Numerical simulations are essential for studying the solar atmosphere, especially in the context of the coronal heating problem. Understanding how numerical factors and boundary conditions (BC) influence the energetic structure of these models is crucial for unraveling coronal heating mechanisms. We investigate how the computational domain dimensions, upper BC, and vertical grid resolution influence the relaxed thermal structure, energetics, and long-term stability of 2D solar atmosphere simulations with a vertical magnetic field. Using the MAGEC code, we conducted parametric studies varying domain width and height, vertical grid stretching, and top BC, including hot-plate, closed, unrestricted temperature, background heating, and non-reflecting characteristic configurations. We evaluated average temperature profiles for parameter dependence and temporal stability, and analyzed the energetic budget as a function of height, isolating contributions from radiative losses, thermal conduction, pressure work, and internal energy flux. Models with larger vertical domains show higher average coronal temperatures and steeper transition region gradients. Among the less artificial BC, non-reflecting characteristics most effectively delay coronal cooling. We determined the threshold height at which a dynamic top BC can mimic fixed-temperature setups, and established the maximum allowable grid stretching that preserves physical accuracy while reducing computational costs. The energetic terms change significantly with the chosen BC, with specific mechanisms acting as cooling agents in different atmospheric layers. Our results demonstrate that domain height, vertical grid design, and BC critically dictate the relaxed thermal structure and energetic balance of the simulated solar atmosphere.
We propose that coronal heating in EUV coronal plumes is weaker, not stronger, than in adjacent non-plume coronal magnetic funnels. This expectation stems from (i) the observation that an EUV plume is born as the magnetic flux at the foot of the plume's magnetic funnel becomes tightly packed together, and (ii) the observation that coronal heating in quiet regions increases in proportion to the coast-line length of the underlying magnetic network. We do not rule out the possibility that coronal heating in EUV plumes might be stronger, not weaker, but we point out how the opposite is plausible. …
The solar coronal heating problem refers to the question why the temperature of the Sun's corona is more than two orders of magnitude higher than that of its surface. Almost 70 years after the discovery, this puzzle is still one of the major challenges in astrophysics. The current basic paradigm of coronal heating is unable to explain all the observational features of the heating. Here we argue that a new paradigm is required to solve the puzzle in a self-consistent manner. The alternative approach is based on the kinetic theory of drift waves. We show, with qualitative and quantitative argume…
Coronal rain consists of cool plasma condensations formed in coronal loops as a result of thermal instability. The standard models of coronal rain formation assume that the heating is quasi-steady and localised at the coronal loop footpoints. We present an observation of magnetic reconnection in the corona and the associated impulsive heating triggering formation of coronal rain condensations. We analyse combined SDO/AIA and IRIS observations of a coronal rain event following a reconnection between threads of a low-lying prominence flux rope and surrounding coronal field lines. The reconnectio…
The hot solar corona exists because of the balance between radiative and conductive cooling and some counteracting heating mechanism which remains one of the major puzzles in solar physics. The coronal thermal equilibrium is perturbed by magnetoacoustic waves which are abundantly present in the corona, causing a misbalance between the heating and cooling rates. Due to this misbalance, the wave experiences a back-reaction, either losing or gaining energy from the energy supply that heats the plasma, at the time scales comparable to the wave period. In particular, the plasma can be subject to wa…
We highlight ten key aspects of coronal heating that must be understood before we can consider the problem to be solved. (1) All coronal heating is impulsive. (2) The details of coronal heating matter. (3) The corona is filled with elemental magnetic stands. (4) The corona is densely populated with current sheets. (5) The strands must reconnect to prevent an infinite buildup of stress. (6) Nanoflares repeat with different frequencies. (7) What is the characteristic magnitude of energy release? (8) What causes the collective behavior responsible for loops? (9) What are the onset conditions for …
The Interface Region Imaging Spectrograph (IRIS) has observed bright spots at the transition region footpoints associated with heating in the overlying loops, as observed by coronal imagers. Some of these brightenings show significant blueshifts in the Si iv line at 1402.77 A (logT[K] = 4.9). Such blueshifts cannot be reproduced by coronal loop models assuming heating by thermal conduction only, but are consistent with electron beam heating, highlighting for the first time the possible importance of non-thermal electrons in the heating of non-flaring active regions. Here we report on the coron…
The question why the solar corona is much hotter than the visible solar surface still puzzles solar researchers. Most theories of the coronal heating involve a tight coupling between the coronal magnetic field and the associated thermal structure. This coupling is based on two facts: (i) the magnetic field is the main source of the energy in the corona and (ii) the heat transfer preferentially happens along the magnetic field, while is suppressed across it. However, most of the information about the coronal heating is derived from analysis of EUV or soft X-ray emissions, which are not explicit…
How magnetic energy is injected and released in the solar corona, keeping it heated to several million degrees, remains elusive. Coronal heating generally increases with increasing magnetic field strength. From comparison of a non-linear force-free model of the three-dimensional active-region coronal field to observed extreme-ultraviolet loops, we find that (1) umbra-to-umbra coronal loops, despite being rooted in the strongest magnetic flux, are invisible, and (2) the brightest loops have one foot in an umbra or penumbra and the other foot in another sunspot's penumbra or in unipolar or mixed…
