the W1 (∼3.4 μ m) and W2 (∼4.6 μ m) bands obtained from the Wide-Field Infrared Survey Explorer. The estimated dust torus size ranges from 1000 to 3000 days, using both the cross-correlation analysis and light-curve modeling through “MICA.” The measured lag has been corrected by (1 + z ) −0.37 , to account for cosmological time dilation and the torus temperature-gradient scaling. We conduct a linear regression analysis for both the W1 and W2 bands to examine the radius–luminosity ( R – L BOL ) relationship under two conditions: one where the slope is fixed at 0.5 and one where it is allowed to vary. For the fixed slope of 0.5, we find the ratio of R BLR : R W1 : R W2 to be 1: 9: 12, indicating that the torus lies outside the BLR and that its size increases with wavelength. Furthermore, we determine the relationship between torus size and L BOL , yielding best-fit slopes of 0.413 ± 0.047 for the W1 band and 0.397 ± 0.058 for the W2 band. Both slopes are shallower than predicted by the dust radiation equilibrium model. Furthermore, our findings indicate that the torus size systematically decreases as the Eddington ratio increases, a trend that can be explained by the self-shadowing effects of slim disks.

Radiative cooling is a sustainable alternative to conventional vapor compression-based systems. However, achieving subfreezing temperatures remains a significant challenge particularly in humid environments where a strong atmospheric back-radiation and parasitic heat transfer often necessitate the use of vacuum chambers. Angular-selective thermal emission has been proposed as a strategy to mitigate radiative heat gain from the atmosphere. Nevertheless, a fundamental drawback of employing thermal emission selectivity, whether spectral or angular, is the accompanying reduction in the emitter's total radiated power which diminishes the emitter's ability to overcome environmental heating. In this work, we investigate the use of angular shields to introduce angularly selective thermal emission without reducing the emitter's radiated power. We analyze the effects of spectral selectivity, humidity, and parasitic heating on the system's net radiative flux and equilibrium temperature. Our analysis shows that spectrally selective thermal emission is necessary for efficient cooling. While engineered angular emission outperforms angular shields under high humidity, angular shields outperform in scenarios with parasitic heating, owing to their preservation of the emitter's omnidirectional emission. Angular shielding can enable subfreezing temperatures with simple insulation when the average atmospheric transmittance exceeds 70%.

For 3D strongly nonlinear equilibrium radiation diffusion equation, a kind of new meshfree iteration methods based on Richtmyer, factorization, and Newton linearization techniques in complex domains is provided. The new methods avoid the difficulty of mesh generation while ensuring high accuracy. Through specific numerical experiments, it is shown that the new methods have good approximation performance for solving 3D strongly nonlinear problems in complex domains, and all achieve good precision with iteration counts of 2 nearly under the given parameters. The comparison between finite element method (FEM) with the presented methods shows that our new methods match with FEM when the time step is relatively small, but avoid mesh generating.

A fast hierarchical radial basis functions method for solving the 2D equilibrium radiation diffusion equation with interfaces and discontinuous coefficients

Abstract Ultra-hot Jupiters (dayside temperatures Tday>2200 K) are a class of gas-giant exoplanets that, due to extreme stellar irradiation, show a peculiar combination of thermochemical properties in the form of molecular dissociation, atomic ionization, and inverted thermal structures. Atmospheric characterization of gas giants lying in the transitional regime between hot and ultra-hot Jupiters can help in understanding the physical mechanisms that cause the fundamental thermochemical transition in atmospheres between the two classes of hot gas giants. Using high-resolution cross-correlation spectroscopy with the IGRINS spectrograph on Gemini South (1.4 to 2.5 μm), we present the day-side high-resolution spectrum of WASP-122b (Tday=2258± 54 K), a gas-giant situated at this transition. We detect the signal from H2O, based on which we find that WASP-122b has a significantly metal-depleted atmosphere with metallicity log10[ZP/Z⊙] = −1.48 ±0.25 dex (0.033$_{-0.016}^{+0.018}$ × solar), and solar/sub-solar C/O ratio = 0.36±0.22 (3σ upper limit 0.82). Drastically low atmospheric metallicity pushes the contribution function to higher pressures, resulting in the planetary spectral lines to originate from a narrow region around 1 bar where the thermal profile is non-inverted. This is inconsistent with solar composition radiative convective equilibrium (RCTE) which predicts an inverted atmosphere with spectral lines in emission. The measured sub-solar metallicity and solar/sub-solar C/O ratio is inconsistent with expectations from core-accretion. We find the planetary signal to be significantly shifted in KP and Vsys, which is in tension with the predictions from global circulation models and require further investigation. Our results highlight the detailed information content of high-resolution spectroscopy data and their ability to constrain complex atmospheric thermal structures and compositions of exoplanets.

