1 Introduction

The primary goal of the Daniel K. Inouye Solar Telescope (DKIST) is to address long-standing problems in solar physics, such as the operation of the solar dynamo and the heating and acceleration of the solar chromospheric and coronal plasma, but its scientific impact will extend well beyond the Sun. DKIST data will contribute to our understanding of fundamental physical processes, such as the generation and annihilation of magnetic field in plasmas of very high electrical conductivity, the role of turbulence under extreme conditions not achievable in terrestrial laboratories, and the quantum mechanical underpinnings of polarization spectroscopy essential to the interpretation of a broad range of astrophysical observations. The anticipated high spatial and temporal resolution high-precision spectropolarimetric observations of the continuously reorganizing and reconfiguring solar magnetic field will allow detailed study of the underlying impulsive energy release and particle-acceleration mechanisms responsible for the formation of particle beams and plasma ejecta. These processes are ubiquitous in astrophysics, critical to the stability of laboratory plasmas, and directly impact our ability to robustly extend human technology into the Earth’s space environment.

With a post-focus suite of five instruments (see de Wijn et al., 2021; Fehlmann et al., 2021; Jaeggli et al., 2021; von der Lühe et al., 2021; Wöger et al., 2021), the DKIST’s novel capabilities come with extreme flexibility and consequent complexity. Significant effort is required to understand how to best leverage that flexibility to achieve the rich scientific goals uniquely accessible by DKIST soon after the start of operations. The strategy of the National Solar Observatory (NSO) has been to actively engage a large cross-section of the US and international solar and space physics community in defining these goals and how to achieve them. This was done, not only to expand the range of science to be pursued, but to help ensure via early assessment that the anticipated critical science can indeed be addressed using the DKIST telescope and the anticipated post-focus instrument suite.

At the heart of the DKIST Critical Science Plan, described here, are scientific goals formulated by the DKIST Science Working Group after consideration of the Science Use Cases contributed by the community via an Atlassian® Jira® development interface. Science Use Case development was partially facilitated by a series of Critical Science Plan Workshops hosted jointly by the NSO and community partners (www.nso.edu/telescopes/dki-solar-telescope/csp/dkist-csp-workshops/). Although participation in those workshops was not mandatory for Science Use Case development, they served as an efficient way to acquaint the community with the telescope and instrument capabilities, the range of operational possibilities, and some of the challenges unique to ground-based observing at DKIST precision and scales. In turn, the DKIST project acquired a sense of the range and popularity of different observing configurations and an understanding of what will be required to meet the critical early scientific objectives.

This DKIST Critical Science Plan (CSP) is a snapshot of some of the scientific pursuits that the Daniel K. Inouye Solar Telescope hopes to enable as start-of-operations nears. The first-light DKIST images, released publicly on 29 January 2020 (www.nso.edu/inouye-solar-telescope-first-light/), only hint at the extraordinary capabilities that will accompany full commissioning of the five facility instruments (see Rimmele et al., 2020). The CSP is an attempt to anticipate some of what those capabilities will enable. After a very brief synopsis of DKIST’s capabilities, the article is divided into four broad sections: Magneto-convection and Dynamo processes, Flares and Eruptive Activity, Magnetic Connectivity through the Non-Eruptive Solar Atmosphere, and Long-Term Studies of the Sun, Special Topics, and Broader Implications. Each of these includes an introductory discussion followed by a more detailed exposition of specific research topics. The primarily focus is on issues to which DKIST will uniquely contribute. References are necessarily incomplete; they are exempli gratia only, even where not explicitly so noted.

2 Unique DKIST Capabilities

This section provides a very brief overview of the unique capabilities that DKIST will contribute. The full capabilities are discussed in detail in the accompanying articles (Rimmele et al., 2020; Davey et al., 2021; de Wijn et al., 2021; Fehlmann et al., 2021; Harrington et al., 2021; Jaeggli et al., 2021; Tritschler et al., 2021; von der Lühe et al., 2021; Wöger et al., 2021).

The DKIST primary mirror has a diameter of 4 meters, a size chosen so that small-scale plasma dynamics in the solar atmosphere can be well resolved, while simultaneously making polarization measurements of weak magnetic fields. The all-reflective, clear-aperture, off-axis optical configuration of the telescope allows broad wavelength access and minimizes scattered light, yielding the dynamic range sensitivity necessary for studies of the full solar atmosphere from the deep photosphere to \(1.5~{\mathrm{R}}_{\odot}\) (0.5 solar radii above the photosphere).

DKIST’s first-light instrument suite consists of the Cryogenic Near-Infrared Spectro-Polarimeter (CryoNIRSP: Fehlmann et al., 2021), the Diffraction-Limited Near-Infrared Spectropolarimeter (DL-NIRSP: Jaeggli et al., 2021), the Visible Broadband Imager (VBI: Wöger et al., 2021), the Visible Spectro-Polarimeter (ViSP: de Wijn et al., 2021), and the Visible Tunable Filter (VTF: von der Lühe et al., 2021). These five instruments will allow observations over the wavelength range 380 to 5000 nm. With the exception of CryoNIRSP, they can be used individually or in combination, and employ a common integrated high-order adaptive-optics system (Rimmele et al., 2020), which enables diffraction-limited observations with resolution ranging from about 0.02 arcseconds at the shortest wavelength to 0.09 arcseconds at 1500 nm. The stand-alone, cryogenically cooled CryoNIRSP will make seeing-limited observations with 0.15 arcsecond critical spatial sampling along the spectrograph slit over the spectral range 1000 to 5000 nm. Scattering by the Earth’s atmosphere, and thus the background sky-brightness, is generally low at the observatory site on Haleakalā, and is further reduced at long wavelengths. This will allow regular DKIST observations of the faint solar corona in the near to mid infrared. All instruments employ specially developed high-frame-rate, large-format cameras capable of non-destructive detector reads to improve signal to noise using longer exposures, and importantly, all instruments, with the exception of VBI (a narrow-band diffraction-limited filtergraph), are highly sensitive spectropolarimeters. Careful calibration of the instrument and telescope polarimetric contributions (Harrington, Sueoka, and White, 2019; Harrington et al., 2021, and the references therein) will allow measurement of magnetic flux densities of less than one Gauss both on and off the solar disk.

3 Magneto-Convection and Dynamo Processes

Magnetic fields on the Sun are highly structured and multi-scale. Field is found not only on the scale of active regions and sunspots but down to the smallest spatial scales observed. The small-scale fields may originate at larger scales and result as the endpoint of a turbulent cascade, or they may be induced directly by small-scale motions, perhaps in the photosphere itself, the result of a turbulent fluctuation dynamo (also called a small-scale or local dynamo). Many questions remain about the field distributions observed, about how and why the field is organized as it is in the solar photosphere.

On the largest scale, the global solar magnetic-activity cycle reflects dynamo processes that operate with remarkable regularity. The most conspicuous aspect of the global-scale dynamo is the cyclic appearance and disappearance of large areas of strong magnetic field organized into sunspots and active regions. These come and go with the solar cycle on spatial and temporal scales that suggest an origin in the deep convection zone or in the overshoot region just below it. But the solar convection zone is in a highly turbulent state and spans many pressure scale heights, with the density changing by a factor of over a million between the bottom and the top. If formed near the bottom of the convection zone, these magnetic structures must survive transit across this highly stratified and vigorously convecting region. Alternatively, active regions could re-form in the upper convection zone or in the photosphere itself. Although the vertical scale height in the photosphere is much smaller than the characteristic size of an active region, sunspot, or even a pore, some aspects of active-region evolution support this possibility, with the local dynamics displaying a complex interplay between the magnetic field and magneto-convective motions at all stages including formation and dissolution.

Sunspot umbrae are the most strongly magnetized regions of the Sun accessible to spectropolarimetric observations. They are cool and dark, characterized by magnetic fields that are close to vertical with respect to the photosphere, and exhibit constrained columnar convective motions that are only poorly understood. The surrounding penumbral field is highly inclined, with multiple interleaved magnetic components permeated by strong plasma flows. It is unknown how this multi-component sunspot structure arises. For example, reproduction of the observed penumbral properties by state-of-the-art radiative magneto-hydrodynamic simulations requires upper boundary conditions on the magnetic field whose counterparts on the Sun have yet to be identified. DKIST’s large photon flux at high spatial and temporal resolution is critical to advancing our understanding of sunspot dynamics.

The quiet (non-active region) Sun is magnetized almost everywhere. In the quietest regions (inter-network) the fields appear to be weak and highly inclined. Determining the origin of these small-scale fields is difficult and DKIST will make critical contributions to this problem as well. It will enable simultaneous observations in Zeeman-sensitive and Hanle-sensitive lines, which can be used determine if the Hanle polarization signals measured in the inter-network regions of the Sun are consistent with the field deduced from Zeeman diagnostics. These comparisons will allow assessment of the amount of unresolved flux present as a function of resolution, and careful exploitation of these techniques will lead to precise measurement of the inter-network-field coverage and its spatial distribution as a function of global solar magnetic activity. The observed statistical properties and evolution of the small scale fields on the Sun can then be compared to those in dynamo simulations to untangle the signatures their origin.

Beyond its origin, knowledge of the small-scale magnetic-field distribution on the Sun is key to assessing the role of photospherically generated waves in atmospheric heating. Alfvén and magneto-acoustic waves propagate from the photosphere upward into the atmosphere, guided by local magnetic structures. The magneto-acoustic modes steepen, shock, and dissipate in the chromosphere or undergo mode conversion and make it to greater heights. The underlying magnetic-field distribution is critical to these processes and thus to the heat and momentum budget of the atmosphere. Small-scale fields also play an important role in modulating the solar radiative output. Small concentrations of magnetic field are sites of reduced gas pressure and density, and thus opacity. An amalgam of small-scale field elements reduces the average temperature gradient of a region, locally changing the radiative output and thus contributing to variations in global solar spectral irradiance. Many small-scale magnetic structures remain unresolved by current instruments, and changes in their size and contrast distributions with the solar cycle are unknown. Since weakly magnetized internetwork regions cover the bulk of the solar surface, currently unresolved field elements may play a significant role in global spectral-irradiance trends. DKIST will play a critical role in unraveling their contributions.

Several critical science topics in this research area are discussed in detail below, including i) the formation, structure, and dynamics of small-scale photospheric magnetic fields, ii) wave generation and propagation, iii) magneto-convective modulation of the solar luminosity, and iv) active-region evolution and sunspot fine structure.

3.1 Small-Scale Photospheric Magnetic Fields: Formation, Structure, Dynamics

Is there a small-scale dynamo operating in the solar photosphere? What is the relative importance of local amplification, flux emergence, flux cancelation, and non-local transport in small-scale field evolution? How turbulent are granular flows? How dependent is quiet-Sun magnetism on the solar cycle?

Convection in the solar photosphere is driven by rapid radiative losses from a thin layer that is less than a pressure scale height in vertical extent. In this layer, the internal, kinetic, and magnetic energy of the plasma are all comparable (within a factor of a few). This leads to vigorous dynamics with strong coupling between these three energy reservoirs. While the solar convection zone is generally believed to be a highly turbulent medium, this is less than obvious in observations of the solar photosphere (Nordlund et al., 1997). Plasma that is transported upward into the photosphere, and is observed as bright hot granules, has undergone significant horizontal expansion and is expected to show nearly laminar flow structure even at DKIST resolution. A higher degree of turbulence may be found in the intergranular downflow lanes, but in these regions it likely develops as an advected instability at the interface between upflows and downflows as the fluid moves downward out of the photospheric boundary layer. Turbulence may thus only be apparent in high-spatial-resolution measurements of the deep photosphere, and then only with the anticipated high contrast achievable by DKIST.

Small-scale magnetic field is ubiquitous in the solar photosphere (Figure 1) and, in terms of unsigned flux density, it exceeds the total active-region magnetic field at all phases of the solar cycle (e.g. Lites et al., 2008; de Wijn et al., 2009; Lites, 2011; Bellot Rubio and Orozco Suárez, 2019). In quiet-Sun regions, the field has an average strength of about one-third the value it would have in equipartition with the kinetic energy of the flows (mean field strengths of about 200 G: Danilovic, Schüssler, and Solanki, 2010), but since most of the field is concentrated into small-scale elements in the downflow lanes (e.g. Bellot Rubio and Orozco Suárez, 2019), the field strength reaches much higher local values and strong feedback on the convection is expected. A detailed understanding of the interaction between the flow and the small-scale magnetic field, and the possible role of the field in the suppression of turbulence within intergranular downflows, is still elusive due to the resolution limits of current observations. This has broader significance, as the development of turbulence in the shear layers of intergranular downflow lanes may contribute to spectral-line broadening (Section 6.2). Furthermore, even in the quiet Sun, a small fraction of the magnetic field is locally amplified to a strength of a few kilogauss. This may occur through the convective-collapse process (Parker, 1978; Webb and Roberts, 1978; Spruit, 1979; Spruit and Zweibel, 1979; Grossmann-Doerth, Schüssler, and Steiner, 1998), with some observational evidence for that mechanism (e.g. Hewitt et al., 2014), although significant uncertainty remains (Venkatakrishnan, 1986; Bushby et al., 2008; Borrero et al., 2017). Only the largest of the kilogauss elements are resolved with current instrumentation. DKIST will allow dynamical studies of the formation and evolution of individual kilogauss elements and detailed statistical analysis of the quiet-Sun flux concentration size and strength distributions and their solar-cycle dependencies. Since modulation of the solar radiative output by magnetic flux elements is the primary cause of solar-irradiance variations, these studies will also be critically important in that context (see Section 3.3 below).