The heating of the solar chromosphere and corona to the observed high temperatures, imply the presence of ongoing heating that balances the strong radiative and thermal conduction losses expected in the solar atmosphere. It has been theorized for decades that the required heating mechanisms of the chromospheric and coronal parts of the active regions, quiet-Sun, and coronal holes are associated with the solar magnetic fields. However, the exact physical process that transport and dissipate the magnetic energy which ultimately leads to the solar plasma heating are not yet fully understood. The …
2.5-dimensional magnetohydrodynamic (MHD) simulations are performed with high spatial resolution in order to distinguish between competing models of the coronal heating problem. A single coronal loop powered by Alfvén waves excited in the photosphere is the target of the present study. The coronal structure is reproduced in our simulations as a natural consequence of the transportation and dissipation of Alfvén waves. Further, the coronal structure is maintained as the spatial resolution is changed from 25 to 3 km, although the temperature at the loop top increases with the spatial resolution.…
Solar Coronal Heating is a Nonlinear Quantum Mechanical Phenomenon. Corona is a powerful source of X-rays and ionisations & emissions of such radiations are quantum mechanical and levels are highly unstable to order of femto-seconds. A linear method of energy transfer like collisional ionisation to such levels is practically not feasible. We have proposed gire as the mechanism of this problem and discussed the physics, found it as a nonlinear process of multi photon absorption, similar to the multiple ionisation by ultra fast laser. Here, we are discussing the energy budget for ionisations of …
Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades the problem has been known as the coronal heating problem, but it is now clear that `coronal heating' cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, c…
The Parker hypothesis (Parker (1972)) assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of long-duration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject…
Recent observational and numerical studies show a variety of thermal structures in the solar chromosphere. Given that the thermal interplay across the transition region is a key to coronal heating, it is worth investigating how different thermal structures of the chromosphere yield different coronal properties. In this work, by MHD simulations of Alfvén-wave heating of coronal loops, we study how the coronal properties are affected by the chromospheric temperature. To this end, instead of solving the radiative transfer equation, we employ a simple radiative loss function so that the chromosphe…
We model nanoflare heating of extrapolated active-region coronal loops via the acceleration of electrons and protons in Harris-type current sheets. The kinetic energy of the accelerated particles is estimated using semi-analytical and test-particle-tracing approaches. Vector magnetograms and photospheric Doppler velocity maps of NOAA active region 09114, recorded by the Imaging Vector Magnetograph (IVM), were used for this analysis. A current-free field extrapolation of the active-region corona was first constructed. The corresponding Poynting fluxes at the footpoints of 5000 extrapolated coro…
To simulate the energy balance of coronal plasmas on macroscopic scales, we often require the specification of the coronal heating mechanism in some functional form. To go beyond empirical formulations and to build a more physically motivated heating function, we investigate the wave-turbulence-driven (WTD) phenomenology for the heating of closed coronal loops. Our implementation is designed to capture the large-scale propagation, reflection, and dissipation of wave turbulence along a loop. The parameter space of this model is explored by solving the coupled WTD and hydrodynamic evolution in 1…
Nanoflare models for heating the solar corona usually assume magnetic braiding and reconnection as the source of the energy. However, recent observations at record spatial resolution from the {\sc Sunrise} balloon mission suggest that photospheric magnetic flux cancellation is much more common than previously realised. We therefore examine the possibility of three-dimensional reconnection driven by flux cancellation as a cause of chromospheric and coronal heating. In particular, we estimate how the heights and amount of energy release produced by flux cancellation depend on flux size, flux can…
It has been found that the Kelvin-Helmholtz instability (KHI) induced by both transverse and torsional oscillations in coronal loops can reinforce the effects of wave heating. In this study, we model a coronal loop as a system of individual strands, and we study wave heating effects by considering a combined transverse and torsional driver at the loop footpoint. We deposit the same energy into the multi-stranded loop and an equivalent monolithic loop, and then observe a faster increase in the internal energy and temperature in the multi-stranded model. Therefore, the multi-stranded model is mo…
To understand the nonlinear dynamics of the Parker scenario for coronal heating, long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out. A loop is modeled as a box extended along the direction of the strong magnetic field $B_0$ in which the system is embedded. At the top and bottom plates, which represent the photosphere, velocity fields mimicking photospheric motions are imposed. We show that the nonlinear dynamics is described by different regimes of MHD anisotropic turbulence, with spectra characterized by intertial range power laws who…
Aims: To study the presence of superoscillations in coronal magnetoacoustic waves and its possible role in heating coronal loops through the strong and localized gradients they generate on the wave. Methods: An analytic model is built for the transition between a sausage and a kink wave modes propagating along field lines in the corona. We compute in this model the local frequencies, the wave gradients and the associated heating rates due to compressive viscosity. Results: We find superoscillations associated with the transition between wave modes accompanying the wave dislocation that shifts …
A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upwards in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvenic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data.
