The central message of the collection is that coronal rain and prominences, long treated as separate phenomena, are in fact closely related expressions of the same underlying physics: coronal condensation. Whether a cooling clump of plasma falls back to the solar surface as rain or hangs suspended for days as a prominence depends largely on the magnetic topology in which it forms. Condensations that form in closed, steeply curved loops tend to drain rapidly along field lines as rain, while those that settle into magnetic dips can remain buoyantly supported as prominences. Their different lifetimes and appearances are therefore not arbitrary but are dictated by the interplay of radiative losses, heating, gravity, flows, and magnetic forces, all acting on plasma that spans several orders of magnitude in temperature and density.

The theoretical foundation is revisited by Thomas Waters and Andrew Stricklan, who re-examine the radiative cooling of optically thin plasma and identify a catastrophic cooling mode distinct from the classical thermal instability. This mode is governed by the isochoric instability criterion, which applies to plasma compressed at constant volume, and crucially it cannot be stabilized by thermal conduction. That means condensations can form under conditions where conventional thermal-instability arguments would predict a stable equilibrium. The result widens the theoretical window within which rapid cooling in hot, low-density plasmas should be interpreted, and it may explain observations of abrupt, near-catastrophic temperature drops in coronal loops that standard theory has struggled to accommodate.

A sweeping theoretical and numerical perspective comes from Rony Keppens, Yuhang Zhou, and Chengcai Xia, whose review places prominences and coronal rain within a unified framework of multiphase coronal plasma. They trace how gravity, flows, heating prescriptions, and magnetic topology shape both the linear growth of instabilities and their full nonlinear magnetohydrodynamic evolution. Their assessment is candid about what remains unsolved: the fine structure of prominences, their internal dynamics, and their complete life cycle from birth to eruption remain major challenges for numerical studies. Complementing this, Valeriia Liakh and Jack Jenkins review a decade and a half of prominence and coronal rain modeling with the open-source MPI-AMRVAC code, following the progression from simplified one-dimensional setups to multidimensional simulations that self-consistently produce cool condensations, and charting a path toward three-dimensional models that include partial ionization, realistic radiative transfer, and the full mass cycle between chromosphere and corona.

Radiation becomes a formidable complication once plasma cools enough to become optically thick, because photons can then be absorbed as well as emitted. Petr Heinzel and colleagues demonstrate through non-local thermodynamic equilibrium, or non-LTE, radiative transfer calculations that the optically thin loss functions commonly used in simulations break down for cool, dense condensations. Realistic net radiative rates must include both losses and gains from the absorption of incident radiation, and their models quantify how condensations relax toward radiative equilibrium on timescales that depend on plasma pressure and geometric thickness. In a companion review, Heinzel and Stanislav Gunár survey five decades of non-LTE prominence modeling, from one-dimensional slabs to two-dimensional and emerging three-dimensional multi-thread structures, and argue that coupling dynamic MHD models with multidimensional radiative transfer is now essential for interpreting rapidly moving eruptive prominences captured by modern instruments.

On the observational side, disentangling emission from plasma at wildly different temperatures along the same line of sight is the central challenge. Paolo Antolin and colleagues extend a technique called Response Fitting to separate cool, warm, and hot contributions within several passbands of the Atmospheric Imaging Assembly on the Solar Dynamics Observatory and the slit-jaw imager of the Interface Region Imaging Spectrograph. The method improves the decomposition of the AIA 94 and 304 angstrom channels and allows the hot Fe XXI flare emission contaminating the IRIS 1330 and 1400 angstrom passbands to be estimated. Applied to a joint AIA-IRIS observation, it reveals an approximately seven-fold increase in cool plasma associated with flare-driven coronal rain, and because it is computationally efficient it opens the door to near-real-time thermal diagnostics of the solar atmosphere.

That diagnostic power is already yielding surprises. Seray Şahin and Paolo Antolin used IRIS and SDO/AIA observations of coronal-rain showers neighboring a modest C7.5 flare to test whether a flare can influence loops that are not themselves flaring. They compared the amount, intensity, and velocity of rain across the pre-flare, impulsive, and gradual phases, finding that the number of detected rain events rose by roughly 27 percent from the pre-flare to the impulsive phase, while average intensity and downflow velocity increased by about 17 and 18 percent respectively by the gradual phase. The implication is striking: a flare can alter the thermodynamic conditions of neighboring, apparently quiescent loops, and the tidy distinction between quiescent and flare-driven coronal rain is not always clear-cut.

Thermal non-equilibrium, in which plasma on closed loops undergoes repeated cycles of heating, cooling, and condensation, has also now been caught operating far beyond its usual habitat. Clara Froment and Sophie Masson report long-period extreme-ultraviolet pulsations and recurring coronal-rain showers in a non-eruptive pseudo-streamer observed over roughly two and a half days with SDO/AIA. The ordering of the EUV emission peaks and the appearance of rain near the end of each cooling cycle provide strong evidence for thermal non-equilibrium cycles occurring both beneath the pseudo-streamer dome and in regions dominated by open or large-scale magnetic fields. Continuous interchange reconnection accompanied the evolution, suggesting that the interaction between reconnection and thermal non-equilibrium may govern how condensations are released and transported near open-closed magnetic boundaries, with possible consequences for the solar wind itself.

Two further studies round out the physical picture. Pengfei Chen introduces the evocatively named concept of solar filament physiognomy, the practice of inferring magnetic properties from the appearance and fine structure of filaments in imaging observations, a valuable complement in an era when direct measurements of the coronal magnetic field remain difficult. Lorenzo Melis and Roberto Soler analyze the Kelvin-Helmholtz instability at the interface between partially ionized prominence plasma and the fully ionized corona, showing that compressibility and acoustic effects matter at observed flow speeds and that ambipolar diffusion generally destabilizes the interface, lowering the threshold velocity and broadening the unstable parameter range. And Yuhong Fan’s review of MHD simulations of prominence-forming flux ropes demonstrates that prominence material is no passive tracer: its weight modifies the equilibrium, stability, and eruptive evolution of the flux rope that hosts it, ultimately shaping coronal mass ejections.

