Dissipative Torsional Alfvén Waves Detected in Solar Photospheric Flux Tubes

The search for what heats the Sun’s outer atmosphere to millions of degrees has occupied solar physicists for more than eight decades, and a new theoretical study now suggests the answer may begin in some of the smallest and most turbulent structures visible on the solar surface. In research published in the journal Solar Physics, Lucas Romero and Roberto Soler of the Universitat de les Illes Balears in Palma de Mallorca, Spain, have carried out a detailed mathematical analysis of torsional Alfvén waves in magnetic flux tubes anchored in the solar photosphere, revealing that the dense, resistive environment at the Sun’s visible surface is far more hospitable to these twisting waves than previously appreciated. The work, appearing as volume 301, article 129 of Solar Physics, reconstructs the complete spectrum of wave modes that can rattle through photospheric flux tubes and finds that a striking number of them are capable of carrying energy upward into the Sun’s higher atmospheric layers.

Torsional Alfvén waves are a distinctive species of magnetohydrodynamic, or MHD, wave. Unlike sound waves or the compressible magnetoacoustic waves that alternately squeeze and rarify plasma, Alfvén waves are incompressible: they shear the plasma sideways, or in the torsional case, twist it azimuthally around a magnetic field line, much like the rotational wriggle that travels along a twisted rope when one end is flicked. Because these waves involve no compression, they are difficult to detect directly, but they are exceptionally good at transporting energy along magnetic field lines without losing it to pressure work. The idea that Alfvén waves might heat the solar corona dates back to Hannes Alfvén’s own 1947 paper, and the concept has survived decades of scrutiny because the energy budget works: the corona requires a steady supply of roughly the amount of energy that small-scale, ubiquitous magnetic motions could plausibly deliver.

The footpoints of the Sun’s magnetic flux tubes are marked on the solar surface by photospheric bright points, compact regions of intense emission where bundles of magnetic field concentrate. These bright points are not passive markers. They are whipped about constantly by the churning convection of the photosphere, the granulation pattern produced by hot plasma rising and cooler plasma sinking in cells roughly a thousand kilometers across. Convective motions, including horizontal granular flows and small-scale vortexes, shake and twist the footpoints of flux tubes, and each twist has the potential to launch a torsional Alfvén wave traveling upward along the tube. Previous observational work has detected torsional motions in spicules and in the chromosphere, and recent high-resolution instruments such as DKIST have captured evidence of small-scale Alfvénic waves in the corona itself. What has remained theoretically murky is precisely what kinds of torsional modes the photosphere can actually sustain, and whether the extreme physical conditions there allow propagating waves to exist at all.

The photosphere is a hostile environment for wave propagation in several respects. The plasma there is only partially ionized, meaning a substantial fraction of the gas consists of neutral atoms that collide frequently with charged particles. It is also dense compared to the corona, and the magnetic field is strongly structured, with flux tubes embedded in a field-free or weakly magnetized surrounding plasma. To address this complexity, Romero and Soler formulated the problem in terms of the linearized resistive magnetohydrodynamic equations, which include the effects of finite electrical resistivity, the property that allows magnetic fields to diffuse through plasma and dissipate wave energy as heat. Their model is a cylindrical flux tube whose physical properties, including density and Alfvén speed, vary smoothly in the radial direction rather than changing abruptly at the tube boundary, a more realistic configuration than the idealized step-function tubes used in much earlier work.

Solving the resistive MHD equations in such an inhomogeneous geometry is not trivial. The researchers employed a combination of analytical and semi-analytical methods to compute the eigenvalues and eigenfunctions of the torsional wave problem, essentially mapping out the complete menu of natural oscillations that the flux tube supports. In an idealized, uniform tube, torsional Alfvén waves form a continuum of frequencies associated with each cylindrical shell of plasma oscillating at its own local Alfvén speed. When resistivity is included and the tube has a nonuniform structure, this continuum becomes discretized, and additional families of internal modes confined within the tube can appear. The mathematical machinery involves, among other techniques, the formulation of a quadratic eigenvalue problem, a well-studied problem in numerical analysis, and the careful treatment of boundary conditions at an artificial outer radius where the computational domain is truncated.