Figure 1
figure 1

Top: Swedish Solar Telescope (Scharmer et al., 2003)/CRisp Imaging Spectro-Polarimeter (Scharmer et al., 2008) observation of the quiet Sun with \(0.15^{\prime\prime}\) resolution (\(\approx100~\text{km}\)), displaying Stokes–\(I\) and Stokes–\(V\). Images courtesy L. Bellot Rubio (IAA-CSIC), S. Esteban Pozuelo (IAA-CSIC), and A. Ortiz (ITA, University of Oslo) www.est-east.eu/est/index.php?option=com_content&view=article&id=774&lang=en?quiet-sun-magnetic-fields-2-2-2. Red boxes are 6.1 × 6.1 Mm, which is the size of the simulations below. Bottom: quiet-Sun simulation with 4-km grid spacing (comparable to an effective DKIST resolution of 20 km) displaying bolometric intensity and vertical magnetic-field strength (in the range \(\pm200~\text{G}\)) at optical depth 0.1. Simulation images from Rempel (2014), copyright by AAS.

Beyond the quiet Sun, numerous small-scale magnetic loop-like structures are found in regions that are unipolar on larger scales, including both active-region plage (Wang, 2016; Wang, Ugarte-Urra, and Reep, 2019) and coronal holes (Wang, Warren, and Muglach, 2016). While difficult to discern in magnetograms, where minority-polarity signatures are often absent, these structures are readily apparent in EUV images. They have horizontal scales of \(\approx2\,\text{--}\,5~\text{Mm}\) and evolve on timescales of minutes. In Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) images of active-region plage, the structures sometimes show an inverted-Y configuration, suggestive of magnetic reconnection. This role is supported by their presence in the cores of bright coronal plumes, again even when no minority-polarity flux is visible in photospheric magnetograms, where they appear to cluster and contribute to coronal-plume energization, heating, and emission when flow convergence causes interchange reconnection between them. Reflecting this dynamic, coronal-plume emission changes on timescales of hours to a day as the supergranular flow field evolves (Wang, Warren, and Muglach, 2016; Avallone et al., 2018; Qi et al., 2019). Previous magnetogram-based studies (e.g. Hagenaar, DeRosa, and Schrijver, 2008) measured ephemeral region emergence rates inside unipolar regions that were at least a factor of three lower than those in the quiet Sun. The discovery of ubiquitous small-scale loops with very weak if any minority-polarity signatures suggests that magnetograms may significantly underestimate the amount of mixed-polarity flux in plage, strong network, and coronal-hole regions. That mixed-polarity flux may play an important role in coronal heating as it reconnects with the large-scale overlying fields, both in active regions (Wang, 2016; Wang, Ugarte-Urra, and Reep, 2019) and in coronal holes where it may also help to drive the solar wind (Wang, Warren, and Muglach, 2016). High-resolution, high-sensitivity magnetic-field measurements with DKIST will be able to quantitatively assess this suggestion.

The small-scale magnetic field in the solar photosphere is maintained by a combination of several processes: i) dispersal of active region flux; ii) turbulent amplification by photospheric flows; and iii) small-scale flux emergence from deeper regions. While process i) reflects contributions from the large-scale global dynamo, processes ii) and iii) are linked to a turbulent-fluctuation dynamo that relies on the chaotic nature of flows in the uppermost layers of the convection zone. Some numerical simulations of turbulent-fluctuation dynamos in the solar context have been successful in generating small-scale magnetic field with flux densities similar to those suggested by current observations, but these and all numerical-fluctuation dynamo models operate at magnetic Prandtl numbers (ratio of viscosity and magnetic diffusivity) close to unity (e.g. Cattaneo, 1999; Vögler and Schüssler, 2007; Rempel, 2014; Khomenko et al., 2017). By contrast, the magnetic Prandtl number in the solar photosphere, if based on molecular values of the diffusivities, may be as low as \(10^{-5}\). Producing a fluctuation dynamo at small magnetic Prandtl number and large Reynolds number, the parameter regime most relevant to the Sun, is an unmet challenge for both numerical simulations and laboratory experiments. This makes the solar photosphere a unique plasma laboratory.

Moreover, even Prandtl-number-unity models of the solar-fluctuation dynamo can generate total unsigned magnetic-flux densities close to those observed only when the advection of flux from deeper layers is allowed (Rempel, 2014), not if the dynamo is strictly local, operating only in the photosphere. This suggests that the observed level of quiet-Sun magnetism requires a significant amount of magnetic-field recirculation within the convection zone, with convective motions bringing substantial amounts of field up into the photosphere from below (Stein, Bercik, and Nordlund, 2003; Rempel, 2014, 2018). The behavior of the solar dynamo across many coupled scales may thus be critical to its operation (e.g. Charbonneau, 2016; Wright and Drake, 2016; Beaudoin et al., 2016), and a more complete understanding of the solar fluctuation-dynamo may require quantitative assessment of the relative importance of local field amplification and non-local field transport (see, e.g. Gošić et al., 2016, for recent observational efforts).

Global-scale transport of small-scale field is already a central ingredient of many global dynamo models (see reviews by Charbonneau, 2014; Cameron, Dikpati, and Brandenburg, 2017), with the accumulation of small-scale field elements of a dominant polarity in the polar regions critical to the reversal of the global dipole moment. For this reason, the measured solar polar field strength is often cited as the most reliable indicator for solar-cycle predictions (e.g. Bhowmik and Nandy, 2018). The behavior of the small-scale polar fields can be directly assessed via synoptic DKIST observations (Section 6.1), and the flux transport that results from supergranular diffusion and meridional circulation can be better quantified by high-resolution DKIST studies of magnetic-element displacement statistics (Agrawal et al., 2018). Relatedly, global-scale/long-period modulation of macrospicules has been reported (e.g. Kiss, Gyenge, and Erdélyi, 2017; Kiss and Erdélyi, 2018), and spicules and other chromospheric dynamical events are key targets for further DKIST study (Section 5.1). DKIST will thus enable quantitative assessment of the small-scale field evolution which may underlie the global behavior.

3.2 Acoustic–Gravity Wave Excitation

What excites the solar acoustic oscillations? How do observed source properties effect helioseismic inferences? What physics underlies flare-induced acoustic wave emission?

Magnetohydrodynamic wave generation, propagation, mode conversion, and dissipation are central processes in the energy and momentum budget of the solar atmosphere. Those issues are largely discussed in Section 5.4. Here we focus on the role of DKIST in determining the source of the solar \(p\)-modes and the potential for gravity-wave observations and diagnostics in the lower solar atmosphere.

Acoustic-mode excitation on the Sun, and other stochastically excited stars, likely results from small-scale dynamical processes associated with convection (Figure 2), but the detailed source properties are not known. Some theoretical work points to turbulent excitation dominated by Reynolds-stress induced pressure fluctuations, the Lighthill mechanism (Lighthill, 1952; Goldreich and Keeley, 1977; Goldreich and Kumar, 1990; Balmforth, 1992a,b), possibly occurring within intergranular lanes, while other work suggests that the dominant source is associated with pressure perturbations caused by local radiative cooling in the photosphere (Stein and Nordlund, 1991; Goldreich, Murray, and Kumar, 1994; Rast, 1999) and the sudden formation of new downflow plumes, with the latter process often occuring during the fragmentation of large granules (Rast, 1995). Additionally, some flares are strong acoustic-wave sources (e.g. Kosovichev and Zharkova, 1998; Ambastha, Basu, and Antia, 2003; Donea and Lindsey, 2005), and the mechanisms associated with acoustic emission during flaring is also only partially understood (Lindsey et al., 2014).

Figure 2
figure 2

Filtered Doppler velocity (left) and a simultaneous continuum image of the same area (right) from the first flight of the IMaX instrument on the Sunrise balloon-borne observatory. Time series of these images suggest the launching of parallel wavefronts (center of lefthand image) by new downflow-lane formation during granule fragmentation. From Roth et al. (2010), copyright by AAS.

There is observational support for both of the hydrodynamic mechanisms suggested above (Rimmele et al., 1995; Chaplin et al., 1998; Goode et al., 1998; Straus et al., 1999; Skartlien and Rast, 2000; Severino et al., 2001; Bello González et al., 2010; Roth et al., 2010), but it is unclear which process dominates, how much power is radiated by each, and how well that power is coupled to the solar \(p\)-modes. Unambiguous characterization of the \(p\)-mode sources requires separating local wave motions from higher-amplitude compressible convective flows and wave coherence patches. This is theoretically challenging, and observationally likely requires high spatial and temporal resolution observations (on the order of tens of kilometers at 15-second cadence) over a range of heights from the deep to middle photosphere. A statistically significant number of individual events must be studied to assess their physical characteristics and energy contributions, and thus their importance, and it is only with DKIST that the required observational capabilities will become regularly available. Moreover, direct measurement of pressure fluctuations along with the temperature and velocity fields are needed to fully characterize the excitation mechanisms, and pressure-sensitive spectral diagnostics are only now being developed in preparation for DKIST start of operations.

The precise nature of the \(p\)-mode excitation events, their efficiency, phasing, and relative importance to mode excitation, is critical to both local and global helioseismic inferences. For global helioseismology, and local methods that employ the mode spectrum such as ring-diagram analysis (Haber et al., 2002; Gizon and Birch, 2002, and the references therein), precise determination of the modal frequencies and frequency shifts depends on the assumed power-spectral-line shape with which the modes are fit. One source of systematic error in the measured solar \(p\)-mode frequencies is the unknown non-Lorentzian shape of the spectral lines. Line profiles vary with wavenumber and frequency depending on the source depth and physical properties (e.g. Gabriel, 1992; Duvall et al., 1993; Gabriel, 1995; Rast and Bogdan, 1998; Nigam et al., 1998; Skartlien and Rast, 2000). Similarly, local helioseismological deductions are sensitive to the phase relationship between the waves and their source. For example, travel-time kernels used in time–distance helioseismology depend on the assumptions about the source phasing and characteristics (Gizon and Birch, 2002; Birch, Kosovichev, and Duvall, 2004). Source properties may be particularly critical for multi-height local helioseismology if the source is spatially and temporally extended, as it is likely to be.

Additionally, the local acoustic wave field can be used to diagnose magnetic structures ranging in size from small scale elements to sunspots. Mode interaction and conversion at the interface of a magnetized region leads to a range of signatures in the photosphere including wave absorption, mode conversion, and scattering (with associated phase shifts and amplitude changes) that can be used to reveal the subsurface (e.g. Braun, Duvall, and Labonte, 1987, 1988; Spruit and Bogdan, 1992; Braun et al., 1992; Cally, Bogdan, and Zweibel, 1994; Braun, 1995; Cally and Bogdan, 1997; Gizon, Birch, and Spruit, 2010; Liang et al., 2013; Waidele and Roth, 2020, and the references therein) or overlying structure of the field (e.g. Finsterle et al., 2004a,b; Jess et al., 2020, and Section 5.4 below). The combination of new methods for local source identification (Bahauddin and Rast, 2021) and multi-height high spatial and temporal resolution spectropolarimetric measurements with DKIST promises a new era for helioseismic diagnosis of sunspots and smaller-scale magnetic structures.

Finally, the photosphere is the lower boundary of the stably stratified solar atmosphere, and convective overshoot into the lower solar atmosphere drives internal acoustic–gravity waves. These waves probe the physical properties of the layers above and may make a significant contribution to the solar chromosphere energy balance (e.g. Hindman and Zweibel, 1994; Straus et al., 2008). The increased spatial resolution and temporal cadence of DKIST will allow higher spatial and temporal frequency waves to be observed, and the extended high-quality observation periods anticipated will enhance the frequency resolutions achievable. This may allow individual atmospheric gravity-wave-mode identification and detailed study of their convective driving. Gravity-wave excitation is a process that is broadly important in regions more difficult to observe, such as the base of the solar convection zone and in the interior of other stars, and observations of the photosphere and lower solar atmosphere are critical to constraining the underlying excitation processes. Moreover, since the solar atmosphere is highly magnetized, significant mode coupling occurs as the waves propagate upward, and as this coupling depends on the orientation and strength of the local magnetic field, such observations have immediate diagnostic value (Vigeesh, Jackiewicz, and Steiner, 2017; Vigeesh et al., 2019, Section 5.4 below).

3.3 Magneto-Convective Modulation of the Solar Irradiance

How do small-scale magnetic-flux elements contribute to global solar-irradiance variations? How well do observed temperature and pressure stratifications within flux elements agree with atmosphere models employed for irradiance reconstruction?

Observational evidence suggests that solar irradiance is modulated by changes in solar surface magnetism. Based on this hypothesis, empirical techniques have been developed to reproduce total and spectral solar-irradiance variations from observed changes in the coverage of magnetic features over the solar disk. Depending on their size and field strength, different magnetic features show different center-to-limb variation in different spectral regions. Thus both the disk location and disk coverage of the features are needed to model irradiance changes, and full-disk moderate resolution (one to two arcsecond) observations are typically employed (e.g. Chapman, Cookson, and Dobias, 1996; Krivova et al., 2003; Yeo et al., 2017).