Abstract This study aims to use reanalysis and satellite data to reconcile the perspectives among the energetics of monsoon evolution, the convection‐circulation relation on moisture space, and the occurrence of organized convection systems before and after monsoon onset. The observed characteristics of seasonally achieved regional radiative convective equilibrium (RCE) state over the eastern edge of the northwest Pacific region are investigated. The target region exhibits a sharp transition of energy balance from a strong energy‐losing state before summer to a near‐balance state in late summer with a west‐to‐east dry static energy transport. We then define the non‐RCE and RCE periods to derive and contrast the statistics of convective cloud from CloudSat and precipitation events from IMERG data. During the RCE period, upward mass flux and cloud frequency (CF) increase in moist conditions, while downward flux strengthens with the top‐heavy structure and CF at nearly all altitudes decreases in dry conditions. The longwave cloud radiative effect shows a similar change as the CF. The precipitation event of all sizes tends to be suppressed in dry conditions, while only the development of the large‐sized event is more active than during the non‐RCE period in moist conditions. We also found that over 20% of the large‐sized events are associated with tropical cyclones during the RCE period, while the ratio drops to 1.6% during the non‐RCE period. We propose a diagnostic framework by combining the series of analyses to evaluate convection‐circulation coupling under the constraint of regional RCE in global models with various resolution scales.

Abstract An increase in extreme precipitation has been well-established in the transition from disorganized to organized convection, but studies conflict about how precipitation changes with the degree of clustering in organized convection. Mesoscale convective systems (MCSs) are one form of organized convection, and we examine here how precipitation intensities and various moisture-precipitation couplings change with MCS morphology, both in a multidecade tracking dataset and idealized radiative convective equilibrium (RCE) simulations. Both in general and for a given column saturation fraction (CSF), mean and extreme precipitation robustly increase for larger MCSs in the tracking dataset but show limited changes or decrease for larger MCSs in the RCE simulation output. In an attempt to explain this discrepancy, we examine other moisture-precipitation relationships within the two datasets, including how insufficient moisture suppresses precipitation, how saturation deficit generates convective available potential energy (CAPE), how CAPE generates ascent, and how much condensate the systems contain. In both datasets, reduced CAPE production at MCS margins and higher stability from a warmer upper troposphere reduce vertical velocities within the larger MCSs. In both datasets, larger MCSs also contain less condensate, especially above 500 hPa. We then explain how sampling and model biases could contribute to the different responses of precipitation to MCS extent and suggest that a “dual role” of vertical velocity—in determining both condensate formation and sedimentation—should be considered in future studies of precipitation intensity from mesoscale clusters.

Boundary layer separation induced by shock wave/boundary layer interaction is a critical issue in hypersonic vehicle design, where wall temperature effects cannot be neglected. Isothermal cold walls only exist during initial flight phase, while coupled aerodynamic heating and surface radiation drive walls toward radiation equilibrium temperature, whose influence on separation characteristics warrants investigation. This paper investigates the flow separation and skin friction characteristics under isothermal and radiation equilibrium wall conditions for Mach 6 flow over 15° compression ramp. Results show that surface radiation causes non-uniform wall temperature distribution along streamwise direction (decrease → increase → decrease), with flow separation enhancing streamwise attenuation of radiation equilibrium temperature. An increase in wall temperature enlarges the separation bubble, shifts the separation and reattachment points away from the corner, and reduces skin friction. Renard–Deck skin friction decomposition reveals the stage of initial shock wave interference is the key region where wall temperature affects separation characteristics. Elevated wall temperature causes the distribution of the molecular viscous dissipation (Cf1) to become smoother in this stage, reduces the peak values of the space convection term (Cf2) and streamwise heterogeneity term (Cf3), and shifts their positions toward the flat-plate leading edge. This indicates reduced momentum and adverse pressure gradient intensity in the near-wall region, leading to upstream movement of the separation point. The streamwise decay of radiation equilibrium wall temperature enhances the contribution intensity of Cf2 and Cf3, achieving the effect of suppress separation.

