Modeling multiphase plasma in the corona: prominences and rain

Context. Thermal instabilities give rise to condensations in the solar corona, and are the most probable scenario for coronal rain and prominence formation. We revisit the original theoretical treatment done by Field (1965, ApJ, 142, 531) in a homogeneous plasma with heat-loss effects and combine this with state-of-the-art numerical simulations to verify growth-rate predictions and address the long-term non-linear regime. We especially investigate interaction between multiple magnetohydrodynamic (MHD) wave modes and how they in turn trigger thermal mode development. Aims. We assess how well the numerical MHD simulations retrieve the analytically predicted growth rates. We complete the original theory with quantifications of the eigenfunctions, calculated to consistently excite each wave mode. Thermal growth rates are fitted also in the non-linear regime of multiple wave–wave interaction setups, at the onset of thermal instability formation. Methods. We performed 2D numerical MHD simulations, including an additional (radiative) heat-loss term and a constant heating term to the energy equation. We mainly focus on the thermal (i.e. entropy) and slow MHD wave modes and use the wave amplitude as a function of time to make a comparison to predicted growth rates. Results. It is shown that the numerical MHD simulations retrieve analytically predicted growth rates for all modes, of thermal and slow or fast MHD type. In typical coronal conditions, the latter are damped due to radiative losses, but their interaction can cause slowly changing equilibrium conditions which ultimately trigger thermal mode development. Even in these non-linear wave-wave interaction setups, the growth rate of the thermal instability agrees with the exponential profile predicted by linear theory. The non-linear evolutions show systematic field-guided motions of condensations with fairly complex morphologies, resulting from thermal modes excited through damped slow MHD waves. These results are of direct interest to the study of solar coronal rain and prominence fine structure. Our wave–wave interaction setups are relevant for coronal loop sections which are known to host slow wave modes, and hence provide a new route to explain the sudden onset of coronal condensation.

Cool plasmas (≈ 104 K) embedded in a larger, much hotter (>106 K) medium are ubiquitous in different astrophysical systems such as solar & stellar coronae, the circumgalactic (CGM), interstellar (ISM) and intra-cluster (ICM) media. The role of these multiphase plasmas has been highlighted in mass-energy cycles at all such scales, from thermal non-equilibrium (TNE) cycles in the solar atmosphere to precipitation-regulated feedback cycles that drive star and galaxy formation. The properties of the cool plasmas across these multiple scales is strikingly similar, intimately linked to the yet unclear but fundamental mechanisms of coronal and ICM heating and instabilities of thermal or other nature. The solar corona constitutes a formidable and unique astrophysics laboratory where we can spatially and temporally resolve the physics of such multiphase plasma. The multi-faceted and measured response of the solar atmosphere to the heating is exemplified by TNE cycles that manifest through EUV intensity pulsations and through the generation of cool coronal rain and prominences whose mysterious properties are like that of multiphase filamentary structure in the ISM and ICM or to molecular loops in the Galactic centre. Coronal rain also occurs across a wide energetic scale extending to flares, whose features seem recurrent in active stars but remains poorly investigated due to lack of multi-temperature coverage at appropriate resolution. The formation and stability-loss of prominences is of major importance to space weather and their ‘slingshot’ counterparts provide unique diagnostic capabilities to the wind mass-loss rate. These exciting new cross-disciplinary possibilities are part of a Heliophysics Decadal Survey white paper and call for a high-resolution multi-wavelength imaging and spectroscopic solar instrument able to capture the multithermal, dynamic and pervasive nature of the multiphase plasma in the hot solar corona.

This review surveys recent advances in the numerical modeling of solar prominences and coronal rain achieved with the fully open-source adaptive-grid, parallelized Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). We examine how these models have contributed to our understanding of the formation and evolution of cool plasma structures in the solar corona. We first discuss prominence models that focus on prominence formation and their dynamic behaviour. We then turn to coronal rain, highlighting its connection to thermal instability and its role in the exchange of mass and energy between the corona and chromosphere. Particular attention is given to the growing efforts to connect simulations with observations through synthetic emission and spectral diagnostics.