However, both high-spatial-resolution (sub-arcsec) observations and radiative magnetohydrodynamic simulations indicate the presence of magnetic structures too small to be detected at moderate resolution (Figure 3). Spectra modeled on the basis of full-disk moderate-resolution-image features do not necessarily capture the radiative output of the underlying highly structured atmosphere, nor do they distinguish between differently structured atmospheres with the same lower-resolution appearance (Röhrbein, Cameron, and Schüssler, 2011; Criscuoli, Norton, and Whitney, 2017; Peck et al., 2019). The mapping between full-disk imagery, the underlying small-scale structure, and spectral irradiance is only poorly understood butis critical for accurate irradiance modeling, particularly spectral-irradiance modeling (see Ermolli et al., 2013, and the references therein). There thus remains significant uncertainty about whether full-disk magnetic-structure-based irradiance models can account for the observed spectral-irradiance variations. In particular, both the sign and the magnitude of the spectral-irradiance trends with solar cycle are controversial, with some authors reporting out-of-phase irradiance variation in key wavelength bands (Harder et al., 2009) and others reporting in-phase variation across the spectrum (Wehrli, Schmutz, and Shapiro, 2013). While out-of-phase variations have been explained in terms of a change in the mean photospheric temperature gradient with cycle, which atmospheric components contribute most to that mean change remains unclear, particularly as absolute irradiance measurements are disk integrated. Addressing these uncertainties requires developing both an understanding of the statistical distributions of small-scale elements and reliable techniques for measuring the photospheric temperature gradient (Faurobert, Balasubramanian, and Ricort, 2016; Criscuoli and Foukal, 2017).

Figure 3
figure 3

Full-disk images are used in solar-irradiance models because magnetic structure contributions depend on disk position. There are significant differences in the magnetic morphology underlying pixels classified as the same structure at full-disk resolution. These influence solar spectral irradiance and its variability with solar cycle. Image on left from the Precision Solar Photometric Telescope (image courtesy M.P. Rast, lasp.colorado.edu/pspt_access/). Image on right from Rempel (2014).

Unresolved magnetic elements are particularly important to the spectral output of the quiet Sun (Schnerr and Spruit, 2011) and its center-to-limb profile (Peck and Rast, 2015). It is against this that the contrasts and contributions of magnetic structures are often measured. The quiet Sun covers the majority of the solar photosphere and typically its integrated irradiance contribution is taken to be constant in time, but due to the presence of possibly time-varying unresolved magnetic structures this may not be the case. Measuring how the magnetic substructure of the quiet Sun actually changes with the solar cycle is a key DKIST capability. Beyond this, the radiative contributions of magnetic structures such as plage and faculae depend on the fact that they are structured on unresolved scales (Okunev and Kneer, 2005; Criscuoli and Rast, 2009; Uitenbroek and Criscuoli, 2011). Some facular pixels show negative continuum contrast in full-disk images even close to the limb. This may reflect uncertainty in the quiet-Sun profile against which the contrast is measured or underlying substructure in the faculae themselves (e.g. Topka, Tarbell, and Title, 1997). Measuring the radiative properties of composite features and understanding the physical mechanisms that determine their spectral output is an important next step in the development of irradiance reconstruction and modeling techniques. Models must be capable of statistically accounting for contributions from a distribution of small-scale magnetic features unresolved in full-disk images.

Finally, the astrophysical implications of small-scale fields extend beyond the Sun. The spectral-energy distribution of stars is a key fundamental input in the modeling of planetary atmospheres (e.g. Hu, Seager, and Bains, 2012; Miguel and Kaltenegger, 2014). In particular, UV radiation is responsible for the production and destruction of molecular species that are the anticipated biomarkers to be used in future exoplanet atmospheric characterization missions. More critically, UV variability is important in determining the climate and habitability of (e.g. Scalo et al., 2007; France et al., 2013; Linsky, France, and Ayres, 2013; O’Malley-James and Kaltenegger, 2019) and biogenic processes on (Buccino, Lemarchand, and Mauas, 2007) extrasolar planets. While not sensitive to UV radiation directly, DKIST observations of the Sun can be used to develop, constrain, and test models of stellar chromospheres and/or proxies to reliably reconstruct UV spectra from measurements obtained at longer wavelengths. Moreover, accounting for magnetic modulation of stellar brightness is crucial to the detection and correct interpretation of stellar light curves and their use in exoplanet characterization (e.g. Apai et al., 2018; Rackham, Apai, and Giampapa, 2019). DKIST’s ability to probe the physical mechanisms underlying stellar brightness variations will thus contribute to both stellar astrophysics and the modeling of host-star contributions to exoplanet transit photometry and spectroscopy.

3.4 Active Region Evolution and Sunspot Fine Structure

Why sunspots? Why is magnetic flux concentrated into sunspots? How do they form? Why do they have penumbrae? What is the dynamical and magnetic substructure of sunspot umbrae and penumbrae, and what are the magnetic and dynamical links to the chromosphere, transition region, and corona above?

Sunspots are the most prominent manifestation of strong magnetic fields in the solar atmosphere. They consist of a central dark umbra, within which the magnetic field is primarily vertically oriented, and a brighter penumbra, with weaker and more inclined fields. Both regions exhibit small-scale structure, such as umbral dots and penumbral filaments, and rich dynamics with mass flows and wave motions spanning the photosphere and chromosphere. The range of observed behaviors reflects the presence of magnetic fields of varying strengths and inclination angles, making sunspots ideal for studying magneto-convective processes in complex magnetic-field geometries.

However, despite significant advances over the past decades, observationally characterizing the field geometry and associated flow dynamics in sunspot umbrae and penumbrae presents formidable challenges. These are due to small scales present, the low umbral photon counts, and the difficulties associated with interpreting the distorted spectral-line profiles observed (Borrero and Ichimoto, 2011; Rempel and Schlichenmaier, 2011; Hinode Review Team et al., 2019). As a result, we do not yet know the magnetic topology or flow structure of the penumbra at the smallest scales, nor how these vary with height in the atmosphere. In state-of-the-art numerical models (e.g. Heinemann et al., 2007; Rempel, Schüssler, and Knölker, 2009; Rempel, 2011, 2012a,b), penumbral filaments reflect overturning convection in highly inclined magnetic-field regions, with the Evershed flow being the main flow component oriented in the radial direction. These models predict the existence of vertical downflows at the edges of penumbral filaments where the overturning plasma descends below the solar surface, but systematic study of such downflows on the Sun is very difficult due to their intrinsically small sizes (e.g. Esteban Pozuelo, Bellot Rubio, and de la Cruz Rodríguez, 2015, 2016, and the references therein). Supersonic vertical velocities at the outer end of penumbral filaments have been reported (Figure 4) and can be associated with penumbral field lines dipping down below the solar surface (Tiwari et al., 2013; van Noort et al., 2013; Esteban Pozuelo, Bellot Rubio, and de la Cruz Rodríguez, 2016), but similar flows have also been detected in the inner penumbra without relation to the Evershed flow (Louis et al., 2011). In both regions, very large field strengths (on the order of 7 kG and 5 kG, respectively, compared to typical peak umbral values of 2 – 3 kG) have been associated with the high-speed flows (Siu-Tapia et al., 2017; Okamoto and Sakurai, 2018), but because the observed Stokes profiles show anomalous shapes, these determinations are uncertain. Multi-line, very high-spatial-resolution, spectropolarimetric observations by DKIST will allow improved inference of both the field strengths and flow velocities and clarify the origin of the supersonic flows and the processes leading to local field amplification beyond umbral values.

Figure 4
figure 4

Sunspot in Active Region 11302. Observed in intensity (left), circular polarization (middle), and line-of-sight velocity (right) with the CRisp Imaging Spectro-Polarimeter (Scharmer et al., 2008) at the Swedish Solar Telescope (Scharmer et al., 2003) on 28 September 2011. Penumbral fine structure is apparent in all three maps, showing details down to the diffraction limit of the telescope (0.15 arcsec). Lateral edges of penumbral filaments appear to harbor localized short-lived vertical downflows (shown red). Adapted from Esteban Pozuelo, Bellot Rubio, and de la Cruz Rodríguez (2015, 2016).

More fundamentally, the formation of the penumbra itself remains a mystery (e.g. Rezaei, Bello González, and Schlichenmaier, 2012). The process lasts only a few hours, making it difficult to capture, and observations have not yet identified the mechanism triggering the process around a naked pore. There are indications that the chromospheric magnetic field may play a prominent role. In simulations (Rempel, 2012a,b) sunspots only form an extended penumbra if the field inclination at the top boundary is artificially enhanced. The nature and origin of a similar field on the Sun, if it exists, is unknown. Penumbrae are a robust feature of sunspots and are present under a wide range of conditions, whereas the presence of penumbrae in sunspot simulations requires this special boundary condition. This critical difference may be related to the fact that the dynamics of a penumbra during formation are observationally very different from those seen once it is mature. Instead of a regular Evershed outflow, “counter” Evershed inflows, toward the umbra, are observed during formation. These inward-directed flows turn into the classical radial outward Evershed flow as the penumbra stabilizes (Schlichenmaier, González, and Rezaei, 2011). This important transition and other chromospheric precursors (Shimizu, Ichimoto, and Suematsu, 2012; Murabito et al., 2017) likely hold clues about the penumbral formation process, a process missing from the simulations. High-sensitivity DKIST measurements of the vector magnetic field and flow in both the photosphere and the chromosphere during penumbra formation will allow an assessment of the relative importance of photospheric magneto-convective processes and the evolution of overlying chromospheric magnetic fields.

In umbrae, strong magnetic fields severely constrain convective motions, and numerical simulations suggest that umbral dots are the signature of convective plumes (Schüssler and Vögler, 2006). Direct observational confirmation is difficult due to the small sizes and low contrast of the structures as well as the overall low photon counts in sunspot umbrae. These conspire to dramatically reduce the signal-to-noise ratio of the observations, particularly when spectropolarimetric measurements are needed to determine the magnetic-field configuration along with the flow. Interestingly, umbral dots may not be uniformly distributed throughout the umbra, with recent measurements suggesting the existence of very dark, fully non-convective umbral regions (Löhner-Böttcher et al., 2018). DKIST’s off-axis design and consequent low scattered-light properties will allow high-precision high-resolution Doppler and spectropolarimetric measurements of even the darkest regions of the umbra.

The magnetic topology and dynamics of the chromosphere above sunspots are also poorly understood. Few high-spatial-resolution observations extending from the photosphere up into the chromosphere with the required sensitivity have been made, so the connectivity with height is uncertain. Nonetheless, intense chromospheric activity is observed above sunspots on small spatial scales. Examples include short dynamic fibrils, umbral and penumbral microjets, penumbral bright dots, and jets at the edges of light bridges (e.g. Katsukawa et al., 2007; Louis et al., 2008; Shimizu et al., 2009; Rouppe van der Voort and de la Cruz Rodríguez, 2013; Yurchyshyn et al., 2014; Louis, Beck, and Ichimoto, 2014; Tian et al., 2014; Alpert et al., 2016; Robustini et al., 2016; Tian et al., 2018). These phenomena likely involve shocks and/or magnetic reconnection, and they are expected to be a source of chromospheric heating (e.g. Bard and Carlsson, 2010; Felipe, Khomenko, and Collados, 2011; de la Cruz Rodríguez et al., 2013; Henriques et al., 2017; Nelson et al., 2017b), and they may have far-reaching effects, up into the overlying transition region and corona (e.g. Samanta et al., 2017; Tian et al., 2018, and the references therein), with some penumbral micro-jets (perhaps those that are particularly large) displaying signatures at transition-region temperatures (Vissers, Rouppe van der Voort, and Carlsson, 2015; Tiwari et al., 2016).

Studying the dynamic chromosphere above sunspots is challenging. Low photon counts pose even more of a difficulty for observations of chromospheric features than they do for studies of the umbral photosphere. The finely structured faint absorption features that are apparent as dark fibril-shaped inhomogeneities within chromospheric umbral flashes (e.g. Socas-Navarro et al., 2009; Henriques et al., 2015) are so small and faint that they can only be observed with great difficulty using pre-DKIST telescopes and instrumentation. Even emission features are difficult to observe with spatial and temporal resolutions sufficient to distinguish the responsible physical mechanisms. For example, much of the spatial and temporal structuring of umbral micro-jets that was originally thought to be reconnection related (Bharti, Hirzberger, and Solanki, 2013; Nelson et al., 2017b) may instead be the signature of a shock/compression front forming in the corrugated sunspot atmosphere, with the time varying emission reflecting local density/velocity structures that enhance or delay the shock along a steepening compression front (Henriques et al., 2020). DKIST will enable spectropolarimetric measurements of such dim small-scale features with sufficient polarimetric sensitivity to constrain their physical properties. In combination with tools such as inversion-based semi-empirical modeling (e.g. de la Cruz Rodríguez et al., 2013) and numerical simulation, DKIST will advance our fundamental understanding of these phenomena and enable their use as diagnostics of the three-dimensional physical conditions at the event sites.