Taken together, the collection sketches a field in transition, where observers, theorists, and modelers converge on a single coupled system. Future models must move toward fully three-dimensional treatments that combine MHD with non-LTE radiative transfer, non-equilibrium ionization, and multi-fluid effects, while synthetic observables will be essential for meaningful comparison with the rapidly improving data from the Daniel K. Inouye Solar Telescope, Solar Orbiter, and Proba-3. The ultimate goal is to follow condensations continuously, from their thermodynamic formation through their drainage, suspension, or eruption, and thereby assemble a comprehensive picture of the coronal mass and energy cycle. In that picture, the rain that falls through the Sun’s corona and the great crimson prominences that arch above its limb are not curiosities but signposts pointing to the same fundamental physics.

Subject of Research: Coronal cooling and the formation, evolution, and eruption of cool plasma in the solar corona

Article Title: Coronal Cooling: Rain, Prominences, and Eruptions – Editorial

Article References: Şahin, S., Druett, M. K., Liakh, V., Popescu Braileanu, B., & Rees-Crockford, T. (2026). Coronal Cooling: Rain, Prominences, and Eruptions – Editorial. Solar Physics, 301(10), Article 151. https://doi.org/10.1007/s11207-026-02746-7

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02746-7

Keywords: solar physics, coronal rain, prominences, solar filaments, thermal instability, radiative transfer, MHD simulations, coronal mass ejections, SDO/AIA, IRIS, thermal non-equilibrium, solar corona

The research team, led by Aditya Khuller, a senior research scientist at the University of Washington’s Applied Physics Laboratory, set out to resolve a stubborn disagreement in the planetary science community. “We know there is water ice in the area surrounding the north pole of Mars, but there has been widespread disagreement as to how dusty that ice is,” Khuller said. The stakes of that disagreement are higher than they might first appear. Dust content determines how dark the ice is, and darkness determines temperature. “If it is dustier, the ice will be darker. Just like a dark T-shirt in the sun makes you warmer, dusty ice gets warmer and vaporizes faster on Mars,” Khuller explained. In the thin Martian atmosphere, where water vapor sublimates directly from ice to gas, even small differences in dust concentration can meaningfully change how quickly polar ice is lost to the atmosphere.

The methodological heart of the study lies in a cross-planetary detective story. For years, the leading technique for estimating the physical properties of Martian ice was an analytical approach originally developed for studying soil on the Moon. Several years ago, Khuller noticed something troubling: when he tested the accuracy of that lunar-derived method against measurements on Earth, the results seemed off. The discrepancy suggested that decades of estimates about Martian ice composition might rest on a shaky foundation. Rather than simply flagging the problem, Khuller and Pari Mohan, who recently graduated from the University of Washington with a degree in geoscience, decided to redo the calculations entirely using a different framework.

That framework came from an unexpected corner of the university. Steve Warren, professor emeritus of Earth and space sciences at the University of Washington, has spent decades perfecting methods for analyzing snow and ice on our own planet. His radiative transfer techniques, refined through years of studying how light interacts with snow crystals and embedded impurities, had been used successfully to study terrestrial snow and ice for decades. “His methods had been used successfully to study snow and ice on Earth for decades. So I thought it would be interesting to adapt these Earth-tested methods to Mars,” Khuller said. The adaptation required accounting for the very different conditions on Mars, including its lower atmospheric pressure, different illumination geometry, and the peculiar way dust grains scatter light within ice matrices.

The data underpinning the new analysis came from a combination of sources spanning half a century of Mars exploration. NASA celebrated its first successful mission to Mars 50 years ago with the Viking program, and in 2008 the Mars Phoenix lander achieved a major milestone by successfully sampling ice near the north pole. That triumph carried particular weight because it followed the loss of the Mars Polar Lander, which went missing near the south pole in 1999. The University of Washington researchers combined the Phoenix mission’s ground-truth measurements with observations from orbiting satellites, allowing them to connect what the lander touched on the surface with what spacecraft see from above. This pairing of surface and orbital data is essential, because orbiters can survey vast swaths of the polar terrain but need calibration against direct measurements.

The results paint a strikingly different picture of the north polar cap. Rather than a uniformly dirty slab of ice, the polar layered deposits are structured, in Khuller’s words, “like an ice-cream sandwich,” with layers of dustier ice interleaved between slabs of much cleaner ice. The team traced the origin of this layering to an annual cycle. A dusty layer of frost forms over the ice cap every Martian winter, and when summer arrives, that seasonal frost sublimates away, exposing the older, cleaner ice beneath. “By looking at how the brightness changed over time, we figured out that there is a frost that forms in the winter and it’s more dusty. In the Martian summer it goes away, exposing cleaner, older ice,” Khuller said. The brightness changes observed from orbit over successive seasons provided the key signature distinguishing seasonal frost from the permanent ice below.

The quantitative correction is substantial. Previous estimates had suggested that the top layer of the polar ice contained as much as 25 percent dust by mass, a figure that would make the ice dark and thermally aggressive under the Martian sun. The new study finds the true value is closer to 3 percent, a nearly tenfold reduction. That difference transforms scientific understanding of the ice cap’s radiative properties: cleaner ice reflects far more sunlight, stays colder, and sublimates more slowly. It also changes how researchers should interpret the layered deposits as climate archives, since the amount of dust locked into each layer is one of the primary proxies for the conditions under which that ice formed.