Context. Thermal non-equilibrium (TNE) produces several observables that can be used to constrain the spatial and temporal distribution of solar coronal heating. Its manifestations include prominence formation, coronal rain, and long-period intensity pulsations in coronal loops. The recent observation of abundant periodic coronal rain associated with intensity pulsations allowed for these two phenomena to be unified as the result of TNE condensation and evaporation cycles. On the other hand, many observed intensity pulsation events show little to no coronal rain formation. Aims. Our goal is to understand why some TNE cycles produce such abundant coronal rain, while others produce little to no rain. Methods. We reconstructed the geometry of the periodic coronal rain event, using images from the Extreme Ultraviolet Imager (EUVI) onboard the Solar Terrestrial Relations Observatory (STEREO), and magnetograms from the Helioseismic and Magnetic Imager (HMI). We then performed 1D hydrodynamic simulations of this event for different heating parameters and variations of the loop geometry (9000 simulations in total). We compared the resulting behaviour to simulations of TNE cycles that do not produce coronal rain. Results. Our simulations show that both prominences and TNE cycles (with and without coronal rain) can form within the same magnetic structure. We show that the formation of coronal rain during TNE cycles depends on the asymmetry of the loop and of the heating. Asymmetric loops are overall less likely to produce coronal rain, regardless of the heating. In symmetric loops, coronal rain forms when the heating is also symmetric. In asymmetric loops, rain forms only when the heating compensates for the asymmetry.

Context. Coronal rain is the most dramatic cooling phenomenon of the solar corona. Recent observations in the visible and UV spectrum have shown that coronal rain is a pervasive phenomenon in active regions. Its strong link with coronal heating through the thermal non-equilibrium (TNE) – thermal instability (TI) scenario makes it an essential diagnostic tool for the heating properties. Another puzzling feature of the solar corona in addition to the heating is its filamentary structure and variability, particularly in the extreme UV (EUV). Aims. We aim to identify observable features of the TNE-TI scenario underlying coronal rain at small and large spatial scales to understand the role it plays in the solar corona. Methods. We used EUV datasets at an unprecedented spatial resolution of ≈240 km from the High Resolution Imager (HRI) in the EUV (HRIEUV) of the Extreme Ultraviolet Imager (EUI) and SPICE on board Solar Orbiter from the perihelion in March and April 2022. Results. EUV absorption features produced by coronal rain are detected at scales as small as 260 km. As the rain falls, heating and compression is produced immediately downstream, leading to a small EUV brightening that accompanies the fall and produces a fireball phenomenon in the solar corona. Just prior to impact, a flash-like EUV brightening downstream of the rain, lasting a few minutes, is observed for the fastest events. For the first time, we detect the atmospheric response to the impact of the rain on the chromosphere, and it consists of upward-propagating rebound shocks and flows that partly reheat the loop. The observed widths of the rain clumps are 500 ± 200 km. They exhibit a broad velocity distribution of 10 − 150 km s−1and peak below 50 km s−1. Coronal strands of similar widths are observed along the same loops. They are co-spatial with cool filamentary structure seen with SPICE, which we interpret as the condensation corona transition region. Prior to the appearance of the rain, sequential loop brightenings are detected in gradually cooler lines from coronal to chromospheric temperatures. This matches the expected cooling. Despite the large rain showers, most cannot be detected in AIA 171 in quadrature, indicating that line-of-sight effects play a major role in the visibility of coronal rain. The AIA 304 and SPICE observations still reveal that only a small fraction of the rain can be captured by HRIEUV. Conclusions. Coronal rain generates EUV structure and variability over a wide range of scales, from coronal loops to the smallest resolvable scales. This establishes the major role that TNE-TI plays in the observed EUV morphology and variability of the corona.