The transition region above sunspot umbrae poses additional observational challenges. It is also highly dynamic and structured at very small scales, with fast downflows and coincident strong emission, and that emission typically occurs at the short wavelengths characteristic of both transition-region and upper-chromospheric temperatures and densities (e.g. Chitta, Peter, and Young, 2016; Samanta, Tian, and Prasad Choudhary, 2018; Nelson, Krishna Prasad, and Mathioudakis, 2020). Nonetheless, it has been demonstrated that ground-based observations of sufficient spatial and temporal resolution can be combined with short-wavelength spaced-based measurements to improve transition region inversions (de la Cruz Rodríguez, Leenaarts, and Asensio Ramos, 2016; Bose et al., 2019). Simultaneous high-cadence DKIST multi-line time series combined Interface Region Imaging Spectrograph (IRIS), Hinode, Solar Orbiter (SO), and SDO observations will help clarify the relationships between the rich chromospheric dynamics above sunspots and the heating of the overlying solar transition region and corona.

Finally, the disappearance and dissolution of sunspots is not well understood. High-cadence, high-resolution magnetogram sequences are required to assess and quantify the role of small moving magnetic features, which stream out from the penumbral border and merge with the surrounding network magnetic field during sunspot dissolution (e.g. Hagenaar and Shine, 2005). While these features seem to be associated with the slow disaggregation of the sunspot magnetic bundle, only limited measurements of their individual magnetic topologies, configurations, and flux, and thus of their integrated contributions to sunspot decay, have been made (e.g. Kubo, Shimizu, and Tsuneta, 2007).

4 Flares and Eruptive Activity

Solar flares and coronal mass ejections are spectacular phenomena that are not only critical to the space-weather environment of Earth, but reflect processes ubiquitous in astrophysical plasmas. The Sun, by its proximity, allows the unique possibility of high-resolution studies of the physics of magnetic reconnection, the related acceleration of particles to relativistic energies, the heating of the plasma to more than 10 million Kelvin, and the excitation of plasma waves. Flares and mass-ejection events are a template for magnetic activity on a variety of stars, some much more active than the Sun, with implications for the habitability of exoplanets. Moreover, the underlying physical processes are common to even more energetic astrophysical events that produce relativistic jets, beams, and shocks.

The solar atmosphere is a dynamic magnetized plasma of very high electrical conductivity that can form and sustain complex current systems. When these currents abruptly reconfigure during magnetic-field reconnection events, particle acceleration and bulk plasma ejection can result. Intense electromagnetic radiation occurs when the energy of accelerated non-thermal particles or accompanying plasma waves is deposited and thermalized. Observationally, solar flares are transient bursts of electromagnetic radiation over a wide range of wavelengths, from radio to X-ray (or even shorter in some cases). Coronal mass ejections (CMEs) occur when a magnetic-flux system with substantial magnetic free energy, initially confined by overlying field, evolves so that the outward magnetic pressure-force on the trapped plasma overcome the inward magnetic-tension force of the overlying fields. The energetic flux system can then escape into interplanetary space, with the consequent expulsion of magnetized coronal plasma into the heliosphere. Subsequent flaring often occurs as the magnetic field in the wake of the coronal mass ejection relaxes back to a lower energy state. Many flares occur without CMEs, and some CMEs occur without substantial enhancement of radiative emission, but it is common for both phenomena to occur as part of a solar eruptive event.

Much of the research on solar flares and CMEs over the last decades has focused on the evolution of temperature and density structures within the corona. DKIST’s ability to regularly and systematically measure coronal magnetic fields will enable more direct evaluation of the connections between the local plasma properties, the radiative signatures of flares and CMEs, and the field evolution. The ability of DKIST to readily probe the lower solar atmosphere at very high spatial resolution will allow determination of the physical conditions deep in the atmosphere during flaring and eruptive events, and DKIST measurements of subtle changes in the intensity and topology of the photospheric magnetic fields underlying flaring regions will help in assessing the amount of magnetic energy released during these events. Spatially resolved rapid imaging and spectroscopy of the chromospheric foot points of flares will allow determination of the actual extent of the sites of flare-energy deposition, providing strong constraints on particle-acceleration mechanisms. Determination of the penetration depth of the flare disturbance into the lower atmosphere, facilitated by DKIST’s multi-wavelength capabilities, will help define the roles of proposed energy-transport mechanisms and the relative importance of waves and particle beams. Together these capabilities will elucidate the mechanisms that underly the rapid conversion and deposition of the energy stored in stressed magnetic fields during flaring and plasma-ejection events.

Several critical science topics in this research area are discussed in detail below, including i) flare and CME precursors, ii) changes in the magnetic field associated with flares and CMEs, iii) energy deposition during flares, and iv) the fundamental structure and evolution of flare ribbons.

4.1 Flare and Coronal Mass Ejection (CME) Precursors

What triggers coronal mass ejections and solar flares? What are the relative importance of mechanisms proposed, such as flux emergence, current-sheet instabilities, and small-scale flux cancellation? When, where, and how do large-scale flux ropes form?

Solar flares and coronal mass ejections result when magnetic energy stored in the solar corona is released. The release is sudden (over a few to tens of minutes) compared to the timescale over which energy is built up and stored (many hours to days, e.g. Schrijver, 2009). Despite decades of study, the physical mechanisms that trigger flares and/or CMEs remain elusive. Understanding the conditions that lead up to a CME or flare and identifying the trigger mechanisms that initiate them are central to developing the predictive capabilities necessary for successful forecasting of their space weather impacts.

While no “necessary and sufficient” conditions for flaring or CME initiation have been identified, various precursor phenomena have been reported to occur in chromospheric and coronal observations in the minutes to hours preceding flares or CMEs (for reviews see, e.g., Chen, 2011; Shibata and Magara, 2011; Green et al., 2018). In addition to possible magnetic-field and flow diagnostics (e.g. Park et al., 2018; Kontogiannis et al., 2019; Korsós et al., 2020b, discussed in Section 4.2), these include multiple small-scale brightenings in \(\text{H}\alpha \) (Martres, Soru-Escaut, and Nakagawa, 1977; Druett et al., 2017) and/or soft x-ray (e.g. Tappin, 1991), plasmoid ejection (e.g. Hudson, 1994; Kim et al., 2009), S-shaped or inverse-S (sigmoidal) soft x-ray emission (Canfield, Hudson, and McKenzie, 1999), and the slow rise and darkening of chromospheric filaments (filament activation: e.g. Martin, 1980; Schuck et al., 2004). There is also some evidence for spectral-line broadening before flares (e.g. Harra et al., 2009; Woods et al., 2017) and pre-flare thermal X-ray enhancements without evidence of non-thermal particles (Benz, Battaglia, and Güdel, 2017).

The limited spatial resolution, cadence, and wavelength coverage of many previous observations have hampered efforts to understand the physical nature of these potential precursor signals, but recent high-resolution spectropolarimetric observations with the 1.6-m Goode Solar Telescope suggest that very small-scale polarity inversions, currents, and magnetic loops in the low atmosphere are associated with the main flare initiation (Wang et al., 2017a). Magnetohydrodynamic simulations also show that the introduction of small opposite-polarity bipoles or reversed-magnetic-shear structures into a highly sheared larger-scale field can destabilize the field (e.g. Kusano et al., 2012; Muhamad et al., 2017). Reconnection between these small magnetic perturbations and the pre-existing sheared loops can result in flux-rope eruption and large-scale flaring.

Resolving these small-scale precursors is important for CME modeling. It has been known for some time that, at least in some cases, the onset of a coronal mass ejection can precede flaring by several minutes, with the CME itself coinciding with precursor indicators (e.g. Harrison et al., 1985; Harrison and Sime, 1989). This suggests that some precursors may serve as early signatures of the erupting fields. Current CME models (Toriumi and Wang, 2019) can be grouped into two broad classes: flux-rope models (Low, 1996; Lin and Forbes, 2000; Fan and Gibson, 2007), which assume that a flux rope exists before the eruption onset (Figure 5), in which case the precursors reflect the flux rope’s sudden rise, and sheared magnetic-arcade models (van Ballegooijen and Martens, 1989; Mikic and Linker, 1994; Antiochos, DeVore, and Klimchuk, 1999; Longcope and Beveridge, 2007; Karpen, Antiochos, and DeVore, 2012; Doyle et al., 2019), which postulate that the flux rope is formed during the initial stages of the flare, implying that precursor signatures are the manifestation of the flux-rope formation process itself. Not all models embrace this dichotomy, for example the flux-cancelation model (e.g. Amari et al., 2010) involves elements of both. Careful DKIST studies of small-scale precursors are critical to discriminating between these possibilities.

Figure 5
figure 5

Nonlinear force-free magnetic-field reconstruction of NOAA Active Region 9077 before the X5.7/3B (10:24 UT) flare on 14 July 2000 (SOL2004-714T1024), based on vector magnetograms taken at the Huairou Station of the Beijing Astronomical Observatory. The photospheric longitudinal magnetogram is shown in the background for reference. Field lines trace the magnetic flux-rope above the neutral line and the overlying arcade field. Axes are marked in units of arcseconds. From Yan et al. (2001), copyright by AAS.

4.2 Changes in Magnetic Field Associated with Flares and CMEs

What are the differences between the pre- and post-flare/CME magnetic-field configurations? How do the magnetic-field changes depend on height and time? What are the theoretical and practical implications of these changes? For example, how are flare emission and CME energy related to the magnetic restructuring?

Flares and coronal mass ejections are one of the most spectacular manifestations of solar activity (e.g. Webb and Howard, 2012). Flares occur when stressed magnetic fields in the low corona abruptly reconfigure, accessing a lower energy state. The rapid conversion of magnetic energy into plasma heating and bulk motion causes abrupt increase in the coronal and chromospheric active-region emission over a wide range of wavelengths. The field reconfiguration also propagates downward into the lower and denser atmospheric, with resulting changes in the photospheric magnetic field (Figure 6). This recnfiguration can be either transient or longer lived (Sudol and Harvey, 2005; Wang and Liu, 2015). Flares are often accompanied by CMEs and the onset of CMEs has been associated with flaring, although flares without CMEs and CMEs without flaring also occur (e.g. Kawabata et al., 2018, and the references therein).

Figure 6
figure 6

Photospheric magnetic-field changes associated with a flare. The initial photospheric-field vectors \({\boldsymbol{B}}_{i}\), the change in magnetic field \(\delta {\boldsymbol{B}}\), indicating coronal restructuring during the flare/CME, and final state \({\boldsymbol{B}}_{f}\). The associated change in the connectivity of the coronal field is represented by the dashed lines. The changes agree with the expectation that the photospheric field should become more horizontal. Adapted from Hudson, Fisher, and Welsch (2008).

Direct measurement of the pre-flare/pre-CME magnetic field and the post-flare/post-CME reconfigured field has both conceptual and practical importance, contributing to our understanding of the underlying reconnection processes and flare-precursor configurations (e.g. Kontogiannis et al., 2019; Korsós et al., 2020a,b). A significant open question is whether precursor signatures, such as those based on the magnetic-field helicity or gradient for example, are robust and reliable over a range flare of energies. The anticipated spatial resolution of DKIST measurements will allow fine-scale determination of these precursor properties (Section 4.1). Beyond their contribution to the possible improvement of flare and CME initiation predictions, such measurements of the underlying magnetic field play a critical role in assessing CME geo-effectiveness. While all CMEs are large plasma-containing magnetic structures expelled from the Sun, they exhibit a variety of forms. Some have the classical “three-part” structure: a bright front, interpreted as compressed plasma ahead of a flux rope, along with a dark-cavity and a bright compact core (Riley et al., 2008, and the references therein). Others display a more complex geometry or can appear as narrow jets (Webb and Howard, 2012). These forms reflect differences in internal magnetic morphologies, which subsequently determine interplanetary effects, including the formation of interplanetary shocks (an important source of solar energetic particles) and initiation of transient disturbances at Earth (upon interaction with the Earth’s magnetosphere): both components of space weather.

Direct measurement of the pre- and post-flare/CME magnetic-field morphology is very challenging. The magnetic-field changes often occur on very short time scales, and they propagate quickly through the layers of the solar atmosphere (e.g. Wang and Liu, 2015; Wang et al., 2017a; Petrie, 2019). Outside of the photosphere, low photon counts make it hard to achieve the needed sensitivity at the required cadence, and multi-wavelength full-Stokes studies are consequently difficult (Kleint, 2017). It is such studies that are, however, key to quantitative knowledge of flare and CME magnetism. While existing white-light CME observations provide information on the mass content of the CME and x-ray and EUV observations provide diagnostics of the flare and CME plasma thermal properties, regular measurements of the magnetic-field strength and orientation, at multiple heights and extending into the corona, are essential to the further development and validation of eruption models. These require DKIST capabilities.

Importantly, DKIST on-disk, limb, and off-limb capabilities will allow quantitative assessment of the relationship between plasma-sheet observations and reconnection current-sheet properties. Current sheets are an important component of most solar-flare models. They are an essential element of post-CME flaring, and thin off-limb high-density high-temperature plasma structures, suggestive of current sheets, are observed above limb flares following eruptions (e.g. Savage et al., 2010; Liu, 2013; Seaton, Bartz, and Darnel, 2017). Spectroscopic observations have led to detailed understanding of the plasma properties within these structures (Li et al., 2018; Warren et al., 2018), with implications for the underlying reconnection and field-reconfiguration processes (Longcope et al., 2018). Direct measurements, using DKIST instrumentation, of the magnetic field in and around these plasma sheets will allow more accurate assessments of the amount of flux opened by an eruption, better understanding of the evolution of the post-eruption field, and clarification of the mechanisms underlying the slow (sub-Alfvénic) outflows observed during flare-reconnection events (e.g. Wang et al., 2017b, and the references therein).