We present a thoughtfully curated collection of laboratory demonstrations, simulations, and straightforward experiments that explore the fundamental processes underlying greenhouse effect (GHE), climate, atmospheric physics, and Earth’s energy balance. The objective is to connect theory and practice in climate science education and address common student misconceptions. The activities are structured to guide students in constructing simple models of Earth’s radiative equilibrium. Experimental activities cover essential concepts such as the electromagnetic spectrum, radiation–matter interaction, thermal radiation, and energy balance. Physical experiments include visualizing the spectrum with a homemade spectroscope and an infrared (IR) thermal camera, studying absorption and selective transparency when light interacts with different materials, measuring the power emitted by a heated filament, and using simple models, such as black and white discs or a leaking bucket, to understand radiative equilibrium and steady states. This sequence was piloted in a physics education laboratory class with 85 university students enrolled in mathematics and physics courses for future teachers. To assess comprehension improvement, pre- and post-tests involving the production of drawings and explanations related to the GHE were administered to all students. These activities also aim to promote critical thinking and counter climate misinformation and denial. The results showed a significant improvement in understanding fundamental GHE concepts. Additionally, a small subset of students was interviewed to explore the psychological and social dimensions related to the climate crisis.

Observations have revealed unique temperature profiles in hot Jupiter atmospheres. We propose that the energy transport by vertical mixing could lead to such thermal features. In our new scenario, strong absorbers, TiO, and VO are not necessary. Vertical mixing could be naturally excited by atmospheric circulation or internal gravity wave breaking. We perform radiative transfer calculations by taking into account the vertical-mixing-driven energy transport. The radiative equilibrium is replaced by the radiative-mixing equilibrium. We investigate how the mixing strength, K zz, affects the atmospheric temperature–pressure profile. Strong mixing can heat the lower atmosphere and cool the upper atmosphere. This effect has important effects on the atmosphere's thermal features that would form without mixing. In certain circumstances, it can induce temperature inversions in scenarios where the temperature monotonically increases with increasing pressure under conditions of lower thermal band opacity. Temperature inversions show up as K zz increases with altitude due to shear interaction with the convection layer. The atmospheric thermal structure of HD 209458b can be well fitted with K zz ∝ (P/1 bar)−1/2 cm2 s−1. Our findings suggest vertical mixing promotes temperature inversions and lowers K zz estimates compared to prior studies. Incorporating chemical species into vertical mixing will significantly affect the thermal profile due to their temperature sensitivity.

Meshfree methods for nonlinear equilibrium radiation diffusion equation with interface and discontinuous coefficient

This study provides penetrative investigation of the effects of carbon dioxide concentration on time-dependent temperature and energy fluxes on the ground surface subject to solar irradiation. While global warming significantly impacts human life, the factors responsible remain controversial. This work considers unsteady one-dimensional heat conduction and radiative heat transfer, including collimated and diffuse components as functions of longitude, latitude, and altitude. Diffuse radiation depends on the different absorption bands of carbon dioxide and water vapor, as functions of wavelength, temperature, concentrations or pressure. The predicted results using COMSOL computer code show that the effects of carbon dioxide concentration on ground surface temperature are negligibly small, for example, over a 5-year period. Time-dependent ground surface temperature strongly depends on the absorption or dissipation of diffuse radiation and heat conduction. Diffuse radiation has a damping effect on temperature variation. Temperature changes due to solar irradiation absorption in the atmosphere are also negligibly small, despite solar irradiation being much greater than diffuse radiation and heat conduction. The absorption or dissipation of diffuse radiation depends on the dominant absorption bands centered at 4.3 and 15 μm of carbon dioxide at different times. This study, from the viewpoint of energy conservation, identifies diffuse radiation as a critical factor influencing the rate of temperature change at the ground surface, without assuming radiative or thermal equilibrium or modeling convection. Poor management of this radiation would hinder efforts to avoid droughts, water scarcity, severe fires, rising sea levels, flooding, catastrophic storms, and biodiversity loss.