Those layers contain key details about the climate of Mars thousands of years ago, when the ice is thought to have formed from snowfall. Mars experiences massive ice ages that have deposited shallow ice across roughly one-third of the planet’s surface, and the driver of this dramatic variability lies in planetary mechanics. Earth’s axial tilt is stabilized by the gravitational influence of its relatively large moon, which keeps our seasons within a narrow, predictable range over tens of thousands of years. Mars, possessing only two small moons, lacks that stabilizing hand. Its axial tilt, or obliquity, “oscillates wildly,” Khuller said, swinging through large excursions over geological timescales. Those oscillations redistribute sunlight across the planet’s latitudes, driving the advance and retreat of ice ages and leaving their signature in the alternating layers of the polar caps.

The cleaner ice also reshapes thinking about habitability. In a previous study, Khuller and colleagues proposed that layers of dust and ice could create conditions suitable for life on Mars. Dark, dusty layers absorb sunlight and could warm the surrounding ice enough to form pockets of meltwater within otherwise frozen deposits. These pockets, enriched with nutrients supplied by the dust grains, could potentially host bacteria and other primitive life forms. The analogy comes from Earth, where similar pockets of shallow, dusty meltwater within ice are often teeming with microbial life during summer. In winter, the liquid water freezes and the microbes go dormant, reviving when the next summer thaws their icy refuge. “The fact that Mars and Earth both have these similar layers of water ice and dust is interesting,” Khuller said. “Why does one planet have life and the other doesn’t?”

Answering that question may take years, but the new dust measurements sharpen the picture of where to look and what to expect. Cleaner ice absorbs less sunlight than previously assumed, which alters calculations of where and whether meltwater pockets could form within the polar layered deposits, and it refines models of how the ice cap responds to seasonal and long-term climate cycles. Khuller hopes to build on the work by applying these improved, Earth-tested analytical methods to other regions of the red planet, extending the corrected picture of ice composition beyond the north pole. As missions continue to probe the Martian surface and orbiters keep watch over the polar caps, the layered ice of Mars stands as one of the most promising archives of the planet’s climatic memory, and one that now appears considerably cleaner, and perhaps more revealing, than scientists had believed.

Subject of Research: Dust content of exposed water ice at the north polar cap of Mars

Article Title: The north pole of Mars is less dusty than scientists thought

Article References: The north pole of Mars is less dusty than scientists thought. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: Mars, north polar cap, water ice, dust content, Mars Phoenix, climate record, polar layered deposits, radiative transfer, ice ages, axial tilt, astrobiology, University of Washington

The historical arc of the field is one of steady, incremental extension into adjacent problems. The first synthetic supernova spectrum was presented by David Branch in 1980, who adapted the Schuster-Schwarzschild approach from stellar atmospheres and introduced the Sobolev formalism for line transfer. His tools, which eventually became the widely used SYNOW code, allowed detailed comparisons between white dwarf explosion models and observations of Type I supernovae. In the same year, Timothy Axelrod’s doctoral thesis laid the foundation for nebular-phase modeling, establishing the treatment of non-thermal and non-local thermodynamic equilibrium (NLTE) physics that still sets the standard for many codes today. The explosion of SN 1987A then drew new workers into the field, including Claes Fransson in Stockholm and Leon Lucy in London, whose Monte Carlo techniques would prove transformative.

Around 2005, a wave of development swept through the field, much of it inspired by Lucy’s work on Monte Carlo methods. Three-dimensional codes operating under the assumption of local thermodynamic equilibrium (LTE) appeared, including SEDONA and ARTIS, while one-dimensional NLTE codes such as SUMO, NERO, and CMFGEN were developed for higher-fidelity spectral calculations. The first public Schuster-Schwarzschild code, TARDIS, was released in 2014 and remains popular for rapid line identification. When the first kilonova, AT2017gfo, was discovered in 2017 following the gravitational-wave detection GW170817, the supernova toolkit was ready to be adapted. Metzger and colleagues extended SEDONA to kilonovae as early as 2010, and codes such as SuperNu, POSSIS, and a kilonova version of SUMO followed, opening the door to NLTE modeling of neutron star merger ejecta.

The review emphasizes that astrophysics grows by small extension steps into related areas, a process that takes decades. Sometimes growth in computing power drives these steps, but more often they are application-driven. This has a practical consequence: methods derived under computing constraints orders of magnitude stricter than today’s may carry simplifications that are no longer necessary. Studying the history of a code or methodology therefore reveals where modern computing power can be exploited to improve upon legacy approximations, a point the author urges researchers to keep in mind whenever they adopt an existing model.

Why invest such effort in spectral synthesis? The review identifies three main science drivers. First, identifying which elements produce which line features and determining the elemental abundances in the ejecta. For decades this seemed almost insurmountable, because supernovae blend lines through rapid Doppler expansion, cascade energy over six orders of magnitude, and involve non-thermal effects, asymmetries, molecules, and dust. Today, clear diagnostic methods exist for seventeen elements from hydrogen to nickel, and direct full-ejecta spectral tests of explosion models have been performed for all major supernova classes. Second, understanding the origin of the elements across the periodic table: with AT2017gfo, the upper two-thirds of the table opened for direct analysis, with diagnostic potential already established for elements including strontium, yttrium, tellurium, lanthanum, cerium, neodymium, and tungsten. Third, determining the progenitor systems and explosion mechanisms, since spectra diagnose both the hydrostatic life of the progenitor star and the physics of its death, from neutrino-driven core collapse to accretion disk outflows near black holes.

The physical situation these codes must capture is extreme. The ejecta expand homologously, with faster fragments outrunning slower ones, at characteristic velocities of roughly 5,000 kilometers per second for core-collapse supernovae, 8,000 for thermonuclear supernovae, and 50,000 for kilonovae. Kilonovae carry about one hundred times less mass than supernovae but comparable kinetic energy, hence their higher speeds and their rise and decline over just days. Both classes are powered by radioactivity: supernovae chiefly by the decay of nickel-56 and cobalt-56, kilonovae by a vast array of radioactive r-process nuclides whose energy is carried mainly by leptons rather than gamma rays. Because the ejecta are semi-transparent, with line opacity producing lingering radiative transfer effects for years or even decades, much of the optical and infrared spectra of both supernovae and kilonovae is formed by fluorescence.