The presence and interplay of continuous cooling and heating processes maintaining the corona of the Sun at the observed one million K temperature were recently understood to have crucial effects on the dynamics and stability of magnetoacoustic (MA) waves. These essentially compressive waves perturb the coronal thermal equilibrium, leading to the phenomenon of a wave-induced thermal misbalance (TM). Representing an additional natural mechanism for the exchange of energy between the plasma and the wave, TM makes the corona an active medium for MA waves, so that the wave can not only lose but also gain energy from the coronal heating source (similarly to burning gases, lasers and masers). We review recent achievements in this newly emerging research field, focussing on the effects that slow-mode MA waves experience as a back-reaction of this perturbed coronal thermal equilibrium. The new effects include enhanced frequency-dependent damping or amplification of slow waves, and effective, not associated with the coronal plasma non-uniformity, dispersion. We also discuss the possibility to probe the unknown coronal heating function by observations of slow waves and linear theory of thermal instabilities. The manifold of the new properties that slow waves acquire from a thermodynamically active nature of the solar corona indicate a clear need for accounting for the effects of combined coronal heating/cooling processes not only for traditional problems of the formation and evolution of prominences and coronal rain, but also for an adequate modelling and interpretation of magnetohydrodynamic waves.

The condensations composing coronal rain, falling down along loop-like structures observed in cool chromospheric lines such as Hα and Ca ii H, have long been a spectacular phenomenon of the solar corona. However, considered a peculiar sporadic phenomenon, it has not received much attention. This picture is rapidly changing due to recent high-resolution observations with instruments such as the Hinode/Solar Optical Telescope (SOT), CRISP of the Swedish 1-m Solar Telescope, and the Solar Dynamics Observatory. Furthermore, numerical simulations have shown that coronal rain is the loss of thermal equilibrium of loops linked to footpoint heating. This result has highlighted the importance that coronal rain can play in the field of coronal heating. In this work, we further stress the importance of coronal rain by showing the role it can play in the understanding of the coronal magnetic field topology. We analyze Hinode/SOT observations in the Ca ii H line of a loop in which coronal rain puts in evidence in-phase transverse oscillations of multiple strand-like structures. The periods, amplitudes, transverse velocities, and phase velocities are calculated, allowing an estimation of the energy flux of the wave and the coronal magnetic field inside the loop through means of coronal seismology. We discuss the possible interpretations of the wave as either standing or propagating torsional Alfvén or fast kink waves. An estimate of the plasma beta parameter of the condensations indicates a condition that may allow the often observed separation and elongation processes of the condensations. We also show that the wave pressure from the transverse wave can be responsible for the observed low downward acceleration of coronal rain.

An analytical model of prominence dynamics

The complex interaction of the magnetic field with matter is the key to some of the most puzzling observed phenomena at multiple scales across the Universe, from tokamak plasma confinement experiments in the laboratory to the filamentary structure of the interstellar medium. A major astrophysical puzzle is the phenomenon of coronal heating, upon which the most external layer of the solar atmosphere, the corona, is sustained at multi-million degree temperatures on average. However, the corona also conceals a cooling problem. Indeed, recent observations indicate that, even more mysteriously, like snowflakes in the oven, the corona hosts large amounts of cool material termed coronal rain, hundreds of times colder and denser, that constitute the seed of the famous prominences. Numerical simulations have shown that this cold material does not stem from the inefficiency of coronal heating mechanisms, but results from the specific spatio-temporal properties of these. As such, a large fraction of coronal loops, the basic constituents of the solar corona, are suspected to be in a state of thermal non-equilibrium (TNE), characterised by heating (evaporation) and cooling (condensation) cycles whose telltale observational signatures are long-period intensity pulsations in hot lines and thermal instability-driven coronal rain in cool lines, both now ubiquitously observed. In this paper, we review this yet largely unexplored strong connection between the observed properties of hot and cool material in TNE and instability and the underlying coronal heating mechanisms. Focus is set on the long-observed coronal rain, for which significant research already exists, contrary to the recently discovered long-period intensity pulsations. We further identify the outstanding open questions in what constitutes a new, rapidly growing field of solar physics.