The concepts of radiative and adiabatic equilibria, introduced by Karl Schwarzschild in his seminal paper Ueber das Gleichgewicht der Sonnenatmosphäre published in January 1906, are the founding blocks of the theory of radiative transfer, stellar structure, and solar physics. Careful reading of the paper and its later English translation reveals small formal inaccuracies and ambiguities but with no consequences whatsoever for the final outcomes and conclusions. This paper offers their adjustments with respective derivations using contemporary formalism and sets Schwarzschild’s paper in context with a historical and modern perspective. Particular attention is paid to Schwarzschild’s largely forgotten limb-darkening formula for adiabatic equilibrium. The paper also reproduces Schwarzschild’s radiative equilibrium protomodel of the Sun’s atmosphere in graphical form and compares it with modern models presented in some of the most cited papers in stellar and solar physics.

Abstract High‐latitude vegetation experience different temperatures than the ambient air temperature. While lacking a regional plant temperature product, we drove the dynamic ecosystem model, LPJ‐GUESS, with widely used ERA5‐land surface temperature (Tsurf, at radiative equilibrium) and air temperature to understand ecosystem process responses to these two temperatures. We show that tundra plants' growth is stimulated by warmer Tsurf in the summer, but in the boreal forests, colder Tsurf in the non‐summer months constrains leaf development and enzyme activity the following growing season. Tsurf drives higher productivity of tundra plant individuals but leads to less productive individuals in the boreal forest, although with compensatory changes (almost 68%) in vegetation structure. We demonstrate the importance of forcing temperature in simulating high‐latitude ecosystem processes and call for a community effort to measure plant temperatures across canopy heights and seasons to reduce uncertainties in estimating high‐latitude plant responses and feedback to climate.

We present slick (the Scalable Line Intensity Computation Kit), a software package that calculates realistic CO, [C i], and [C ii] luminosities for clouds and galaxies formed in hydrodynamic simulations. Built on the radiative transfer code despotic, slick computes the thermal, radiative, and statistical equilibrium in concentric zones of model clouds, based on their physical properties and individual environments. We validate our results by applying slick to the high-resolution run of the Simba simulations, testing the derived luminosities against empirical and theoretical/analytic relations. To simulate the line emission from a universe of emitting clouds, we have incorporated random forest machine learning (ML) methods into our approach, allowing us to predict cosmologically evolving properties of CO, [C i], and [C ii] emission from galaxies such as luminosity functions. We tested this model in 100,000 gas particles, and 2500 galaxies, reaching an average accuracy of ∼99.8% for all lines. Finally, we present the first model light cones created with realistic and ML-predicted CO, [C i], and [C ii] luminosities in cosmological hydrodynamical simulations, from z = 0 to z = 10.

In the present paper we consider the full nonlocal thermodynamic equilibrium (non-LTE) radiation transfer problem. This formalism allows us to account for deviation from equilibrium distribution of both the radiation field and the massive particles. In the present study, two-level atoms with broadened upper level represent the massive particles. In the absence of velocity-changing collisions, we demonstrate the analytic equivalence of the full non-LTE source function with the corresponding standard non-LTE partial frequency redistribution (PFR) model. We present an iterative method based on operator splitting techniques that can be used to numerically solve the problem at hand. We benchmark it against the standard non-LTE transfer problem for a two-level atom with PFR. We illustrate the deviation of the velocity distribution function of excited atoms from the equilibrium distribution. We also discuss the dependence of the emission profile and the velocity distribution function on elastic collisions and velocity-changing collisions.

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

Alkali metal depletion in the deep Jovian atmosphere: The role of anions