Temperature emerges as the most fundamental quantity in the modeling. It governs ionization and excitation, sets the regime of spectral formation, and strongly influences opacity. The governing law is energy conservation, expressed either through the internal energy of the gas or, equivalently in NLTE treatments, through the evolution of thermal kinetic energy balanced by heating and cooling. Codes differ in whether they retain the time-derivative terms: STELLA, SuperNu, CMFGEN, and, since 2022, SUMO can solve the time-dependent energy equation with implicit or semi-implicit finite-difference schemes, typically using time steps of about ten percent, which is well matched to both the homologous expansion timescale and radioactive decay timescales. The review shows that this choice of stepping has a solid physical anchoring for both supernova and kilonova applications across all conceivable epochs.

The treatment of line cooling exposes a subtle but consequential divide between LTE and NLTE approaches. In LTE codes, a parameterized thermalization probability is often assigned to line absorptions, and surprisingly, realistic light curves and spectra require this probability to be near unity, effectively mimicking the fluorescence process that the simplified treatment omits. But when radioactivity dominates the heating, such an inflated absorption coefficient can drive temperature estimates a factor of ten too low, likely explaining why LTE codes yield significantly lower temperatures than NLTE ones from quite early phases. In NLTE, cooling is computed from net electron collision rates, which represent the small difference between two large terms and demand careful formulation. A code comparison for a simple Type Ia test model shows that even state-of-the-art tools produce temperature profiles that vary considerably, underscoring how much work remains to achieve robust temperature determinations.

Solving the NLTE rate equations presents its own numerical challenges. With potentially more than one hundred thousand levels per grid cell, the full system is split into blocks, typically one per ion, and solved iteratively. Matrix storage scales with the square of the system size and inversion time with its cube, so the standard LAPACK routine DGESV, based on LU decomposition, remains efficient only up to a few hundred levels. Superlevels, which bundle groups of levels assuming LTE distributions within them, offer dramatic savings: in one full-composition Type Ia model, 10,605 levels were grouped into 2,338 superlevels, saving a factor of sixteen in storage and up to sixty-four in matrix inversion time. Negative populations, false singularities, and oscillating Newton-Raphson steps all require layered fall-back strategies, and co-solving all ions of an element, as done in recent 3D codes, reduces such pathologies.

Radioactive powering completes the triad of central modeling blocks. High-energy decay particles transfer their energy through ionization, excitation, and heating, with the Bethe stopping-power formula, derived in the early 1930s, describing the continuous energy loss of fast particles. Gamma rays Compton-scatter to create primary electrons of 0.1 to 1 megaelectronvolt, which cascade into secondaries; the distribution of these secondaries, measured experimentally by Opal and colleagues, feeds into steady-state Boltzmann solutions of the degradation spectrum. For kilonovae, time-dependent thermalization effects become important within weeks, and modeling the powering has already allowed constraints to be placed on the composition of AT2017gfo. Looking forward, the review charts a roadmap: better physical treatments, accurate atomic data for trans-iron elements, 3D hydrodynamic explosion models, and high-quality observations from the ultraviolet to the mid-infrared. Eighteen of the thirty lightest elements now have good or moderate diagnostic potential, and with kilonova spectroscopy advancing rapidly, the goal of determining the origin of the elements directly at their production sites is coming within reach.

Subject of Research: Computational spectral synthesis modeling of supernova and kilonova spectra to infer ejecta composition and explosion physics

Article Title: Spectral synthesis techniques for supernovae and kilonovae

Article References: Jerkstrand, A. (2025). Spectral synthesis techniques for supernovae and kilonovae. Living Reviews in Computational Astrophysics, 11(1), Article 1. https://doi.org/10.1007/s41115-025-00022-2

Image Credits: AI Generated

DOI: 10.1007/s41115-025-00022-2

Keywords: supernovae, kilonovae, spectral synthesis, radiative transfer, NLTE modeling, r-process nucleosynthesis, Monte Carlo methods, neutron star mergers, radioactive powering, astrophysical transients, computational astrophysics, origin of the elements

The review, led by Hubert Klahr, Hans Baehr, Julio David Melon Fuksman, and Thomas Pfeil of the Max Planck Institute for Solar System Research, arrives at a moment when observational facilities such as the Atacama Large Millimeter/submillimeter Array are delivering breathtaking images of planet-forming disks. Rings, gaps, spiral arms, and hints of long-lived vortices appear routinely in the data, but interpreting these structures requires models that faithfully capture the underlying physics. The authors argue that the first step is deceptively simple: before adding magnetic fields, self-gravity, or dust feedback, a simulation must correctly reproduce the pure hydrodynamic behavior of an irradiated disk, and that behavior is far from trivial.

Disks around young stars are born as byproducts of star formation, a buffer for the excess angular momentum of a collapsing molecular cloud core. During the first tens of thousands of years, the star acquires most of its mass through the disk, a phase in which the disk’s own self-gravity supplies the main torque driving accretion. But after this main accretion phase, enough material remains to build planetary systems over the following ten million years, until winds and photoevaporation strip the gas away. Crucially, for planet formation, an overly vigorous accretion flow toward the star can wash away nascent planets, so understanding when and how disks settle into a calmer state matters enormously.

One of the review’s central themes is baroclinicity, the misalignment between surfaces of constant pressure and constant density in a disk. Because stellar irradiation heats the disk surface while viscous dissipation may warm the midplane, disks develop both radial and vertical temperature gradients. In such a configuration, pressure and density contours are inclined with respect to one another, a situation familiar from Earth’s atmosphere and oceans that also drives instabilities in disks. These effects were long missed in simulations because they are too weak to emerge at low resolution or with overly dissipative numerical schemes. Only recently, with increased computing power, have researchers been able to confirm the analytic predictions of thermal baroclinic instability theory with full numerical experiments.

