Jack M. Jenkins and Rony Keppens
Centre for Mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200B Bus 2400, B-3001 Leuven, Belgium
Since 1185, it has been oftentimes remarked upon how red clouds dance along the edge of the moon during solar eclipses . With the advancements in understanding and technology that enabled us to look directly at the Sun, we learned that this phenomenon is in fact embedded within the solar atmosphere and visible during eclipses due to their extension high above the solar limb. The aptly named 'Prominences', also called 'filaments', are nowadays routinely observed by a multitude of observatories, be that in space or on the ground. Despite this coverage, and wealth of historical study, a most fundamental of questions remains: why, as in Figure 1, do they look as they do ?
Figure 1. Comparison between the appearance of the filament/prominence solar phenomenon. The filament appears dark as it is projected against the solar disk and so absorbs/scatters some of the background illumination. The prominence appears bright as it is projected against the darkness of space and so we see local emission only. Filament image courtesy O. Engvold (wwwmpa.mapgarching.mpg.de). Prominence image adapted from the EST Solar Gallery.
As magnificent, arched plasma arcades, they extend several tens of million metres into the solar atmosphere, the corona, which is characterised by its low density and hot, million Kelvin temperature. By assuming the solar atmosphere to be stratified according to hydrostatic equilibrium then it has a density profile that drops exponentially in magnitude with a specific scale height. Observationally, we know solar prominences to be very dense and cold, a similar order of magnitude in both cases to the chromospheric layer of the solar atmosphere that lies below the base of the corona. The atmospheric scale height here is a mere few hundred kilometres; hydrostatic equilibrium cannot be responsible for the elevated suspension of solar prominences. Instead, we now know the magnetic field of the solar corona to be capable of self-generating topologies that hold prominence material at such great heights. A necessary component of these magnetic field 'models' is a near horizontal, concave-up orientation such that the tension of the magnetic field (the Lorentz force) acts against gravity and suspends the prominence plasma .
Although largely theoretical in origin, the orientation hypothesis is frequently backed-up by spectropolarimetric observations. Be it a prominence or a filament, the internal magnetic field is routinely measured with a horizontal orientation to the solar surface. From the filament image above, the threaded appearance of the internal structure suggests at least first-order correlation with a horizontal field structure . For prominences, on the other hand, we immediately find a contradiction as the equivalent threaded appearance is oriented, instead, vertically. The picture only gets more complex when considering the time-evolution, as wonderfully captured in the movie below. As the plasma of the solar corona is understood to adhere to Alfvén's frozen-in theorem, it should be bound to, and run along, the magnetic field. How can this be apparently true for a filament, but not so for a prominence if they're the same phenomenon? And so, we arrive at the solar prominence/filament paradox.
As part of the ERC advanced PROMINENT project led by Prof. Dr. Rony Keppens at KU Leuven in Belgium, we wanted to explore this question and so developed a fully three-dimensional model using the open source, MPI-AMRVAC toolkit that included the formation and evolution of a prominence/filament structure . Herein we solved the full set of nonideal magnetohydrodynamic equations, including the non-adiabatic source terms. The resulting distribution and evolution of plasma parameters within the simulation domain, such as density, temperature, etc. were then converted to observational proxies so as to represent what would be theoretically seen by the aforementioned observatories [6, 7]. A selection of these synthetic syntheses is available in Figure 2.
Figure 2. The appearance of the simulation according to either the filament (top row) or prominence (bottom row) projection. Prominence projections panels have the simulation domain rotated such that the line-of-sight runs parallel to the magnetic field threading the low-altitude condensations. From the left to right, the columns represent the emission/absorption measured by the broad 171 and 304 Å passband Atmospheric Imaging Assembly (AIA) cameras onboard the Solar Dynamics Observatory (SDO), and Hydrogen Hα narrowband filters of the Global Oscillation Network Group observatories.
The use of the adaptive mesh refinement computational method, in combination with approximate radiative transfer aspects, has yielded the highest resolution and most accurate simulated representation of a solar filament/prominence to date. Most crucially, we found the development of the vertical structuring within the prominence projection occurred entirely self-consistently, meaning we did not force the development artificially, in addition to the horizontal and threaded appearance of the filament. Such an approach can come across as ill-constrained, but since we are not certain which process is responsible for the observed internal structuring of prominences - although theories do of course exist - we wanted to avoid any confirmation bias associated with directly adopting any specific theory. To this end, we initially constructed the 'flux rope' topology following observational constraints , but we emphasise how the formation of coronal condensations via the thermal instability that ultimately built the prominence/filament (in addition to all subsequent evolutions) occurred entirely self-consistently.
Figure 3. Comparison between the dimensions of prominence fine structures present within an observation versus the simulation. The panels on the left are an observation of a prominence, taken at 06:33 on 11 June 2011, with both Hydrogen Hα 6563 Å and SDO/AIA 171 Å filters. The right panels compare the widths of the fine structures present within the observation and the prominence projection of Figure 2, degraded to the same resolution as the observations.
The primary conclusion of the study centres on the physical process responsible for the development and evolution of the plasma seen within the prominence projection, and subsequently offering a solution to the prominence/filament paradox. Specifically, the leading theory invoked to explain the generation of the vertical internal structuring is that of the (magnetic) Rayleigh-Taylor instability (mRTi). We show, however, that although the behaviour is consistent with the mRTi, and hence its historical invocation, the initial condition requirements are unnecessarily restrictive. We close the study by presenting the gravitational interchange instability  as the generalisation necessary to enshrine the prominence-local dynamics as equivalent to those recorded elsewhere in the cosmos (cf. the Crab nebula).
However, Figure 3 clearly demonstrates how the comparably limited resolution of the routine, modern observations represents the final hurdle. The agreement that we found is qualitatively excellent, but additional high-resolution images, like those presented in Figure 1, from both the very latest (Solar Orbiter, Daniel K. Inouye Solar Telescope) and planned (European Solar Telescope) instrumentation are paramount to validating our conclusions further.
The full publication associated with this work can be found HERE.
An open access ReadCube is also available at https://rdcu.be/cRprE.
 Vyssotsky, A. N. 1949, Meddelanden fran Lunds Astronomiska Observatorium Serie II, 126, 3
 Gibson, S. E. 2018, Living Reviews in Solar Physics, 15, 7
 Kippenhahn, R. & Schlüter, A. 1957, Zeitschrift f ̈ur Astrophysik, 43, 36
 Wang, S., Jenkins, J. M., Martínez Pillet, V., et al. 2020, The Astrophysical Journal, 892, 75
 Keppens, R., Teunissen, J., Xia, C., et al. 2020, ArXiv
 Heinzel, P., Gunár, S., & Anzer, U. 2015, Astronomy & Astrophysics, 579, A16
 Zhao, X., Xia, C., Van Doorsselaere, T., et al. 2019, The Astrophysical Journal, 872, 190
 van Ballegooijen, A. A. & Martens, P. C. H. 1989, The Astrophysical Journal, 343, 971
 Goedbloed, J.P., Keppens, R. and Poedts, S., 2010. Advanced magnetohydrodynamics: with applications to laboratory and astrophysical plasmas. Cambridge University Press