The DKIST instrument suite will enable regular multi-wavelength spectropolarimetric measurements at high temporal cadence and spatial resolution in the solar photosphere, chromosphere and low corona. These will allow assessment of the local magnetic-field properties, and determination of flare- and CME-induced changes in that field, simultaneously over several heights in the solar atmosphere. When coupled to x-ray and EUV/UV observations from available and future space observatories, DKIST will, for the first time, allow us to directly connect coronal magnetic-field evolution to flare and CME emission and plasma properties. It will enable the careful measurement of the magnetic-field reconfiguration that occurs at the origin of space-weather events.

4.3 Energy Deposition During Flares

Waves or beams? How is flare energy transported from the corona to the chromosphere? Where are the non-thermal particles produced? What is the origin of the flare optical continuum? How compact are flare kernels? What explains the large widths of chromospheric flare emission lines?

Flare energy, liberated in the corona, is transported to and dissipated in the chromosphere and upper photosphere, resulting in localized heating and intense bursts of radiation across the electromagnetic spectrum. This leads to chromospheric expansion and drives mass motions, upward-moving chromospheric “evaporation”, and downward-flowing “condensation”. In some locations, hard x-ray (HXR) bremsstrahlung emission is observed, revealing the presence of non-thermal electrons containing a significant fraction of the total flare energy. Ultimately, the majority of a solar flare’s radiated energy is emitted in near-UV and optical lines and continua (e.g. Woods et al., 2004), and these provide rich diagnostics of the energy transport and deposition processes (Figure 7).

Figure 7
figure 7

Optical flare ribbons at the time of the hard x-ray peak (X6.5, S06E63, SOL2006-12-06T18:43:38.5). (aHinode/SOT G-band, (b) the same image as (a) after pre-flare subtraction, (c) TRACE 160 nm image taken nearly simultaneously, and (d) through (f) RHESSI contours (levels 15, 30, 45, 60, 75, and 90 percent of the peak flux) in the 25 – 100 keV range for 4-, 8-, and 16-second temporal integrations, respectively. From Krucker et al. (2011), copyright by AAS.

One of the longest-standing and most-important questions in flare physics is the origin of the optical continuum, which was first observed during the famous Carrington–Hodgson flare of 1859 and generally accounts for a large fraction of the total flare emission (Neidig, 1989). There are two primary candidates (e.g. Heinzel et al., 2017): the optical component of an enhanced black body (photospheric \(\text{H}^{-}\) continuum enhancement) or hydrogen-recombination continuum (Paschen and Balmer). It is difficult to disentangle these two contributions (Kerr and Fletcher, 2014), but doing so would allow flare-energy transport and deposition-height discrimination since the former implies penetration of a significant amount of energy down into the photosphere while the latter carries information about evolution of the ionization state higher up in the chromosphere. Understanding the relative contribution of these would significantly constrain the transport mechanisms. Moreover, as the continuum emission carries away a large fraction of the flare energy, making it unavailable to drive a dynamical response, determining its origin is relevant to understanding why some flares are important acoustic sources while others are not (Lindsey et al., 2014).

High-temporal-cadence high-spatial-resolution observations will help to distinguish these processes (Hudson, Wolfson, and Metcalf, 2006; Xu et al., 2006; Fletcher et al., 2007; Martínez Oliveros et al., 2011, 2012; Kleint et al., 2016; Yurchyshyn et al., 2017). The standard flare model suggests that flare energy is transported from the corona to the chromosphere by beams of non-thermal electrons. If this is correct, the only way to significantly heat the photosphere is by reprocessing the electron-beam energy via back-warming by Balmer and Paschen continuum radiation originating in the mid to high chromosphere (Allred et al., 2005). Radiation-hydrodynamical models can predict the light curves of Balmer and Paschen continua consistent with the temporal evolution of the electron-beam energy deposition (Heinzel and Kleint, 2014; Kowalski et al., 2015). Of particular importance are observations near the Paschen limit. While the Balmer limit is not observable with the DKIST, the Paschen limit (820.5 nm) is, and, as with the Balmer limit (Kowalski et al., 2017a), observations of Paschen line broadening near the Paschen limit and the presence or absence of a continuum jump there (Neidig and Wiborg, 1984) can constrain the charge density and optical depth of the flaring solar chromosphere (Kowalski et al., 2015). Achieving high spatial resolution and spectral resolution is critical because unequivocal evidence for small, dense chromospheric condensations during the impulsive phase of solar flares has been established (Kowalski et al., 2017b), and these sites of intense localized heating are likely key to the interpretation of flare spectra.

While the standard flare model invokes energy transported from the corona to the chromosphere by beams of non-thermal electrons, the dominant energy transport mechanism is still under debate. Chromospheric heating to megaKelvin temperatures can start before observable HXR emission begins (Fletcher et al., 2013), and the apparent low height of HXR and optical sources during limb flares appears inconsistent with the expected penetration depths of accelerated electrons (Hudson, Wolfson, and Metcalf, 2006; Krucker et al., 2010; Martínez Oliveros et al., 2012). Moreover, the electron-beam densities implied by the HXR intensities observed suggest that a very large fraction of the pre-flare coronal thermal-electron population is accelerated (Krucker et al., 2010; Fletcher et al., 2013; Krucker and Battaglia, 2014), so it is unclear whether the electron-beam requirements can be met at coronal densities. Finally, issues involving the origin, amplitude, and stability of the return currents required to support these dense coronal beams are not fully resolved (Alaoui and Holman, 2017). Together these considerations suggest that additional modes of energy transport may be required, as do very recent modeling results indicating that electron beams are incapable of producing coronal rain, which is often found shortly after the onset of loop flares (Reep, Antolin, and Bradshaw, 2020). Proposed additional transport mechanisms include ion beams (Hurford et al., 2006; Zharkova and Zharkov, 2007), heat conduction (Longcope, 2014; Graham, Fletcher, and Labrosse, 2015; Longcope, Qiu, and Brewer, 2016), and Alfvén waves (Russell and Fletcher, 2013; Reep and Russell, 2016; Reep et al., 2018). Each results in different energy-deposition rates as a function of height in the solar chromosphere, influencing the local atmospheric properties (e.g. Kerr et al., 2016) such as temperature, density, bulk and turbulent velocities, ionization fractions, and atomic-level populations as a function of time, and thus in turn each has a potentially unique spectral evolution signatures. Multi-height DKIST observations, hand-in-hand with advanced radiation hydrodynamics simulations, will be critical to using those signatures to differentiate between the proposed energy transport and deposition mechanisms.

4.4 The Fundamental Structure and Evolution of Flare Ribbons

What is the mapping between the evolution of a flare ribbon and the reconnection process? What does flare-ribbon evolution tell us about changes in the overlying three-dimensional field and the particle-acceleration and heating processes?

Flare ribbons are localized, elongated brightenings in the chromosphere and photosphere. They are the sites of energy deposition at the foot points of the magnetic loops involved in flare reconnection. The brightening, due to the increased temperature of the flaring chromospheric plasma, is believed to be primarily due to collisional heating by flare-accelerated non-thermal electrons, although questions about the viability of this mechanism remain (Section 4.3 above). The brightest parts of a flare ribbon can be subject to localized heating of \(10^{12}~\text{ergs}\,\text{cm}^{-2}\,\text{s}^{-1}\) (Krucker et al., 2011), on the order of 100,000 times the energy flux required to heat the quiet solar chromosphere. The detailed structure and evolution of flare ribbons can provide insight into the fundamental length and time scales of flare-energy deposition and the link between particle acceleration and the evolving coronal magnetic field.

Flare ribbons occur in pairs that show a characteristic temporal evolution, reflecting changes in the overlying magnetic field. Conjugate ribbons separate in time, mapping out the progress of coronal magnetic reconnection. When observed simultaneously with the photospheric or chromospheric magnetic field, the motions of ribbons as a whole, and of the individual sources composing them, can be used to obtain the coronal magnetic-reconnection rate (Isobe et al., 2002; Qiu et al., 2002; Fletcher, 2009; Liu et al., 2018). Distinct brightenings are often observed to run along the ribbons, and have been linked to properties of three-dimensional “slip-running” reconnection (Dudík et al., 2014). Moreover, since the evolution of the flare ribbon reflects changes in the large-scale coronal magnetic field, careful observations can inform our understanding of the dynamics of eruptive (CME) events (e.g. Sun et al., 2017; Hinterreiter et al., 2018).

At small scales, flare ribbons show significant substructure (Figure 8), which on arcsecond scales is well aligned with regions of high vertical photospheric current density (Janvier et al., 2014). These numerous small-scale emission sources appear differently at different wavelengths, reflecting structured energy deposition. In line cores, flare ribbons appear stranded, as if a small portion of numerous magnetic loop tops in the chromosphere are illuminated (e.g. Mikuła et al., 2017). In the visible and infrared continua or in the far wings of spectral lines, individual sources are very compact with clear evidence for sub-arcsecond (100 km) structure, suggesting very small scales for individual flaring loops or current dissipation sites (Sharykin and Kosovichev, 2014; Jing et al., 2016). The sizes of the sources vary with wavelength, and this has been interpreted as being due to the narrowing with depth of the chromospheric magnetic-flux tube along which energy is being deposited (Xu et al., 2012). Additionally, individual source sites display a “core–halo” continuum-intensity substructure (Neidig et al., 1993; Hudson, Wolfson, and Metcalf, 2006; Xu et al., 2006; Isobe et al., 2007). This may be a signature of spatially varying heating across the magnetic structures or of two heating components: direct heating by energetic particles in the core and indirect heating by radiative back-warming in the halo (Neidig et al., 1993; Xu et al., 2006).

Figure 8
figure 8

Image of a flare ribbon taken with the 1.6 m Goode Solar Telescope’s Visible Imaging Spectrometer (VIS), \(+0.1~\mbox{nm}\) off-band the \(\text{H}\alpha\) 656.3 nm line center (0.007 nm band pass), showing the ribbon crossing sunspots, coronal rain in the post-flare loops, and fine-scale brightenings at the foot points of the falling plasma in the chromosphere. From Jing et al. (2016).

Flare kernels are the very brightest of these sources in flare ribbons, and they are the locations most clearly associated with the strong hard X-ray emission generated by non-thermal electrons. In the very earliest stages of a flare, flare kernels can expand significantly on timescales less than one second (Xu et al., 2010), possibly as a result of reconnection spreading through a highly stressed region of the coronal magnetic field. As discussed above, flare ribbons themselves also spatially propagate as the site of reconnection changes. At the leading edge of a propagating ribbon, sites of particularly large Doppler line broadening are observed (Jing et al., 2016; Panos et al., 2018), suggesting that the strongest energy input into the lower chromosphere and photosphere occurs at the locations of the most recently reconnected field. DKIST’s aperture and adaptive-optics capabilities will enable regular sub-arcsecond measurements of the underlying spatial and temporal correlations, the height-dependent flows, and the evolving kernel substructure, to determine the flare energy flux into the solar chromosphere and the fundamental scales at which discrete coronal reconnection occurs (Xu et al., 2012; Graham and Cauzzi, 2015).

Moreover, the DKIST-VISP spectral bandpass will be wide enough to measure the exceptionally strong shock fronts that can accompany large flares. The magnitude of the observed Doppler red shifts in current observations of C-class solar flare ribbons (such as those obtained with CRisp Imaging Spectro-Polarimeter (Scharmer et al., 2008) on the 1 m Swedish Solar Telescope (Scharmer et al., 2003)) can exceed 0.1 nm relative to the \(\text{H}\alpha \) line center (Druett et al., 2017). These large red shifts are attributed to the development of a shock fronts in the upper chromosphere that propagate downwards towards the photosphere with velocities up to \(50~\text{km}\,\text{s}^{-1}\) soon after flare onset and electron-beam injection. Supporting models of \(\text{H}\alpha \) line formation indicate that stronger flares yield even stronger shock fronts with even greater Doppler red shifts, up to 0.4 nm, not yet observed with modern instruments. DKIST’s ability to capture these larger red shifts within the VISP spectral band pass will contribute significantly to a detailed understanding of solar-flare electron-beam properties and how they scale with flare energy.

5 Magnetic Connectivity Through the Non-eruptive Solar Atmosphere

The solar magnetic field extends from the solar interior, across the photosphere, through the chromosphere and transition region, and into the corona, permeating the entire volume and out into the heliosphere. Plasma motions in the solar convective envelope produce a highly structured photospheric magnetic-field distribution, which can be considered the boundary condition for the magnetic field above. As the photospheric boundary field evolves, the field above must reconfigure, and, because the atmosphere extends over many scale heights, the energetics and dynamics of the response are diverse and multi-scaled. A central goal of the DKIST science mission is a quantitative understanding of the complex interplay between flows, radiation, heat conduction, wave propagation and dissipation, and reconnection in the solar atmosphere. This understanding is critical to the resolution of long-standing problems in solar and stellar astrophysics such as chromospheric and coronal heating, the origin and acceleration of the solar wind, and the propagation of magnetic disturbances into the heliosphere.