The review catalogues the family of instabilities that radiation hydrodynamic simulations must capture. The vertical shear instability, or VSI, arises from the vertical gradient of rotation in a baroclinic disk and operates best when thermal relaxation is extremely fast, since rapid cooling prevents the stable vertical stratification from suppressing the unstable shear. The convective overstability, in contrast, is strongest when the thermal relaxation time is comparable to the orbital period; it grows from epicyclic oscillations of gas parcels displaced radially in a weakly convective environment. The Goldreich-Schubert-Fricke instability, a close cousin of the VSI inherited from the theory of rotating stars, operates alongside the convective overstability, and recent work has shown that any disk unstable to one is unstable to the other, because both depend equally on the disk’s baroclinicity. A third mechanism, the subcritical baroclinic instability, generates long-lived anticyclonic vortices from radial entropy gradients combined with thermal relaxation, though it lacks a linear growth-rate prediction and is therefore harder to use as a code benchmark.

To help researchers validate their codes, the authors lay out a systematic testing procedure. The method begins by constructing an equilibrium disk model, typically through a so-called 1+1-dimensional calculation that solves for vertical hydrostatic balance at each radius while enforcing energy conservation with flux-limited diffusion and physically motivated dust opacities. This equilibrium serves both as an initial condition for multidimensional simulations and as the basis for perturbation theory: analytic linear analysis yields predicted growth rates for unstable modes. A code that reproduces those growth rates in the linear regime can then be trusted to explore the nonlinear turbulence that follows. If a code fails to match the predicted growth, the review notes, this signals insufficient resolution or a numerically dissipative scheme rather than a failure of the underlying theory.

The practical details of such tests are demanding. In local axisymmetric simulations carved from a global disk model, the authors demonstrate that resolving roughly 256 cells per pressure scale height is required to reproduce growth rates down to ten thousandths of the orbital frequency. Numerical schemes matter as well: high-order reconstruction methods combined with accurate Riemann solvers recover the predicted linear growth, whereas more diffusive approximate solvers can suppress instability entirely. Even the handling of cooling, implemented through thermal relaxation of the pressure toward an equilibrium value, must be treated carefully, with operator splitting modified so that relaxation times shorter than the dynamical step remain stable. These benchmarks, the authors argue, should become standard practice for any group embarking on radiation hydrodynamic disk simulations.

Beyond linear tests, the review surveys how different radiative transfer approximations shape the outcomes of full three-dimensional simulations. Flux-limited diffusion, the workhorse of earlier decades, is computationally efficient and accurate in optically thick regions but smears out shadows and introduces unphysical diffusion where radiation streams freely. The M1 two-moment method, implemented in codes such as PLUTO, preserves the direction of radiative fluxes and captures shadowing, but it artificially merges crossing beams of light, which can overestimate midplane temperatures by more than 40 percent in single-group calculations. A newer half-moment scheme reduces that error to a few percent, while discrete ordinates and Monte Carlo methods offer the greatest accuracy at the highest cost. The review’s message is that no single method suits every problem, and the choice must weigh computational expense against the physics one needs to capture, whether self-shadowing, scattering, or frequency-dependent heating.

The consequences of getting radiation transport right extend deep into planet formation theory. Global simulations of the vertical shear instability show that the resulting turbulence generates stresses whose strength depends on the square of the radial temperature gradient and on the local cooling time, challenging the classical assumption that turbulent viscosity scales simply with gas pressure. VSI turbulence can spawn long-lived anticyclonic vortices, provided simulations span the full azimuthal extent of the disk, and these storm systems are expected to act as efficient traps for pebbles and dust, potentially accelerating planetesimal formation. In irradiated disks, radiation hydrodynamical studies reveal that the instability can be localized to the surface layers when dust depletion lengthens midplane cooling times, producing a quiescent midplane beneath a vigorously turbulent atmosphere, a stratification with direct consequences for where dust can settle and planets can grow.

The review closes with a forward-looking agenda. The authors recommend abandoning fixed-temperature disk models in favor of self-consistent thermal evolution, since every realistic disk structure is subject to thermal baroclinic instabilities that fixed-temperature setups either suppress artificially or misrepresent. Future work must couple evolving dust populations to the opacity and cooling calculations, treat the separate temperatures of gas, dust, and radiation, and develop well-balanced or low-Mach-number schemes that resolve subsonic fluctuations in a supersonically rotating medium. The payoff is substantial: radiation hydrodynamic simulations calibrated against linear theory will underpin the interpretation of molecular line kinematics and scattered-light images from current and next-generation telescopes, transforming stunning pictures of planet-forming disks into quantitative tests of how worlds are born.

Subject of Research: Numerical radiation hydrodynamics methods and stability tests for simulating protoplanetary disks around young stars

Article Title: Numerical radiation hydrodynamics for circumstellar disks

Article References: Klahr, H., Baehr, H., Melon Fuksman, J. D., & Pfeil, T. (2026). Numerical radiation hydrodynamics for circumstellar disks. Living Reviews in Computational Astrophysics, 12(1), Article 3. https://doi.org/10.1007/s41115-026-00026-6

Image Credits: AI Generated

DOI: 10.1007/s41115-026-00026-6

Keywords: protoplanetary disks, radiation hydrodynamics, planet formation, vertical shear instability, convective overstability, baroclinic instability, radiative transfer, turbulence, numerical simulations, stellar irradiation, computational astrophysics, disk stability

Spectral retrieval is, at its core, a Bayesian inverse problem. Scientists build a parametric model of an atmosphere, generate a synthetic spectrum, and compare it against the observed data, repeating the process tens of thousands of times across a vast parameter space. Bayes’ theorem converts the likelihood of the data given a set of atmospheric parameters into the posterior probability of those parameters given the data. For solar system planets, where orbiters and descent probes provide strong prior knowledge, fast matrix-inversion methods like Optimal Estimation work well. For exoplanets, where nothing is known for certain, those restrictive Gaussian priors can badly bias the answer, so the field turned instead to computationally expensive sampling algorithms.