Decayless kink oscillations are ubiquitously observed in active region coronal loops with an almost constant amplitude for several cycles. Decayless kink oscillations of coronal loops triggered by coronal rain have been analyzed, but the impact of coronal rain formation in an already oscillating loop is unclear. As kink oscillations can help diagnose the local plasma conditions, it is important to understand how these are affected by coronal rain phenomena. In this study, we present the analysis of an event of coronal rain that occurred on 25 April 2014 and was simultaneously observed by Slit-Jaw Imager (SJI) on board Interface Region Imaging Spectrograph (IRIS) and Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO). We investigated the oscillation properties of the coronal loop in AIA images before and after the appearance of coronal rain as observed by SJI. We find signatures of decayless oscillations before and after coronal rain at similar positions to those found during coronal rain. The individual cases show a greater amplitude and period during coronal rain. The mean period is increased by 1.3 times during coronal rain, while the average amplitude is increased by 2 times during rain, in agreement with the expected density increase from coronal rain. The existence of the oscillations in the same loop at the time of no coronal rain indicates the presence of a footpoint driver. The properties of the observed oscillations during coronal rain can result from the combined contribution of coronal rain and a footpoint driver. The oscillation amplitude associated with coronal rain is approximated to be 0.14 Mm. The properties of decayless oscillations are considerably affected by coronal rain, and without prior knowledge of coronal rain in the loop, a significant discrepancy can arise from coronal seismology with respect to the true values.

A model for solar quiescent prominences nested in a ‘Figure 8’ magnetic field topology is developed. This topology is argued to be the natural consequence of the distention of bipolar regions upward into the corona. If this distention is slow enough so that hydrostatic equilibrium holds approximately along the field lines, the transverse gas pressure forces fall exponentially with height whereas the inward Lorentz forces fall as a power law. At a low height in the corona, the pressure forces cannot balance the Lorentz forces provided the field lines remain tied to the photosphere and an inward collapse with subsequent reconnection at the point of closest approach should occur. Because of initial shear in the magnetic field, the reconnection would produce isolated helices above the point of reconnection since field lines would not interact with themselves but with their neighbors. This resulting topology produces a field above the elevated neutral line which is opposite in polarity to that of the photospheric field as in the current sheet models of Kuperus and Tandberg-Hanssen (1967). Raadu and Kuperus (1973), Kuperus and Raadu (1974), and Raadu (1979) and in agreement with recent observations of Leroy (1982), and Leroy et al. (1983).

Context. Coronal rain consists of cool and dense plasma condensations formed in coronal loops as a result of thermal instability. Aims. Previous numerical simulations of thermal instability and coronal rain formation have relied on the practice of artificially adding a coronal heating term to the energy equation. To reproduce large-scale characteristics of the corona, the use of more realistic coronal heating prescription is necessary. Methods. We analysed coronal rain formation and evolution in a three-dimensional radiative magnetohydrodynamic simulation spanning from convection zone to corona which is self-consistently heated by magnetic field braiding as a result of convective motions. Results. We investigate the spatial and temporal evolution of energy dissipation along coronal loops which become thermally unstable. Ohmic dissipation in the model leads to the heating events capable of inducing sufficient chromospheric evaporation into the loop to trigger thermal instability and condensation formation. The cooling of the thermally unstable plasma occurs on timescales that are comparable to the duration of the individual impulsive heating events. The impulsive heating has sufficient duration to trigger thermal instability in the loop but does not last long enough to lead to coronal rain limit cycles. We show that condensations can either survive and fall into the chromosphere or be destroyed by strong bursts of Joule heating associated with a magnetic reconnection events. In addition, we find that condensations can also form along open magnetic field lines. Conclusions. We modelled, for the first time, coronal rain formation in a self-consistent 3D radiative magnetohydrodynamic simulation, in which the heating occurs mainly through the braiding and subsequent Ohmic dissipation of the magnetic field. The heating is stratified enough and lasts for long enough along specific field lines to produce the necessary chromospheric evaporation that triggers thermal instability in the corona.

