Science development study for the Atacama Large Aperture Submillimeter Telescope (AtLAST): Solar and stellar observations.

Observations at (sub-)millimeter wavelengths offer a complementary perspective on our Sun and other stars, offering significant insights into both the thermal and magnetic composition of their chromospheres. Despite the fundamental progress in (sub-)millimeter observations of the Sun, some important aspects require diagnostic capabilities that are not offered by existing observatories. In particular, simultaneously observations of the radiation continuum across an extended frequency range would facilitate the mapping of different layers and thus ultimately the 3D structure of the solar atmosphere. Mapping large regions on the Sun or even the whole solar disk at a very high temporal cadence would be crucial for systematically detecting and following the temporal evolution of flares, while synoptic observations, i.e., daily maps, over periods of years would provide an unprecedented view of the solar activity cycle in this wavelength regime. As our Sun is a fundamental reference for studying the atmospheres of active main sequence stars, observing the Sun and other stars with the same instrument would unlock the enormous diagnostic potential for understanding stellar activity and its impact on exoplanets. The Atacama Large Aperture Submillimeter Telescope (AtLAST), a single-dish telescope with 50m aperture proposed to be built in the Atacama desert in Chile, would be able to provide these observational capabilities. Equipped with a large number of detector elements for probing the radiation continuum across a wide frequency range, AtLAST would address a wide range of scientific topics including the thermal structure and heating of the solar chromosphere, flares and prominences, and the solar activity cycle. In this white paper, the key science cases and their technical requirements for AtLAST are discussed.

Observations of our Sun and other stars at wavelengths of around one millimeter, i.e. in the range between infrared and radio waves, present a valuable complementary perspective. Despite significant technological advancements, certain critical aspects necessitate diagnostic capabilities not offered by current observatories. The proposed Atacama Large Aperture Submillimeter Telescope (AtLAST), featuring a 50-meter aperture and slated for construction at a high altitude in Chile's Atacama desert, promises to address these observational needs. Equipped with novel detectors that would cover a wide frequency range, AtLAST could unlock a plethora of scientific studies contributing to a better understanding of our host star. Simultaneous observations over a broad frequency range at rapid succession would enable the imaging of different layers of the Sun, thus elucidating the three-dimensional thermal and magnetic structure of the solar atmosphere and providing important clues for many long-standing central questions such as how the outermost layers of the Sun are heated to very high temperatures, the nature of large-scale structures like prominences, and how flares and coronal mass ejections, i.e. enormous eruptions, are produced. The latter is of particular interest to modern society due to the potentially devastating impact on the technological infrastructure we depend on today. Another unique possibility would be to study the Sun's long-term evolution in this wavelength range, which would yield important insights into its activity cycle. Moreover, the Sun serves as a fundamental reference for other stars as, due to its proximity, it is the only star that can be investigated in such detail. The results for the Sun would therefore have direct implications for understanding other stars and their impact on exoplanets. This article outlines the key scientific objectives and technical requirements for solar observations with AtLAST.

Data-driven modeling of solar coronal magnetic field evolution and eruptions.

Magnetic fields play a fundamental role in the structure and dynamics of the solar corona. As they are driven by their footpoint motions on the solar surface, which transport energy from the interior of the Sun into its atmosphere, the coronal magnetic fields are stressed continuously with buildup of magnetic nonpotentiality in the form of topology complexity (magnetic helicity) and local electric currents (magnetic free energy). The accumulated nonpotentiality is often released explosively by solar eruptions, manifested as solar flares and coronal mass ejections, during which magnetic energy is converted into mainly kinetic, thermal, and nonthermal energy of the plasma, which can cause adverse space weather. To reveal the physical mechanisms underlying solar eruptions, it is vital to know the three-dimensional (3D) structure and evolution of the coronal magnetic fields. Because of a lack of direct measurements, the 3D coronal magnetic fields are commonly studied using numerical modeling, whereas traditional models mostly aim for a static extrapolation of the coronal field from the observable photospheric magnetic field data. Over the last decade, dynamic models that are driven directly by observation magnetograms have been developed and applied successfully to study solar coronal magnetic field evolution as well as its eruption, which offers a novel avenue for understanding their underlying magnetic topology and mechanism. In this paper, we review the basic methodology of the data-driven coronal models, state-of-the-art developments, their typical applications, and new physics that have been derived using these models. Finally, we provide an outlook for future developments and applications of the data-driven models.

NuSTAR observations of a repeatedly microflaring active region.

We investigate the spatial, temporal, and spectral properties of 10 microflares from AR12721 on 2018 September 9 and 10 observed in X-rays using the Nuclear Spectroscopic Telescope ARray and the Solar Dynamic Observatory's Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager. We find GOES sub-A class equivalent microflare energies of 1026-1028 erg reaching temperatures up to 10 MK with consistent quiescent or hot active region (AR) core plasma temperatures of 3-4 MK. One microflare (SOL2018-09-09T10:33), with an equivalent GOES class of A0.1, has non-thermal hard X-ray emission during its impulsive phase (of non-thermal power ~7 × 1024 erg s-1) making it one of the faintest X-ray microflares to have direct evidence for accelerated electrons. In 4 of the 10 microflares, we find that the X-ray time profile matches fainter and more transient sources in the extreme-ultraviolet, highlighting the need for observations sensitive to only the hottest material that reaches temperatures higher than those of the AR core (>5 MK). Evidence for corresponding photospheric magnetic flux cancellation/emergence present at the footpoints of eight microflares is also observed.