Markov Chain Monte Carlo became the early standard for exoplanet retrieval, but it struggles when the probability landscape is multi-modal, with several distinct families of solutions. Nested Sampling, first trialled for exoplanets in 2013, solved that problem and delivers the Bayesian Evidence as a by-product, which enables model comparison. The catch is cost. Nested sampling’s computational cost scales roughly with the cube of the number of model parameters, and modern retrievals now routinely require between ten thousand and one hundred million forward model evaluations per dataset. A single retrieval of the well-studied hot Jupiter WASP-39b using JWST data consumed on the order of ten thousand core hours.

The forward model itself, a radiative transfer calculation through a modelled atmosphere, is the true bottleneck, since it is evaluated at every sampler step. At its heart lies the radiative transfer equation, balancing absorption, scattering and emission along the light’s path, which differs dramatically between transit, eclipse and direct imaging geometries. Building on this foundation, the model must specify a temperature-pressure profile, often parameterized with the physically motivated Guillot profile or the more flexible six-parameter form introduced by Madhusudhan and Seager in 2009. Both remain restrictive, and studies show that neither fully captures the curvature of real three-dimensional temperature structures, with arithmetic averages of three-dimensional profiles retrieved more faithfully than more realistic weighted ones.

Chemistry introduces another fork in the road. Free-chemistry retrievals let every gas abundance float, allowing the unexpected, such as the surprise detection of sulfur dioxide on WASP-39b that no equilibrium model predicted and which ultimately revealed a photochemical production mechanism. But free chemistry inflates the parameter count enormously. Tying the model to a chemical network slashes the parameters to a handful, like metallicity and carbon-to-oxygen ratio, yet the choice of network matters enormously: in one test, a reduced chemical network produced an apparently good fit while retrieving a metallicity six times solar when the true input was one times solar. The most complex chemical model run inside a retrieval to date, the FRECKLL framework, took about five minutes per evaluation and needed forty thousand samples, roughly 138 days of CPU time spread over 180 cores.

Opacity data adds its own burden. Because exoplanet atmospheres are far hotter than laboratory conditions can safely replicate, absorption line positions and strengths rely on quantum mechanical simulations, generating line lists with millions of entries. Full line-by-line calculations are intractably slow for retrievals, so codes use approximations: correlated-k tables or pre-computed cross sections. Recent tests on the JWST spectrum of WASP-39b showed that cross sections computed below resolutions of roughly fifty thousand can bias retrieved gas abundances, a hidden error source at the very heart of the comparison. Broadening of spectral lines, which depends on the ambient gas composition and temperature, and the enormous numbers of weak methane lines at high temperatures, sometimes collapsed into so-called superlines, add further layers of compromise between accuracy and speed.

Clouds are arguably the hardest problem of all. Aerosols are essentially ubiquitous, shaping spectra through their altitude, particle size, composition and abundance, none of which is well known for any exoplanet. Attempts to predict cloud decks from first principles fail even for Jupiter and Saturn, where ammonia clouds predicted by microphysics models are simply not seen across most of the disk. Exoplanet cloud parameterizations remain crude, often little more than a cloud-top pressure and a wavelength-dependent opacity, and the common extinction-only approximation, which assumes every photon interacting with a cloud is scattered out of the beam, can substantially underestimate atmospheric transmission when forward scattering dominates. Correct multiple-scattering treatment demands Monte Carlo photon tracking, a severe computational penalty.

The star itself is no innocent bystander. The Transit Light Source Effect arises when unocculted starspots or faculae imprint their own spectral fingerprints onto a transiting planet’s spectrum, and recent 3D magnetohydrodynamic simulations show that standard stellar atmosphere models misrepresent spot spectra by more than one hundred parts per million at some wavelengths. Meanwhile, JWST data are now precise enough that one-dimensional, homogeneous atmosphere models are demonstrably inadequate. Retrievals have begun incorporating separate day and night terminator chemistries, and full three-dimensional radiative transfer frameworks like TRIDENT can extract morning-evening and day-night gradients, at a cost of roughly a factor of twenty-five in computation time. Even the choice of how spectra are binned can inject resolution-linked bias that distorts retrieved transit depths.

Interpreting the results demands equal care. Bayes factors comparing models with and without a given molecule are frequently reported as detection significances in sigma, but recent analyses warn that these are relative model preferences, not physical detections. A claimed detection of dimethyl sulphide on the sub-Neptune K2-18b was shown to hinge on a narrowly restricted model space in which alternative hydrocarbons, untested, fit the same data equally well or better. Cross-validation techniques that leave out individual data points have revealed apparent detections resting on a single broadband measurement. Machine learning offers a possible escape: neural network emulators of radiative transfer and chemistry can accelerate retrievals dramatically, but their computational advantage degrades rapidly as dimensionality grows, and quantifying their uncertainties remains an open problem.

The road ahead points toward even heavier demands. The Ariel mission, launching in 2031, will characterize at least a thousand planets, driving a shift toward machine learning pipelines. The extremely large telescopes will bring high-resolution cross-correlation spectroscopy and reflected light imaging, the latter requiring full multiple-scattering models and possibly polarization, techniques not yet implemented in any retrieval code. The Habitable Worlds Observatory aims to image Earth twins in reflected light, where the stakes of every modelling choice become highest. Barstow and Welbanks close with practical advice: treat retrieval software as more than a black box, justify priors and likelihoods explicitly, invest in code efficiency and software engineering, and approach every detection claim, especially for small temperate worlds, with the skepticism the data deserve.