The kinematics of the material motion in a variable magnetic field in the MHD approximation of a strong field and cold plasma is investigated. The variation of magnetic moments of two dipole systems leads to the development of such phenomena as loop prominences, coronal rain and funnel prominences.

Context. Coronal rain results from thermal instability in the solar corona, where runaway in situ cooling causes plasma to condense and drain along the magnetic lines. Coronal rain is observed in 3D spine-fan magnetic configurations. The reconnection of the magnetic field lines around the null point creates jets, seen as denser structures traveling along the field lines. As these dense regions evolve, thermal instability can set in and ultimately form coronal rain. Aims. In this paper we study the importance of partial ionization effects in the formation of coronal rain during the late evolution of 3D spine-fan magnetic reconnection in the solar corona. Methods. We used a two-fluid model consisting of neutral and charged particles coupled by collisions, whereby ionization recombination processes were taken into account. The 3D magnetic field configuration consists of two spine-fan structures and associated null points. We used localized resistivity around the nulls to induce reconnection by driving the bottom boundary below one of the two null points. To trigger the thermal instability, we investigate here how magnetic reconnection generates flows that lead to the accumulation of higher-density structures along magnetic field lines. Results. The dynamics associated with the spine-fan magnetic reconnection produces current sheets around the null point and flows along the field lines. Blobs similar to coronal rain start to appear after 400 seconds in the simulation domain, and follow the field lines from the direction of the perturbed null point. The temperature drop is accompanied by the recombination of charged particles. This leads to a drastic increase in the neutral density contrast within the rain blobs, while charges demonstrate the typical two orders of magnitude increase in density that is found in single fluid settings. Conclusions. Recombination effects become important in coronal rain evolution when the temperature drops considerably in the condensed structures. The neutrals are slowed down by recombination, producing a decoupling in velocity at the size of the blob, but inside the condensing structure the neutrals can move faster across the field lines, creating small-scale structures. The incomplete elastic collisional coupling produces decoupling in velocity, and, associated with this, more efficient frictional heating for the neutrals, followed by a decoupling in temperature. This study presents a novel two-fluid approach to coronal rain, showing that incorporating two-fluid effects is essential to accurately capture its dynamics.

Context. Models of entire prominences with their numerous fine structures distributed within the prominence magnetic field use approximate radiative transfer techniques to visualize the simulated prominences. However, to accurately compare synthetic images of prominences obtained in this way with observations and to precisely analyze the visibility of even the faintest prominence features, it is important to take into account the influence of instrumental properties on the synthetic spectra and images. Aims. In the present work, we investigate how synthetic Hα images of simulated prominences are impacted by the instrumental effects induced by the Narrowband Filter Imager (NFI) of the Solar Optical Telescope (SOT) onboard the Hinode satellite. Methods. To process the synthetic Hα images provided by 3D Whole-Prominence Fine Structure (WPFS) models into SOT-like synthetic Hα images, we take into account the effects of the integration over the theoretical narrow-band transmission profile of NFI Lyot filter, the influence of the stray-light and point spread function (PSF) of Hinode/SOT, and the observed noise level. This allows us to compare the visibility of the prominence fine structures in the SOT-like synthetic Hα images with the synthetic Hα line-center images used by the 3D models and with a pair of Hinode/SOT NFI observations of quiescent prominences. Results. The comparison between the SOT-like synthetic Hα images and the synthetic Hα line-center images shows that all large and small-scale features are very similar in both visualizations and that the same very faint prominence fine structures can be discerned in both. This demonstrates that the computationally efficient Hα line-center visualization technique can be reliably used for the purpose of visualization of complex 3D prominence models. In addition, the qualitative comparison between the SOT-like synthetic images and prominence observations shows that the 3D WPFS models can reproduce large-scale prominence features rather well. However, the distribution of the prominence fine structures is significantly more diffuse in the observations than in the models and the diffuse intensity areas surrounding the observed prominences are also not present in the synthetic images. We also found that the maximum intensities reached in the models are about twice as high as those present in the observations–an indication that the mass-loading assumed in the present 3D WPFS models might be too large.