Understanding the complex, connected solar atmosphere, with its widely varying ionized and partially ionized plasma regimes, requires diverse, flexible, and multi-spectral-line polarimetric instrumentation capable of simultaneously probing many heights at high temporal cadence and over small spatial length scales. DKIST is at the forefront of these observational challenges. Its new capabilities in high-precision spectropolarimetry will allow the inference of magnetic-field properties with spatial and temporal resolutions never before achieved. Those inferences will depend on advanced and challenging inversions. For example, while the distribution of solar photospheric magnetic fields has been routinely measured since the invention of the Zeeman-effect-based magnetograph, measurement of the chromospheric field and its connections to the upper solar atmosphere requires interpretation of spectral lines formed under conditions of non-local thermodynamic equilibrium (NLTE) in which both Zeeman and atomic-level polarization processes are important. DKIST aims to facilitate these with chromospheric data of unprecedented precision.

DKIST is also at the forefront of coronal spectropolarimetry. Extrapolation of the magnetic field into the solar corona is inherently limited by assumptions about the distribution of currents in the magnetized volume. To advance our understanding of, for example, the available free magnetic energy driving solar flares and eruptions, remote sensing of the magnetic field in the corona itself is necessary. DKIST, as the world’s largest coronagraphic polarimeter, will allow the measurement of the full Stokes spectra of the forbidden magnetic-dipole emission lines of highly ionized metals in the corona. These can be used to determine the topology and evolution of the coronal field and, along with DKIST chromospheric diagnostics, its connectivity to the lower atmosphere.

Several critical science topics in this research area are discussed in detail below, including i) the mass and energy cycle in the low solar atmosphere, ii) the origin and acceleration of the solar wind, iii) magnetic reconnection throughout the solar atmosphere, iv) waves in the solar atmosphere, v) impact of flux emergence on the non-eruptive solar atmosphere, vi) multilayer magnetometry, and vii) large-scale magnetic topology, helicity, and structures.

5.1 Mass and Energy Cycle in Low Solar Atmosphere

How important are spicules and other jet-like phenomena to the chromosphere–corona mass cycle? What is the role of spicule heating in the coronal energy balance? Can we characterize and model the coronal-rain phenomenon well enough to understand its role as a return flow?

All coronal plasma has its origins in the lower solar atmosphere, with the coronal mass budget determined by a balance between upward flows (evaporative or eruptive), downward mass transport (e.g. coronal rain), and solar-wind losses. One of the key outstanding challenges to furthering our understanding of the solar atmosphere is determining which of many process that appear to be involved dominates the transfer of mass between the cool chromosphere and hot corona in regions of differing magnetic topology. Previous observations have provided a partial view of the mass cycle, but the small spatial and temporal scales involved have significantly hindered advancement. DKIST will provide a more complete view, especially when combined with coordinated observations using space-based observatories, such as IRIS, Hinode, and Solar Orbiter, or the ground-based radio telescope array ALMA (Atacama Large Millimeter/sub-millimeter Array), which allows complementary temperature and soon polarization diagnostics of the solar chromosphere (see Yokoyama et al., 2018).

Jets play an important role in the chromosphere–corona mass cycle. They are observed to have a wide range of spatial scales, from spicules with widths of a few hundred kilometers, to larger chromospheric jets with widths of \(\approx 1000~\mbox{km}\), to coronal jets with widths of a few thousand kilometers. Recent observations show that some jets are driven by the eruption of a small-scale flux ropes (Sterling et al., 2015) triggered by flux cancelation at the magnetic neutral line (Panesar et al., 2016, 2018; Panesar, Sterling, and Moore, 2017), but the full range of magnetic-field reconfiguration scenarios that lead to the jets observed is not known. DKIST’s spectropolarimetric capabilities will significantly contribute to our understanding of jet initiation, allowing us to better quantify how effectively each jet type injects plasma into the solar atmosphere.

Spicules appear to be the most ubiquitous jet-like feature in the solar chromosphere (Figure 9). They are highly dynamic, vary on time scales of 10 – 30 seconds, and are finely structured, with widths \(<300~\mbox{km}\) and substructure at scales below that. Spicules transport plasma upwards into the solar atmosphere at speeds of \(10\,\text{--}\,200~\text{km}\,\text{s}^{-1}\) and may, either alone (De Pontieu et al., 2011) or in combination with other slower jets (e.g. Morton et al., 2012), play a significant role in the mass and energy balance of the corona and solar wind. Yet, despite having been observed over a wide range of wavelengths from EUV to visible, we do not understand the mechanisms responsible for spicule formation, how they are heated, often to transition-region temperatures or higher (Pereira et al., 2014; Henriques et al., 2016; Samanta et al., 2019), the role that hydromagnetic waves play in their dynamic evolution, or their full impact on the mass and energy balance of the outer solar atmosphere (Pereira, 2019). That coronal signatures of spicules have been observed at the smallest scales above both active regions (De Pontieu et al., 2011) and the quiet Sun (Henriques et al., 2016) suggests that they may play a global role as heat and mass conduits between the chromosphere and corona, but our understanding of their importance is limited by current instrumentation capabilities. Spicule-induced mass transport to coronal heights is estimated by some authors to be two orders of magnitude larger than the solar-wind mass flux (Beckers, 1968; Sterling, 2000), but others suggest that the role of spicules in the mass cycle is rather limited compared to that of more uniform chromospheric evaporation due to small-scale flaring processes (e.g. Klimchuk, 2012). In fact, there is still some debate about the fundamental nature of spicules, whether only one or multiple spicule types exist (De Pontieu et al., 2007a; Zhang et al., 2012, but see Pereira, De Pontieu, and Carlsson, 2012), or whether they are indeed jets of accelerated plasma, with an alternative suggestion that the apparent upward motions are due instead to line-of-sight integration through evolving warped two-dimensional magnetic sheet-like structures (Judge, Tritschler, and Low, 2011; Judge, Reardon, and Cauzzi, 2012; Lipartito et al., 2014).

Figure 9
figure 9

Simultaneous images of spicules in Ca ii H \(396.8~\text{nm}\) (Hinode), C ii \(133.0~\text{nm}\) and Si iv \(140.0~\text{nm}\) (IRIS), and He ii \(30.4~\text{nm}\) (SDO/AIA). Future coordinated observations with DKIST, ALMA, and other observatories are key to addressing unresolved questions about spicule heating and their role in the mass and energy balance of the transition region and corona. Image from Skogsrud et al. (2015). Reproduced with permission; copyright 2015 American Astronomical Society.

DKIST observations, employing a wide range of chromospheric spectral lines, will provide revolutionary new views of the fine-scale structure, magnetic and electric fields (Anan, Casini, and Ichimoto, 2014) within, and thermodynamic evolution of, spicules and other chromospheric jets. DKIST will be able to capture the dynamic evolution of jets at high cadence (\(\lesssim 3~\text{seconds}\)) and make simultaneous measurements (with \(\lesssim 15\)-second cadence) of the chromospheric and photospheric magnetic fields and flows that underlie jet initiation and acceleration. Together these will help clarify issues such as the relationship between jet initiation and the apparently ubiquitous Alfvén pulses that are excited by swirling motions in the solar photosphere (Goodman, 2012; Liu et al., 2019a,b) and the roles and relative importances of processes such as reconnection (Section 5.3 below), magnetic tension amplification by ion–neutral coupling (Martínez-Sykora et al., 2017), micro-filament eruption (Sterling and Moore, 2016), and other small-scale processes.

As already indicated, some have suggested that, while jet-like features are perhaps the most prominent, they may not be the most important component of the chromosphere–corona mass cycle, that more gentle processes play an important, even dominant, role. One sensitive signature of mass transport, momentum flux, and wave heating is the degree of elemental fractionation, i.e. the degree to which elements of low (lower than about 10 eV) first ionization potential (FIP) are enriched or depleted compared to other elements (the FIP or inverse-FIP effects: Meyer, 1985a,b; Feldman, 1992; Feldman and Laming, 2000; Laming, 2015). Because FIP fractionation is sensitive to the thermodynamic and electromagnetic plasma environment, it depends on the atmospheric height of the region being considered, the magnetic-field geometry (open or closed) and connectivity, the heating mechanisms at play, the bulk plasma flow speed, and the dominant magnetohydrodynamic (MHD) wave modes present (Laming, 2015). In fact, spicules themselves may be responsible for the absence of the FIP effect at temperatures below \(10^{6}~\text{K}\) on the Sun (Laming, 2015, and the references therein). These sensitivities, when understood well, allow FIP fractionation measurements to be used to constrain the solar-wind source region and thus the origin of plasma sampled during in-situ heliospheric measurements (e.g. Geiss, Gloeckler, and von Steiger, 1995; Parenti et al., 2000; Brooks and Warren, 2011; Brooks, Ugarte-Urra, and Warren, 2015; Baker et al., 2015). Coordinated observations (Section 6.5), combining chromospheric measurements by DKIST with in-situ measurements of the heliospheric plasma properties by Solar Orbiter and Parker Solar Probe, will allow unprecedented identification and characterization of the sources of the fast and slow solar wind.

Another key aspect of the chromosphere–corona mass cycle is the return flow from the corona to the lower atmosphere. One component of this is prominently visible at the solar limb as coronal rain: a finely structured and multi-thermal flow that appears to be driven by cooling instabilities (e.g. Antolin and Rouppe van der Voort, 2012; Antolin et al., 2015b; Mason, Antiochos, and Viall, 2019, and the references therein). The descending material is visible in the off-limb active corona at transition-region and chromospheric temperatures, and can be observed in what are typically chromospheric optical spectral lines (Kawaguchi, 1970; Schrijver, 2001; Antolin, Shibata, and Vissers, 2010). Current observations are unable to fully resolve coronal rain: the peak of the coronal-rain element-width distribution remains unresolved (Scullion et al., 2014). Thus we do not yet have a full accounting of the total rain drainage rate. Measurements of loop oscillations can be used to determine the thermally unstable mass fraction in a coronal-loop system and thus provide further constraint on that rate. Since coronal-rain condensations are coupled to the magnetic-field lines they track the oscillatory motion of the loops (Kohutova and Verwichte, 2016) and the evolution of the oscillations can be used to deduce the fraction of the loop plasma mass that becomes thermally unstable and drains with time. This seismic estimation provides more than a consistency check on the drainage rate because it also allows measurement of the unresolved coronal-rain mass fraction (Froment et al., 2018), which in turn constrains the fundamental spatial scales of the rain and the fine-scale structure of coronal loops. DKIST observations will push these inferences even further.

One-dimensional hydrodynamic loop models (Mendoza-Briceño, Erdélyi, and Sigalotti, 2002; Müller, Hansteen, and Peter, 2003; Mendoza-Briceño, Sigalotti, and Erdélyi, 2005) produce catastrophic cooling events that generate intermittent and repeating rain-like downflows even when steady, exponentially decaying with height, foot-point concentrated heating is employed. Similarly, 2.5-dimensional and recent three-dimensional simulations form fine-scaled localized rain elements even when a spatially smooth but localized foot-point concentrated heating function is applied (Fang, Xia, and Keppens, 2013; Moschou et al., 2015). These numerical studies, along with observational evidence for foot-point concentrated heating in active regions (Aschwanden, 2001), suggest that studies of coronal rain are important, not just in the context of the mass cycle, but also in constraining heating mechanisms. The statistical properties of the rain depend on the spatial distribution of the heating because the heating location influences the thermal stability of the plasma in a coronal-loop system (Antolin, Shibata, and Vissers, 2010).

Observational contributions to our understanding of coronal rain depend on leveraging the high-resolution and multi-wavelength capabilities of DKIST to unravel its evolving, complex, multi-thermal behavior. With a mix of hot (ionized) and cold (neutral) gas, coronal rain is an ideal context within which to study ion–neutral interaction effects, such as ambipolar diffusion, that are expected to play key roles more broadly in the dynamics of the partially ionized chromosphere. But the rain’s thermal state is complex and difficult to characterize. Hydrogen is likely out of ionization equilibrium and other elemental ionization ratios are poorly constrained (Antolin, Shibata, and Vissers, 2010; Antolin et al., 2015b). DKIST will also be able to provide spectropolarimetric measurements from which the vector magnetic field within rain-producing loop systems can be inferred. Such inferences are fundamental in characterizing the underlying flow instabilities (e.g. Martínez-Gómez et al., 2020), but they will require careful theoretical underpinning. Recent studies have been able to exploit the Zeeman effect in the Ca ii 854.2 nm chromospheric line to assess the presence of strong fields (100 – 300 G) in bright post-flare loops systems (Kuridze et al., 2019), but this approach may be difficult in more quiescent cases, which are characterized by much weaker fields and lower photon counts. Significant progress may be possible if Hanle diagnostics in lines of neutral Helium such as the He i 1083 and 587.6 nm multiplets are employed (Schad, 2018), and polarimetric observations of these two He i multiplets with DKIST may provide the first view of sub-arcsecond scale weak magnetic fields (with sensitivity of a few Gauss) in quiescent loop systems.