One underappreciated aspect of the field’s growth is its sheer diversity of tooling. More than fifty independent retrieval frameworks have now been applied to exoplanets, spanning a wide range of sampling algorithms, temperature and cloud parameterizations, and treatments of chemistry ranging from strict equilibrium assumptions to fully flexible free schemes. Many of these codes are open source, reflecting a community culture that has encouraged sharing and scrutiny, yet diversity alone does not guarantee agreement.

To address that concern, teams have undertaken systematic benchmarking exercises, including model intercomparison projects in which different codes are run against identical synthetic datasets. These efforts have revealed a subtle but consequential finding: small differences in model implementation, producing variations of only a few tens of parts per million in synthetic spectra, can cascade into substantial differences in the values retrieved from the same data. In an era when observational precisions are measured at similar levels, such implementation details are no longer negligible.

The review also situates the field historically. Retrieval was long a workhorse for solar system science, where it constrained the structure of Jupiter’s equatorial cloud decks from Galileo orbiter data, mapped spatial variation in ammonia on Saturn, and probed surface emissivity variations on Venus. The migration of these techniques to exoplanets was accelerated in part by solar system atmospheric scientists joining the field, bringing with them both expertise and an awareness of the pitfalls of applying methods tuned to well-characterized planets to worlds about which almost nothing is known.

That heritage explains a recurring theme: because exoplanet exploration lacks ground truth, the choice of algorithm and prior is itself a scientific decision with measurable consequences. Early investigations using synthetic data demonstrated that methods constrained by Gaussian assumptions could recover incorrect solutions when data were sparse, while broader exploration of parameter space recovered the truth. The authors’ recommendations, from justifying priors explicitly to treating software as more than a black box, flow directly from lessons like these, hard-won across two decades of practice in both solar system and exoplanet contexts.

Subject of Research: Computational challenges in Bayesian spectral retrieval of exoplanet atmospheres

Article Title: Computational challenges in exoplanet atmospheric retrieval

Article References: K. Barstow, J., & Welbanks, L. (2026). Computational challenges in exoplanet atmospheric retrieval. Living Reviews in Computational Astrophysics, 12(1), Article 6. https://doi.org/10.1007/s41115-026-00031-9

Image Credits: AI Generated

DOI: 10.1007/s41115-026-00031-9

Keywords: exoplanets, atmospheric retrieval, JWST, Bayesian inference, nested sampling, radiative transfer, cloud modelling, molecular opacities, machine learning, stellar contamination, WASP-39b, Ariel mission

Radiation transfer is, in essence, the calculation of how emitted light travels through a medium before reaching an observer. In a simplified one-dimensional model, an atmosphere can be represented as a stack of horizontal layers whose properties vary smoothly with depth. Real atmospheres are less orderly. Stars contain rising hot granules and sinking cooler material, magnetic structures, winds, and large-scale convective cells. Exoplanets have day-night temperature contrasts, circulation, clouds, and externally supplied stellar radiation. Kilonovae consist of rapidly expanding, chemically complex ejecta whose geometry and physical state evolve. A three-dimensional model retains variations in all spatial directions, while a time-dependent treatment can follow changes in the gas rather than assuming a permanent steady state.

The NLTE part addresses a second limitation of standard modeling. Local thermodynamic equilibrium assumes that collisions dominate the internal energy distribution of atoms and molecules, allowing their populations to be estimated with Saha-Boltzmann statistics from the local temperature and density. That assumption often fails near an open surface, where photons escape and the radiation field can control excitation and ionization. In NLTE calculations, the population of each energy level is determined by balancing radiative and collisional transitions. The radiation field affects those populations, while the populations in turn alter the opacity and emissivity that shape the radiation field. Solving the problem therefore requires repeated, coupled calculations rather than a single local evaluation.

At the center of the calculation is the radiative-transfer equation for the specific intensity, the amount of radiation traveling in a particular direction at a particular frequency. In a common time-independent form, the change in intensity along a ray depends on the difference between the intensity and the source function, which is the ratio of emissivity to extinction. The calculation integrates this relationship over optical depth, a measure of how opaque the material is. In three dimensions, the code must trace many rays through a spatial grid, interpolate temperature, density, velocity, opacity, and source-function values onto each photon path, and then combine the directional intensities to obtain the mean radiation field. That mean field enters the rate equations governing atomic and molecular populations.

The review emphasizes that numerical choices can influence the answer as much as the underlying physics. Long-characteristics methods follow rays through an entire model and preserve sharp spectral structures well, but they can be expensive. Short-characteristics methods connect neighboring layers and are easier to parallelize, although interpolation can diffuse intense beams. Higher-order interpolation can improve accuracy but may create artificial overshoots, including unphysical negative opacities or intensities. Monotonic schemes suppress those artifacts but may sacrifice accuracy or complicate convergence. The angle quadrature, which selects and weights the rays used to integrate the radiation field, also matters. Relatively few directions may be sufficient for calculating mean intensities in statistical-equilibrium equations, whereas emergent line profiles and centre-to-limb variations generally require more.

One practical compromise is the so-called 1.5D approach. Each vertical column in a three-dimensional atmospheric simulation is treated as an independent one-dimensional atmosphere, preserving the local temperature, density, and velocity structure but ignoring horizontal radiation exchange between columns. The resulting fluxes can then be averaged across the model. This approach can greatly reduce computational demands and has produced useful results for several stellar problems, especially when the photon mean free path is short. However, it is not universally reliable. In extremely metal-poor stars, for example, the review describes cases in which 1.5D and full 3D NLTE calculations produced abundance differences as large as 0.22 dex for iron lines. The approximation must therefore be tested against the specific diagnostic and physical regime.