The results carry a surprising message. Under realistic photospheric conditions, the authors find that a significant number of propagating eigenmodes exist in the spectrum. These include internal modes trapped within the tube’s denser interior, as well as the discretized remnants of the Alfvén continuum associated with the tube’s radially varying structure. The photosphere, in other words, is not a place where torsional waves are immediately smothered by resistive damping and partial ionization effects. Instead, a rich collection of modes can genuinely propagate, each one a potential conduit for convective energy injected at the footpoints to travel toward the chromosphere and beyond.

Equally significant is the finding about where these waves live. The modes are not strictly confined to the interior of the flux tube. Their eigenfunctions, the mathematical functions describing how the wave displacement is distributed in space, extend into the surrounding external plasma as well. This cross-boundary character means that the distinction between body modes trapped inside the tube and surface modes hugging its edge becomes blurred under photospheric conditions. Energy carried by a torsional wave is therefore not locked away inside the magnetic structure but is shared, to some degree, with the plasma outside it. Such coupling has consequences for how wave energy might ultimately be deposited: if wave power leaks into the external medium, the dissipation of that power through resistive heating occurs over a broader spatial region than a simple trapped-mode picture would suggest.

The physical interpretation ties the whole picture together. Granular convection at the solar surface injects energy into magnetic structures through random, rapid footpoint motions. If those motions can excite a broad spectrum of torsional Alfvén modes, as the new spectrum calculations indicate, then the photosphere acts as a natural wave launcher, converting the mechanical work of convection into guided magnetic waves streaming upward. Along the way, finite resistivity converts a portion of the wave energy directly into heat through Ohmic dissipation, and the extended eigenfunctions ensure that some of this heating is distributed outside the tube itself. This mechanism connects naturally to the broader framework of wave heating in partially ionized plasmas, where ion-neutral collisions and resistive effects are known to damp Alfvénic disturbances efficiently in the chromosphere.

The study also carries practical implications for observational solar physics. The new generation of ground-based instruments, most prominently the Daniel K. Inouye Solar Telescope in Hawaii, is now resolving the Sun’s surface at scales fine enough to measure velocities and magnetic fluctuations within individual photospheric bright points. Interpreting those measurements requires theoretical models that predict which wave modes should be present and with what properties. The complete modal spectra computed by Romero and Soler provide exactly such a reference, allowing observers to distinguish genuine physical modes from instrumental or modeling artifacts. The authors themselves demonstrate this rigor in an appendix, identifying spurious, non-physical eigenmodes that arise from the approximate boundary condition of their modal method and showing how those artifacts can be recognized and excluded by checking whether eigenfunctions behave unphysically in the external medium.

The theoretical framework builds on a substantial body of prior work on MHD wave propagation in structured solar plasmas. Earlier studies established how kink waves undergo resonant absorption and phase mixing in nonuniform flux tubes, cascading wave energy to small scales where viscous and resistive dissipation become efficient. Other investigations tracked torsional Alfvén waves as they propagate from the photosphere through the expanding, stratified layers of the low atmosphere toward the corona, quantifying reflection, transmission, and heating. The present study complements this lineage by focusing on the wave spectrum at the very bottom of the chain, at the footpoints where everything begins. By showing that the photospheric environment supports a wealth of propagating torsional modes rather than suppressing them, the study strengthens the case that the Sun’s smallest magnetic structures are active participants in the atmospheric energy budget, not merely passive conduits.

For a problem that has resisted definitive solution since Alfvén first proposed wave heating in the 1940s, progress tends to arrive in increments: each study narrows the space of plausible mechanisms, refines the physical inputs, and sharpens the predictions that telescopes can test. This new analysis contributes one such increment, with an unusually concrete conclusion: the turbulent, resistive, partially ionized photosphere is capable of seeding a broad and propagating spectrum of torsional Alfvén waves, and the energy deposited into those modes by everyday convective shaking is poised to flow upward along the Sun’s magnetic skeleton. The next step belongs to observers, whose instruments are now just beginning to resolve the fine twisting motions that theory says should be there.