5.2 Coronal Heating, Solar Wind Origin and Acceleration

Waves or nanoflares? What are the relative importances of different proposed coronal-heating mechanisms? What are the solar-wind momentum sources? What role does the chromosphere play in coronal heating?

The steep transition from the cool chromosphere to the million-degree and higher corona is the direct result of the cooling catastrophe that results when hydrogen in the solar atmosphere becomes fully ionized so that radiative recombination can no longer cool the optically thin plasma (Woods, Holzer, and MacGregor, 1990a,b). The plasma temperature climbs high enough so that electron conduction back down to the chromosphere, and resulting radiative losses from there, are sufficient to balance the heating above. Solving the coronal-heating problem requires identifying the heat source, which in the statistically steady state balances thermal conduction to the chromosphere and any other smaller direct energy losses from the corona by radiation or advection. Significant progress has been made in the last decades, and it is now apparent that no single heating mechanism is likely universally dominant (e.g. Kuperus, Ionson, and Spicer, 1981; Zirker, 1993; Klimchuk, 2006; Erdélyi and Ballai, 2007; Parnell and De Moortel, 2012; De Moortel and Browning, 2015). The importance of mechanisms such as reconnection, MHD or plasma-wave dissipation, or turbulent dissipation likely vary depending on coronal conditions, particularly the magnetic-field configuration. Moreover, the mechanisms are highly intertwined and interdependent; dissipation of current sheets can produce waves and waves in magnetically structured media can induce current sheets (e.g. Velli et al., 2015), and observations indicate that even on very large scales eruptive flares can trigger oscillations in coronal loops and filament oscillations can induce eruption (e.g. Jess et al., 2015; Russell, Simões, and Fletcher, 2015, and the references therein) and associated flaring. Turbulence is similarly likely ubiquitous, and theoretical work suggests an important role for Alfvén-wave induced turbulence (e.g. van Ballegooijen et al., 2011; Asgari-Targhi et al., 2013; van der Holst et al., 2014).

Thus, while a number of general properties of coronal heating (e.g. De Moortel and Browning, 2015) have been observationally established (that coronal heating is unsteady and impulsive, that coronal magnetic fields store energy that can be dissipated via reconnection, that the corona supports a rich wave field, and that the corona can only be understood in conjunction with its coupling to the chromosphere) details are less certain (e.g. Klimchuk, 2015; Schmelz and Winebarger, 2015). Questions remaining include: What is the relative importance of different heating mechanisms? Do current sheets in the corona play an important role in heating, and if so what plasma processes are involved in their dissipation? What is the fundamental scale of the substructure in multi-thermal coronal loops, and what processes determine this? During small-scale reconnection events, how much energy is dissipated directly, how much is radiated as waves, and how much goes into acceleration of non-thermal electrons (Testa et al., 2014)? How does magnetic reconnection heat the plasma (Longcope and Tarr, 2015)? How and where are the ubiquitous MHD waves in the corona dissipated (e.g. Poedts, 2002; Gupta, 2017)? How far out in the solar wind does heating extend (Martinović, Klein, and Bourouaine, 2019, and the references therein)? What are the characteristic scales and magnitudes of the heating events? What triggers them?

DKIST will be fundamental in answering these questions because it will enable careful, repeated, and frequent measurements of the plasma properties of the inner corona, including the local magnetic-field strength and direction, at multiple heights. These will facilitate the quantitative evaluation of suggested heating processes in varying magnetic environments. Measurement of the line–continuum and line–line intensity ratios of ionic species, such as Fe ix to xv, that are also found in in-situ measurements of the fast and slow solar wind, will allow determination of the electron-density, temperature, and charge-state evolution of the solar-wind plasma, informing our understanding of the acceleration and heating processes (Figure 10, Landi et al., 2012; Landi, Habbal, and Tomczyk, 2016; Boe et al., 2018). Comparison between observations and theoretical studies of fast and slow magneto-acoustic wave-mode conversion, shock formation, and dissipation (e.g. Zhugzhda, Bromm, and Ulmschneider, 1995; Carlsson and Stein, 1997) will help constrain the role of these processes as a function of height in the chromosphere. For example, in models, high-frequency (\(>10~\text{mHz}\)) propagating acoustic waves develop into radiatively damped weak shocks within the first few hundred kilometers above the photosphere (Carlsson and Stein, 2002) while lower-frequency waves (\(\approx4\,\text{--}\,10~\text{mHz}\)) develop into strong shocks in the chromosphere (above 1 Mm) where radiative damping is less effective (Priest, 2000). Multi-height DKIST observations will allow careful measurement of this frequency dependence in regions of differing magnetic-field configurations and thus an assessment of wave-energy deposition with height. Moreover, previous high-resolution observational work has reported evidence for shock-induced turbulence (Reardon et al., 2008), and such turbulence may provide a mechanism for the dispersal of the wave energy beyond the local shock region itself. Turbulence may also play a direct role in wave-mode conversion, coupling the compressive motions to Alfvénic fluctuations which can continue to propagate outward, transmitting energy to higher layers of the solar atmosphere. Alternatively, counter-propagating Alfvén waves may nonlinearly interact to produce MHD turbulence, dissipating the waves, and heating the plasma (van Ballegooijen et al., 2011). DKIST observations can differentiate between these processes in the solar atmosphere and determine their occurrence frequency.

Figure 10
figure 10

Hinode/EIS line-width measurements in an off-disk coronal hole as a function of height (left, from Hahn, Landi, and Savin, 2012). The decrease in width with distance off-limb beyond \(1.1~{\mathrm{R}}_{ \odot }\) suggests wave damping. Mg ix 70.6 nm off-disk line intensity in a polar coronal hole (right, from Landi et al., 2012). Measurements from SOHO/SUMER, with model estimates assuming ionization equilibrium shown in blue and those when employing non-equilibrium ion fractions in red. Image from Skogsrud et al. (2015), copyright by AAS (left, from Hahn, Landi, and Savin, 2012, copyright by AAS)/(right, from Landi et al., 2012, copyright by AAS).

Further, even though direct observation of individual nanoflare heating events lies beyond the capabilities of DKIST, DKIST observations will help distinguish between specific reconnection heating mechanisms. Heating models based on flux cancelation have been previously motivated by high-resolution Imaging Magnetograph eXperiment (IMAX) data from Sunrise (Priest, Chitta, and Syntelis, 2018) and heating events in simulations of three-dimensional kink-unstable flux ropes may be diagnosable using DKIST coronal lines (Snow et al., 2018). With DKIST, high-resolution chromospheric observations of intensity fluctuations and motions at the foot points of hot coronal loops should reveal key telltale signatures of nanoflares in the overlying corona (Testa et al., 2014). When coupled with radiative-hydrodynamic modeling (e.g. Kerr et al., 2016; Polito et al., 2018), such observations may be able to constrain the properties of the non-thermal particles or waves generated at nanoflare sites. Finally, although the details are uncertain, it has been suggested that the chromosphere may play an important role in coronal heating (e.g. Withbroe and Noyes, 1977; Sturrock, 1999; De Pontieu et al., 2017) since chromospheric plasma can be heated to transition-region temperatures and higher and be carried via jets to coronal heights. If so, the jet studies outlined in Section 5.1 are very relevant to this research topic as well.

The hot, outer solar corona escapes the Sun as the solar wind. The solar wind carries plasma out into the heliosphere, where it interactions with the planetary space environments and importantly influences CME arrival times and geo-effectiveness, yet there is no consensus understanding of where the solar wind originates or how it is accelerated. The fast solar wind and slow solar wind have different physical properties (e.g. Feldman, Landi, and Schwadron, 2005; Ebert et al., 2009), likely come from different source regions, and are possibly subject to different acceleration mechanisms. The fast wind originates in coronal holes, but how the detailed properties of the field and plasma within a coronal hole lead to the observed properties of the wind is not clear. For example, additional sources of momentum, beyond Parker’s original gas-pressure gradient mechanism (Parker, 1958, 1963), are required for the plasma to reach the observed fast-wind speeds. Possible momentum sources included large-amplitude MHD waves (Alazraki and Couturier, 1971; Jacques, 1977; De Pontieu et al., 2007b; Thurgood, Morton, and McLaughlin, 2014), Type-II spicules (e.g. De Pontieu et al., 2009; Moore et al., 2011), resonant interactions with ion-cyclotron waves (Hollweg and Isenberg, 2002), and others (e.g. Cranmer and Winebarger, 2019, and the references therein), but these are to date poorly constrained by observations. Similarly, the slow wind has variously been proposed to originate from the edges of coronal holes, closed–open field boundaries within and bordering active regions, streamers (particularly streamer tops), or small coronal holes, but while these locations are all associated with magnetic reconnection between closed magnetic flux systems and open ones that connect to the wind, there is no consensus on the dominant underlying field configuration or acceleration mechanism (e.g. Feldman, Landi, and Schwadron, 2005; Cranmer, 2009). In fact, some of the observed differences between the fast and slow solar winds may have more to do with the expansion properties of the background magnetic fields along which they are streaming than with differences between their source regions (Wang and Sheeley, 2003).

The solar wind can be studied using either remote-sensing or in-situ techniques. In-situ measurements typically provide direct information on plasma properties only after the plasma has undergone much of its evolution, although Parker Solar Probe (PSP) is revolutionizing these measurements, aiming to sample, during its closest perihelia, regions of solar-wind heating and acceleration directly (e.g. Venzmer and Bothmer, 2018). Remote-sensing observations, on the other hand, allow frequent multi-wavelength measurements of the solar-wind source regions, but can be difficult to interpret. Combining these types of measurements (Landi et al., 2012) is already yielding exciting results in the current early-PSP era (Rouillard et al., 2020). DKIST will make significant contributions to these efforts (Section 6.5). Regular off-disk coronal measurements of the magnetic field and the plasma properties will characterize the solar wind as it emerges from its source up to a height of 0.5 solar radii above the limb. Since the visible and infrared spectral lines observed by DKIST largely result from photoexcitation, their intensities decrease more slowly with height (closer to being in proportion to the electron density rather than its square) than do those of EUV spectral lines, which result largely from collisional excitation (e.g. Landi, Habbal, and Tomczyk, 2016; Del Zanna and DeLuca, 2018). This makes plasma and magnetic-field diagnostics to the outer edge of the DKIST coronal field of view possible. Importantly, lower down, in the chromosphere and low transition region, where current space-based EUV observational efforts are focused, DKIST will enable inference of the vector magnetic field via their spectropolarimetric signatures in lines such as He i 1083.0 nm.

DKIST’s capabilities in combination with those of IRIS and Hinode will facilitate studies of solar-wind acceleration physics from the chromosphere through transition region and into the corona. Through coordinated efforts, these observatories will be able to address critical issues such as how the physical properties of the solar wind change with height, how that profile depends on position from the center to the edge of coronal holes, what defines coronal-hole–streamer boundaries, and how does reconnection at the boundary between closed and adjacent open field in active regions yield the observed wind properties. Plasma diagnostics will allow estimates of the mass and energy flow along magnetic-field lines, and coronal line-width studies will help in understanding wave propagation and damping (Hahn, Landi, and Savin, 2012). Combining magnetic-field, electron-density, and temperature measurements will make possible charge-state evolution modeling of the accelerating solar wind and aid in the development of empirical models of the solar-wind speed between 1 and \(1.5~{\mathrm{R}}_{\odot }\) (Landi et al., 2012). Extrapolation to the freeze-in height, with field extrapolations no longer strictly dependent on the photospheric field, will provide further links to in-situ instrumentation on PSP, SO, and Advanced Composition Explorer (ACE) and constrain the solar-wind source locations (Section 6.5).

5.3 Magnetic Reconnection in the Solar Atmosphere

What is the three-dimensional geometry of the magnetic field near reconnection sites? What roles do ion–neutral collisions, current-sheet instabilities, and plasmoid ejection play? How efficiently does the reconnection heat and accelerate the solar plasma?

Magnetic reconnection is a fundamental process that transforms magnetic energy into kinetic and thermal energies in astrophysical plasmas. The magnetic energy is stored, maintained, and amplified over extended periods of time (minutes to hours in magnetic network and hours to weeks in sunspots and active regions) before being released suddenly during reconnection events, with flares occurring on small spatial scales (kilometers) over very short times (minutes). Reconnection events can accelerate plasma in jet-like structures and induce local heating in the chromosphere and above.

In addition to the ubiquitous spicules (Section 5.1), jets are observed in sunspot penumbre (Katsukawa et al., 2007; Tiwari et al., 2018), at the edges of sunspots (Morton, 2012), in light bridges (Toriumi, Katsukawa, and Cheung, 2015; Tian et al., 2018), and in the plage regions surrounding sunspots (Nishizuka et al., 2011). These jets often display morphologies reminiscent of reconnection sites (e.g. Innes et al., 1997; Shibata et al., 2007; Singh et al., 2012), but there are few direct measurements of the local magnetic field and its reconfiguration by reconnection. Localized heating is also observed, for example as Ellerman bombs and UV bursts: point-like brightenings in the wing of chromospheric lines such as H\(\alpha \) and Ca ii (e.g. Vissers et al., 2015; Reid et al., 2016; Rouppe van der Voort et al., 2017; Toriumi, Katsukawa, and Cheung, 2017; Young et al., 2018). These brightenings are often associated with bipolar moving magnetic features near sunspots or colliding bipolar structures in regions of emerging flux, similar to magnetic cancelation events in the quiet Sun (Rouppe van der Voort, Rutten, and Vissers, 2016; Nelson et al., 2017a). Reconnection is again implicated (Figure 11), but again without direct measurements of field reconfiguration. Further, brightening and excess line broadening is observed in transition region and coronal loops, consistent with impulsive reconnection heating, bidirectional flows, and ion-cyclotron turbulence at sites of magnetic braiding of the underlying multi-stranded field (Cirtain et al., 2013; De Pontieu et al., 2014b; Hansteen et al., 2014; Bahauddin, Bradshaw, and Winebarger, 2020).