The scientific payoff is clearest in stellar spectroscopy. Convection gives spectral lines distinctive asymmetric shapes and Doppler shifts because rising and sinking gas contribute different amounts of light at different velocities. Three-dimensional models reproduce observed line bisectors more successfully than traditional hydrostatic one-dimensional models in several comparisons, while predicted convective shifts can reach hundreds of metres per second. Such effects matter for radial-velocity measurements, chemical-abundance studies, and efforts to separate stellar surface variability from planetary signals. Centre-to-limb observations provide another stringent test. For the solar oxygen line near 7772 angstroms, the review reports that 1D LTE models can overestimate the inferred abundance by 0.6 dex when the limb is analyzed, whereas 3D NLTE calculations offer a way to account for the changing geometry and radiation field.

These corrections extend directly to exoplanet research. During a transit, a planet blocks different portions of its host star, each with its own brightness, velocity, magnetic activity, and spectral-line shape. The resulting Rossiter-McLaughlin signal can reveal the projected alignment between stellar rotation and the planetary orbit, but it can also be distorted by inaccurate models of the stellar surface. Studies summarized in the review find that 3D NLTE treatment improves some diagnostics, including those based on sodium and potassium lines, although other features remain to be explored. Three-dimensional and NLTE methods are also being adapted to irradiated planetary atmospheres, where the host star supplies an external radiation field and can drive photoionization, photodissociation, heating, and atmospheric escape. Clouds and global circulation add further spatial complexity.

Kilonovae present a different but equally demanding challenge. Their spectra arise from rapidly expanding material produced in compact-object mergers, with radioactive decays supplying energy and heavy elements providing dense forests of spectral transitions. Expanding shells are often modeled with spherical symmetry and escape-probability approximations, but their composition, velocity structure, and ionization state can evolve rapidly. The review places such systems within the broader push toward time-dependent, multidimensional NLTE calculations, while noting that direct spatially resolved tests are not currently available for exoplanet or kilonova photospheres. Progress will require reliable atomic and molecular data, including transition probabilities, photoionization cross-sections, collision rates, and information for complex ions and molecules. It will also require algorithms that balance physical fidelity with the immense cost of solving millions of coupled radiation and population equations. The central message is not that every observation needs the most elaborate possible model, but that astronomers must understand when common simplifications introduce systematic errors. As high-resolution spectrographs, transit surveys, and time-domain observatories deliver increasingly precise data, 3D NLTE radiation transfer provides a framework for turning subtle spectral details into more dependable knowledge of some of the universe’s most dynamic environments.

A useful distinction in these calculations is between the radiation field inside a model and the observables ultimately compared with data. A simulation can predict an angle- and frequency-dependent specific intensity at the surface, as well as a flux integrated over directions. The intensity contains information about viewing angle and spatial structure, whereas the integrated flux provides a spectral energy distribution for the object as a whole. This difference is important for phenomena such as stellar surface inhomogeneities, where two observers may receive different line profiles from the same model depending on which regions are visible.

The transfer calculation is also only one part of a larger physical modeling chain. A model must first specify or compute the state of the gas, including quantities such as density, temperature, velocity, and composition. Radiation transfer then uses detailed opacities and emissivities on a finer frequency grid to produce a more realistic spectrum than the coarse radiative description used in many underlying fluid or atmosphere calculations. In NLTE work, the sequence is not strictly one-way: the radiation field changes the energy states of atoms and molecules, and those changed populations modify the opacity and emissivity. Iteration is therefore needed until the matter and radiation descriptions become mutually consistent.

The relevant microscopic data can be a major source of uncertainty. The review stresses the need for atomic and molecular information alongside fluid dynamics, statistical mechanics, and energy transport. Rates for radiative and collisional processes determine how strongly particles respond to the radiation field, while the available transitions establish which frequencies can absorb or emit. These inputs become especially consequential when spectra are used to infer detailed chemical abundances. A numerical solution may be internally converged yet still inherit systematic limitations from incomplete or inaccurate physical data.

Geometry is not an optional refinement in every regime. Multidimensional treatment becomes necessary when the structure encountered by a photon varies substantially across space or changes non-monotonically along its path. This criterion can apply to convective stellar surfaces, strongly irradiated atmospheres, or expanding merger ejecta. The review consequently treats 3D NLTE as a family of coupled problems rather than a single universal algorithm. Different systems demand different compromises among spatial resolution, frequency coverage, angular sampling, time dependence, and the representation of matter-radiation coupling.

These methodological issues connect radiation-transfer modeling to several broader observational programs. In stellar studies, synthetic spectra help constrain chemical evolution, convection, magnetism, and mass loss. In exoplanet work, they support interpretation of transit and atmosphere measurements. For kilonovae, evolving spectra can provide clues to the composition and physical state of rapidly changing ejecta. The review also places related applications in a wider computational landscape that includes interstellar-medium diagnostics, circumstellar polarization, dusty galaxy discs, active-galaxy accretion discs, and supernova modeling. Across these settings, the value of greater realism is measured by whether it changes an inferred physical parameter or resolves a discrepancy with observations, not simply by the number of dimensions in the calculation.

Subject of Research: Three-dimensional non-local thermodynamic equilibrium radiation transfer in astrophysical atmospheres

Article Title: 3D NLTE radiation transfer: theory and applications to stars, exoplanets, and kilonovae

Article References: Bergemann, M., & Hoppe, R. (2026). 3D NLTE radiation transfer: theory and applications to stars, exoplanets, and kilonovae. Living Reviews in Computational Astrophysics, 12(1), Article 7. https://doi.org/10.1007/s41115-026-00029-3

Image Credits: AI Generated

DOI: 10.1007/s41115-026-00029-3

Keywords: radiative transfer, 3D modeling, NLTE, stellar atmospheres, exoplanets, kilonovae, spectroscopy, astrophysical simulations, radiation, transfer, theory, applications