The Parker or field line tangling model of coronal heating is investigated through long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy and characterized by current sheets elongated along the axial magnetic field. Increasing the value of the axial magnetic field different regimes of MHD turbulence develop with a bearing on coronal heating rates. In physical …
We study the signatures of different coronal heating regimes on the differential emission measure (DEM) of multi-stranded coronal loops by means of hydrodynamic simulations. We consider heating either uniformly distributed along the loops or localized close to the chromospheric footpoints, in both steady and impulsive conditions. Our simulations show that condensation at the top of the loop forms when the localized heating is impulsive with a pulse cadence time shorter than the plasma cooling time, and the pulse energy is below a certain threshold. A condensation does not produce observable si…
We investigate the relative contributions from the transition region and corona of coronal loops observed by the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Using EBTEL (Enthalpy-Based Thermal Evolution of Loops) hydrodynamic simulations, we model loops with multiple lengths and energy fluxes heated randomly by events drawn from power-law distributions with different slopes and minimum delays between events to investigate how each of these parameters influences observable loop properties. We generate AIA intensities from the corona and transition region for each…
The heating of solar coronal loops is at the center of the problem of coronal heating. Given that the origin of the fast solar wind has been tracked down to atmospheric layers with transition region or even chromospheric temperatures, it is worthy attempting to address whether the mechanisms proposed to provide the basal heating of the solar wind apply to coronal loops as well. We extend the loop studies based on a classical parallel-cascade scenario originally proposed in the solar wind context by considering the effects of loop expansion, and perform a parametric study to directly contrast t…
Context. Photospheric motions shuffle the footpoints of the strong axial magnetic field that threads coronal loops giving rise to turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets where energy is deposited at small-scales and the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km). Aim. In order to understand coronal heating and interpret correctly observations it is crucial to study the thermodynamics of such a sys…
The Sun's corona is millions of degrees hotter than its 5,000 K photosphere. This heating enigma is typically addressed by invoking the deposition at coronal heights of non-thermal energy generated by the interplay between convection and magnetic field near the photosphere. However, it remains unclear how and where coronal heating occurs and how the corona is filled with hot plasma. We show that energy deposition at coronal heights cannot be the only source of coronal heating, by revealing a significant coronal mass supply mechanism that is driven from below, in the chromosphere. We quantify t…
In the quest to solve the long-standing coronal heating problem, it has been suggested half a century ago that coronal loops could be heated by waves. Despite the accumulating observational evidence of the possible importance of coronal waves, still no 3D MHD simulations exist that show significant heating by MHD waves. Here we report on the first 3D coronal loop model heating the plasma against radiative cooling. The coronal loop is driven at the footpoint by transverse oscillations and subsequently the induced Kelvin-Helmholtz instability deforms the loop cross-section and generates small-sc…
Spicules have been proposed as significant contributors to the mass and energy balance of the corona. While previous observations have provided a glimpse of short-lived transient brightenings in the corona that are associated with spicules, these observations have been contested and are the subject of a vigorous debate both on the modeling and the observational side. Therefore, it remains unclear whether plasma is heated to coronal temperatures in association with spicules. We use high-resolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrogr…
Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves. In particular, recent observations show that standing oscillations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. We investigate the consequences for wave-based coronal heating of higher harmonics and what coronal heating observational …
The dynamics of regions of the solar corona are investigated using Atmospheric Imaging Assembly (AIA) 171Å and 193Å data. The coronal emission from the quiet Sun, coronal loop footprints, coronal moss, and from above a sunspot is studied. It is shown that the mean Fourier power spectra in these regions can be described by a power law at lower frequencies that tails to flat spectrum at higher frequencies, plus a Gaussian-shaped contribution that varies depending on the region studied. This Fourier spectral shape is in contrast to the commonly-held assumption that coronal time-series are well de…