Evolution of the Toroidal Flux of CME Flux Ropes during Eruption.

Coronal mass ejections (CMEs) are large-scale explosions of the coronal magnetic field. It is believed that magnetic reconnection significantly builds up the core structure of CMEs, a magnetic flux rope, during the eruption. However, the quantitative evolution of the flux rope, particularly its toroidal flux, is still unclear. In this paper, we study the evolution of the toroidal flux of the CME flux rope for four events. The toroidal flux is estimated as the magnetic flux in the footpoint region of the flux rope, which is identified by a method that simultaneously takes the coronal dimming and the hook of the flare ribbon into account. We find that the toroidal flux of the CME flux rope for all four events shows a two-phase evolution: a rapid increasing phase followed by a decreasing phase. We further compare the evolution of the toroidal flux with that of the Geostationary Operational Environmental Satellites soft X-ray flux and find that they are basically synchronous in time, except that the peak of the former is somewhat delayed. The results suggest that the toroidal flux of the CME flux rope may be first quickly built up by the reconnection mainly taking place in the sheared overlying field and then reduced by the reconnection among the twisted field lines within the flux rope, as enlightened by a recent 3D magnetohydrodynamic simulation of CMEs.

Modeling a Carrington-scale Stellar Superflare and Coronal Mass Ejection from κ 1 Cet.

Observations from the Kepler mission have revealed frequent superflares on young and active solar-like stars. Superflares result from the large-scale restructuring of stellar magnetic fields, and are associated with the eruption of coronal material (a coronal mass ejection, or CME) and energy release that can be orders of magnitude greater than those observed in the largest solar flares. These catastrophic events, if frequent, can significantly impact the potential habitability of terrestrial exoplanets through atmospheric erosion or intense radiation exposure at the surface. We present results from numerical modeling designed to understand how an eruptive superflare from a young solar-type star, κ 1 Cet, could occur and would impact its astrospheric environment. Our data-inspired, three-dimensional magnetohydrodynamic modeling shows that global-scale shear concentrated near the radial-field polarity inversion line can energize the closed-field stellar corona sufficiently to power a global, eruptive superflare that releases approximately the same energy as the extreme 1859 Carrington event from the Sun. We examine proxy measures of synthetic emission during the flare and estimate the observational signatures of our CME-driven shock, both of which could have extreme space-weather impacts on the habitability of any Earth-like exoplanets. We also speculate that the observed 1986 Robinson-Bopp superflare from κ 1 Cet was perhaps as extreme for that star as the Carrington flare was for the Sun.

Identification of Multiple Hard X-Ray Sources in Solar Flares: A Bayesian Analysis of the 2002 February 20 Event.

The hard X-ray emission in a solar flare is typically characterized by a number of discrete sources, each with its own spectral, temporal, and spatial variability. Establishing the relationship among these sources is critical to determining the role of each in the energy release and transport processes that occur within the flare. In this paper we present a novel method to identify and characterize each source of hard X-ray emission. The method permits a quantitative determination of the most likely number of subsources present, and of the relative probabilities that the hard X-ray emission in a given subregion of the flare is represented by a complicated multiple source structure or by a simpler single source. We apply the method to a well-studied flare on 2002 February 20 in order to assess competing claims as to the number of chromospheric footpoint sources present, and hence to the complexity of the underlying magnetic geometry/topology. Contrary to previous claims of the need for multiple sources to account for the chromospheric hard X-ray emission at different locations and times, we find that a simple two-footpoint-plus-coronal-source model is the most probable explanation for the data. We also find that one of the footpoint sources moves quite rapidly throughout the event, a factor that presumably complicated previous analyses. The inferred velocity of the footpoint corresponds to a very high induced electric field, compatible with the fields in thin reconnecting current sheets.

Reduction of Thermal Conductive Flux by Non-local Effects in the Presence of Turbulent Scattering.

The heat flux in a plasma is determined by the degree of anisotropy in the particle distribution function, which is in turn driven by gradients in the ambient density and temperature. When the mean free path at the thermal speed is substantially smaller than the scale length associated with the temperature variation, the heat flux simply depends on the local value of the temperature gradient. However, when the temperature scale length and mean free path are comparable, heat conduction becomes substantially non-local in character: the magnitude of the heat flux now depends on the overall temperature profile and is generally smaller than the locally determined value. In the presence of angular scattering associated with turbulence, the mean free path (and its velocity dependence) can be significantly smaller than its collisional value; this makes the expression for the heat flux more local in character, but also results in a heat flux that is lower than that obtained through a purely collisional analysis. Therefore, whether or not turbulence is present, the heat flux is generally smaller than the value obtained from a local collisional analysis. We here present an analytic expression for the conductive heat flux in terms of a convolution of the local heat flux with a non-local kernel function that incorporates both Coulomb collisions and turbulent scattering. We comment on the need to include both non-local and turbulent scattering effects in the modeling of quasi-static active region loops and in the conductive cooling of post-flare loops.