Figure 11
figure 11

The chromosphere near a sunspot as observed with the Hinode/Solar Optical Telescope through the Ca ii H broadband filter, showing transient brightenings, likely due to heating by reconnection events (middle, from Shimizu, 2015, fiducial boxes added). (a) Numerical simulation of a jet in which intermittent reconnection results from plasmoid instability. From Rouppe van der Voort et al. (2017). (b) Numerical simulation of an Ellerman bomb, in which reconnection occurs between emerging bipolar fields. From Hansteen et al. (2017). Reproduced with permission; copyright 2017 American Astronomical Society.

An important goal of DKIST is to measure the magnetic-field changes associated with reconnection phenomena at high resolution and simultaneously over multiple heights in the solar atmosphere from the photosphere into the chromosphere. Diagnosis of the magnetic field at reconnection sites before and after reconnection events will facilitate reconstruction of the magnetic and thermodynamic history of the plasma in the reconnection volume. It will allow detailed assessment of the total field annihilation, reconnection rate, total magnetic-energy release, and local heating induced. Together with recent in-situ measurements of the underlying microphysical processes in the Earth’s magnetosphere (e.g. Burch et al., 2016; Torbert et al., 2018; Chen et al., 2020; Hesse and Cassak, 2020) and laboratory experiments (e.g. Dong et al., 2012; Gekelman et al., 2016; Olson et al., 2016; Howes, 2018; Takahata, Yanai, and Inomoto, 2019; Seo et al., 2020), such studies will advance our fundamental understanding of the energetics of solar and astrophysical reconnection, determining how the energy is partitioned between bulk flows and random motions, between plasma acceleration and heating (Ji and Daughton, 2011; Coates, 2016; Yamada, Yoo, and Myers, 2016).

A key aspect of DKIST’s contributions to reconnection studies is the particular plasma environment that will be sampled. The lower solar atmosphere (photosphere and chromosphere) is relatively dense and weakly ionized, with an ionization fraction on the order of \(10^{-4}\) at the height of the temperature minimum (e.g. Khomenko, 2017). Weakly ionized plasmas are found over a wide range of astrophysical settings, including the atmospheres of other cool stars, the warm neutral interstellar medium (ionization fraction of \(10^{-2}\): Jenkins, 2013), dense cores of molecular clouds (ionization fraction of \(10^{-7}\): Caselli et al., 1998), and protostellar and protoplanetary disks (ionization fraction \(10^{-10}\) or less: e.g. Armitage, 2019). Importantly, low ionization fractions (in the range of those found in the solar chromosphere) increase reconnection rates. Ion–neutral interactions can lead to increased resistivity and an increase in the effective ion mass, with consequent reduction in the Alfvén speed, steepening of current sheets, heating of the inflow and exhaust regions of reconnection sites, and enhancement of the plasmoid instability (e.g. Zweibel, 1989; Chiueh, 1998; Zweibel et al., 2011; Leake et al., 2012; Mei et al., 2012; Murphy et al., 2012; Zweibel, 2015; Ni et al., 2020). These in turn have important implications for solar phenomena, likely being responsible for increased damping of MHD waves (De Pontieu, Martens, and Hudson, 2001), increased current dissipation and heating of the solar chromosphere (Khomenko and Collados, 2012; Martínez-Sykora, De Pontieu, and Hansteen, 2012), increased flux emergence rates into the corona, reduced Alfvén wave flux from photospheric foot-point motion, and changes in the structure of MHD shocks, prominences, and quiet-Sun magnetic features (see Anan, Ichimoto, and Hillier, 2017, and the references therein). Observational verification of the reconnection implications of partial ionization is more readily achieved in these solar contexts than in more distant astrophysical settings.

5.4 Waves in the Solar Atmosphere

What wave modes are present at what heights in the solar atmosphere? What are their sources? What role do waves play in chromospheric and coronal heating? How do the answers to these questions depend on the local magnetic-field structure?

At least two implications promote the use of DKIST to study magnetohydrodynamic waves in the solar atmosphere (e.g. Kostik and Khomenko, 2013): i) MHD waves carry energy into the solar atmosphere and, if dissipated at the correct heights, may provide at least a partial solution to the long-standing coronal and chromospheric heating problems, and ii) the presence of magnetic fields in the chromosphere and corona modify the waves observed, providing a possible opportunity to use them as diagnostics of the conditions there. The chromosphere is a particularly important region of the solar atmosphere, as it modulates wave transmission into the corona; understanding the solar chromosphere is critical to constraining the mechanisms of wave-energy transfer between the photosphere and the corona (see the review by Jess et al., 2015). Moreover, while it is much cooler than the corona, the chromosphere’s relatively high density and the efficiency of the cooling pathways available there mean that high-energy input is required to sustain radiative losses. Typical radiative losses are estimated to be on the order of \(10^{6}\,\text{--}\,10^{7}~\text{erg}\,\text{cm}^{-2}\,\text{s}^{-1}\) in the chromosphere compared to \(10^{4}\,\text{--}\,10^{6}~\text{erg}\,\text{cm}^{-2}\,\text{s}^{-1}\) in the solar corona (Withbroe and Noyes, 1977; Anderson and Athay, 1989). The solution to the coronal-heating problem may well be coupled to or depend on solution of the chromospheric heating problem (e.g. Carlsson, De Pontieu, and Hansteen, 2019).

The possibility that the Sun’s chromosphere and the corona are heated by the dissipation of MHD waves has led to a substantial body of research, starting over 70 years ago with suggestions that acoustic waves generated by convection are responsible for heating the solar atmosphere (Biermann, 1946; Schwarzschild, 1948). With the observational discovery (Leighton, 1960; Leighton, Noyes, and Simon, 1962) and correct theoretical interpretation (Ulrich, 1970) of the resonant solar acoustic oscillations, the diagnostic potential of the solar \(p\)-modes in the study of the solar interior was realized with helioseismology. This was closely followed by an understanding of the observational and theoretical distinction between those modes and propagating atmospheric waves (see Stein and Leibacher, 1974, for an early summary). In the intervening years, studies of chromospheric and coronal waves have leveraged increasingly sophisticated space- and ground-based instrumentation, and the consequent ever-increasing spatial, spectral, and temporal resolution observations, to advance our understanding of chromospheric and coronal wave behavior. Yet fundamental questions about wave-energy transport and wave heating of the solar atmosphere persist (e.g. Erdélyi and Fedun, 2007). What processes dominate wave generation? What modes are excited? How does the energy generated propagate into the solar corona? What is the role of mode conversion? What are the wave-dissipation mechanisms that allow the solar corona to maintain its multi-million-kelvin temperature?

Answering these questions requires the tracking of waves with height in the solar atmosphere, while simultaneously diagnosing changes in wave energy and the corresponding localized atmospheric heating (Jess et al., 2015). In combination with space-based UV observations, DKIST’s unprecedented multi-height spectropolarimetric measurements will be ideally suited to unraveling the nature of the waves, the energy propagation channels accessed, and the atmospheric heating that results.

In a uniform plasma under the continuum approximation, there are three distinct types of MHD wave modes: the slow and fast magneto-acoustic waves and Alfvén waves. Solar observations are often interpreted in terms of these, but this is a dramatic over-simplification, as the manifestation of these waves in the stratified and highly magnetically structured solar atmosphere is much more complex than in a uniform plasma (e.g. Banerjee et al., 2007; Tomczyk et al., 2007; De Pontieu et al., 2007b; Jess et al., 2009; Morton et al., 2012). In simple isolated magnetic geometries such as slabs or flux tubes, modes of the magnetic structures themselves (surface, body, kink, sausage, etc.) can be identified (e.g. Roberts, 1981a,b; Edwin and Roberts, 1982, 1983), but in general, with space-filling magnetic fields, the modes are mixed and coupled, and the waves are subject to resonant absorption, phase mixing, and guided propagation (e.g. Heyvaerts and Priest, 1983; Nakariakov et al., 1999; Bogdan, 2000; Nakariakov and Verwichte, 2005; Aschwanden, 2006; De Moortel, 2009; Jess et al., 2009; Ruderman and Erdélyi, 2009; Goossens, Erdélyi, and Ruderman, 2011; Morton et al., 2011; Wang, 2011; Mathioudakis, Jess, and Erdélyi, 2013; Priest, 2014; Okamoto et al., 2015; Antolin et al., 2015a; Keys et al., 2018). This makes observations difficult to interpret, but also consequently rich in diagnostic potential.

Additional complexities originate with the sate of the solar chromospheric plasma. While the coronal plasma can be treated as a single, low plasma-\(\beta \), fully ionized fluid, the chromosphere is a multi-fluid, partially ionized medium, with a finite spatially varying plasma-\(\beta \), coupled to a radiation field that is out of thermodynamic equilibrium (e.g. Hansteen, Carlsson, and Gudiksen, 2007). Waves in the solar chromosphere are subject to a highly structured (on sub-arcsecond to global scales) evolving field and flow (e.g. Wedemeyer-Böhm, Lagg, and Nordlund, 2009). Since the manifestations and behaviors of magneto-hydrodynamic waves differ in different magnetic and plasma regimes (high \(\beta \) vs. low \(\beta \), structured vs. unstructured (on the scale of a wave) field, partial vs. full ionization, as examples), wave signatures change as the waves propagate upward into the solar atmosphere, and tracking the wave energy from its source to the site of energy deposition is challenging.

Despite these difficulties, significant progress has been made and is anticipated with future observations (e.g. Banerjee et al., 2007). Convective motions in the photosphere excite both longitudinal and transverse perturbations. Of the compressive wave field excited in the photosphere, only waves above the temperature-minimum acoustic cut-off frequency are expected to propagate into the atmosphere above, steepening, shocking, and dissipating as they propagate into the chromosphere (Zhugzhda, Bromm, and Ulmschneider, 1995; Carlsson and Stein, 1997). On the other hand, transverse Alfvénic perturbations can propagate through the chromosphere and into the corona with only weak damping. This allows these waves to reach greater heights but also makes their role in plasma heating somewhat problematic. One possibility is that the waves undergo mode conversion from Alfvénic to compressive, with the compressive motions providing an avenue for dissipation and heating (e.g. Hollweg, Jackson, and Galloway, 1982; Ulmschneider, Zähringer, and Musielak, 1991; Kalkofen, 1997). The height at which mode conversion occurs is then critical to the height-dependent wave fluxes and consequent heating of the upper atmospheric layers.

Observations of compressive wave motions support this general picture with some modification. High-frequency power (near three minutes in period) dominates the chromospheric wave field as expected, but it does so only in limited inter-network regions devoid of strong photospheric or chromospheric-canopy fields (Vecchio et al., 2007; Vecchio, Cauzzi, and Reardon, 2009). In plage regions, compressive wave power in the chromosphere reaches a maximum well below the acoustic cut-off frequency (e.g. Centeno, Collados, and Trujillo Bueno, 2009), and low-frequency magneto-acoustic waves propagate upward from the photosphere in regions surrounding network elements (Jefferies et al., 2006; Vecchio et al., 2007). The presence of magnetic field thus appears to dramatically influence the frequency of the waves propagating into atmosphere. Several mechanisms have been proposed to facilitate this (Roberts, 2000, 2006): inclined magnetic field can effectively act as a wave-guide to reduce the cut-off frequency (Michalitsanos, 1973; De Pontieu, Erdélyi, and James, 2004) and, even for vertically oriented field, nonadiabatic waves can be evanescent outside of magnetic flux tubes yet propagate within them (Roberts, 1983; Centeno, Collados, and Trujillo Bueno, 2006; Khomenko et al., 2008; Centeno, Collados, and Trujillo Bueno, 2009). These mechanisms can be distinguished by careful measurement of the magnetic-field structures supporting the waves and wave temperature–velocity phase relations (Kostik and Khomenko, 2013, but cf. Heggland, De Pontieu, and Hansteen, 2009). More generally, MHD wave properties, and the propagation characteristics and amplitudes of waves of different frequencies, depend in detail on the magnetic structure of the region, radiative energy exchange, and the ionization state of the plasma (Khomenko et al., 2018).

Direct detection of Alfvén-wave perturbations is even more challenging than detection of compressive waves, but Alfvén waves have been successfully observed in the chromosphere (De Pontieu et al., 2007b; Jess et al., 2009), transition region (De Pontieu et al., 2014a), and solar corona, both as time-varying non-thermal line widths (see review, Mathioudakis, Jess, and Erdélyi, 2013) and directly as linear-polarization and Doppler velocity fluctuations (Figure 12, Tomczyk et al., 2007, but cf. Van Doorsselaere, Nakariakov, and Verwichte,