Energy Deposition by Energetic Electrons in a Diffusive Collisional Transport Model.

A considerable fraction of the energy in a solar flare is released as suprathermal electrons; such electrons play a major role in energy deposition in the ambient atmosphere, and hence the atmospheric response to flare heating. Historically, the transport of these particles has been approximated through a deterministic approach in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or neglected. However, it has recently been pointed out that while neglect of diffusion in energy may indeed be negligible, diffusion in angle is of the same order as deterministic scattering and hence must be included. Here we therefore investigate the effect of angular scattering on the energy deposition profile in the flaring atmosphere. A relatively simple compact expression for the spatial distribution of energy deposition into the ambient plasma is presented and compared with the corresponding deterministic result. For unidirectional injection there is a significant shift in heating from the lower corona to the upper corona; this shift is much smaller for isotropic injection. We also compare the heating profiles due to return current ohmic heating in the diffusional and deterministic models.

Heating and Cooling of Coronal Loops with Turbulent Suppression of Parallel Heat Conduction.

Using the "enthalpy-based thermal evolution of loops" (EBTEL) model, we investigate the hydrodynamics of the plasma in a flaring coronal loop in which heat conduction is limited by turbulent scattering of the electrons that transport the thermal heat flux. The EBTEL equations are solved analytically in each of the two (conduction-dominated and radiation-dominated) cooling phases. Comparison of the results with typical observed cooling times in solar flares shows that the turbulent mean free path λT lies in a range corresponding to a regime in which classical (collision-dominated) conduction plays at most a limited role. We also consider the magnitude and duration of the heat input that is necessary to account for the enhanced values of temperature and density at the beginning of the cooling phase and for the observed cooling times. We find through numerical modeling that in order to produce a peak temperature ≃1.5 × 107 K and a 200 s cooling time consistent with observations, the flare-heating profile must extend over a significant period of time; in particular, its lingering role must be taken into consideration in any description of the cooling phase. Comparison with observationally inferred values of post-flare loop temperatures, densities, and cooling times thus leads to useful constraints on both the magnitude and duration of the magnetic energy release in the loop, as well as on the value of the turbulent mean free path λT .

Flux-Rope Twist in Eruptive Flares and CMEs: Due to Zipper and Main-Phase Reconnection.

The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D "zipper reconnection" propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D "main-phase reconnection" in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn ( 2 π radians of twist), and then main-phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.

SEARCH FOR A SIGNATURE OF TWIST-REMOVAL IN THE MAGNETIC FIELD OF SUNSPOTS IN RELATION WITH MAJOR FLARES.

We investigate the restructuring of the magnetic field in sunspots associated with two flares: the X6.5 flare on 6 December 2006 and the X2.2 flare on 15 February 2011. The observed changes were evaluated with respect to the so-called twist-removal model, in which helicity (twist) is removed from the corona as the result of an eruption. Since no vector magnetograms were available for the X6.5 flare, we applied the azimuthal symmetry approach to line-of-sight magnetograms to reconstruct the pseudo-vector magnetic field and investigate the changes in average twist and inclination of magnetic field in the sunspot around the time of the flare. For the X2.2 flare, results from the full vector magnetograms were compared with the pseudo-vector field data. For both flares, the data show changes consistent with the twist-removal scenario. We also evaluate the validity of the azimuthal symmetry approach on simple isolated round sunspots. In general, the derivations based on the azimuthal symmetry approach agree with true-vector field data though we find that even for symmetric sunspots the distribution of the magnetic field may deviate from an axially symmetric distribution.

HARD X-RAY EMISSION DURING FLARES AND PHOTOSPHERIC FIELD CHANGES.

We study the correlation between abrupt permanent changes of magnetic field during X-class flares observed by the Global Oscillation Network Group and Helioseismic and Magnetic Imager instruments, and the hard X-ray (HXR) emission observed by RHESSI, to relate the photospheric field changes to the coronal restructuring and investigate the origin of the field changes. We find that spatially the early RHESSI emission corresponds well to locations of the strong field changes. The field changes occur predominantly in the regions of strong magnetic field near the polarity inversion line (PIL). The later RHESSI emission does not correspond to significant field changes as the flare footpoints are moving away from the PIL. Most of the field changes start before or around the start time of the detectable HXR signal, and they end at about the same time or later than the detectable HXR flare emission. Some of the field changes propagate with speed close to that of the HXR footpoint at a later phase of the flare. The propagation of the field changes often takes place after the strongest peak in the HXR signal when the footpoints start moving away from the PIL, i.e., the field changes follow the same trajectory as the HXR footpoint, but at an earlier time. Thus, the field changes and HXR emission are spatio-temporally related but not co-spatial nor simultaneous. We also find that in the strongest X-class flares the amplitudes of the field changes peak a few minutes earlier than the peak of the HXR signal. We briefly discuss this observed time delay in terms of the formation of current sheets during eruptions.