Coronal rain consists of cool and dense plasma condensations formed in coronal loops as a result of thermal instability. Previous numerical simulations of thermal instability and coronal rain formation have relied on artificially adding a coronal heating term to the energy equation. To reproduce large-scale characteristics of the corona, using more realistic coronal heating prescription is necessary. We analyse coronal rain formation and evolution in a 3-dimensional radiative magnetohydrodynamic simulation spanning from convection zone to corona which is self-consistently heated by magnetic fi…
It remains unclear which physical processes are responsible for the dramatic increase with height of the temperature in stellar atmospheres, known as the chromospheric ($\sim$10,000 K) and coronal (several million K) heating problems. Statistical studies of sun-like stars reveal that chromospheric and coronal emissions are correlated on a global scale, constraining, in principle, theoretical models of potential heating mechanisms. However, so far, spatially resolved observations of the Sun have surprisingly failed to show a similar correlation on small spatial scales, leaving models poorly con…
A full 3-dimensional compressible magnetohydrodynamic (MHD) simulation is conducted to investigate the thermal responses of a coronal loop to the dynamic dissipation processes of MHD waves. When the foot points of the loop are randomly and continuously forced, the MHD waves become excited and propagate upward. Then, a 1-MK temperature corona is produced naturally as the wave energy dissipates. The excited wave packets become non-linear just above the magnetic canopy, and the wave energy cascades into smaller spatial scales. Moreover, collisions between counter-propagating Alfvén wave packets i…
The heating of the plasma in the solar atmosphere is discussed within both frameworks of fluid and kinetic drift wave theory. We show that the basic ingredient necessary for the heating is the presence of density gradients in the direction perpendicular to the magnetic field vector. Such density gradients are a source of free energy for the excitation of drift waves. We use only well established basic theory, verified experimentally in laboratory plasmas. Two mechanisms of the energy exchange and heating are shown to take place simultaneously: one due to the Landau effect in the direction para…
The mechanism behind coronal heating still elude direct observation and modelling of viable theoretical processes and the subsequent effect on coronal structures is one of the key tools available to assess possible heating mechanisms. Wave-heating via phase-mixing of Magnetohydrodynamics (MHD) transverse waves has been proposed as a possible way to convert magnetic energy into thermal energy but increasingly, MHD models suggest this is not a sufficiently efficient mechanism. We model heating by phase-mixing of transverse MHD waves in various configurations, to investigate whether certain circu…
We propose a novel one-dimensional model that includes both shock and turbulence heating and qualify how these processes contribute to heating the corona and driving the solar wind. Compressible MHD simulations allow us to automatically consider shock formation and dissipation, while turbulent dissipation is modeled via a one-point closure based on Alfvén wave turbulence. Numerical simulations were conducted with different photospheric perpendicular correlation lengths $λ_0$, which is a critical parameter of Alfvén wave turbulence, and different root-mean-square photospheric transverse-wave am…
The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they als…
We simulate a coronal mass ejection (CME) using a three-dimensional magnetohydrodynamic (MHD) code that includes coronal heating, thermal conduction, and radiative cooling in the energy equation. The magnetic flux distribution at 1 R$_s$ is produced by a localized subsurface dipole superimposed on a global dipole field, mimicking the presence of an active region within the global corona. Transverse electric fields are applied near the polarity inversion line to introduce a transverse magnetic field, followed by the imposition of a converging flow to form and destabilize a flux rope, producing …
Context: Thermal non-equilibrium (TNE) produces several observables that can be used to constrain the spatial and temporal distribution of solar coronal heating. Its manifestations include prominence formation, coronal rain, and long-period intensity pulsations in coronal loops. The recent observation of abundant periodic coronal rain associated with intensity pulsations by Auchère et al. allows to unify these two phenomena as the result of TNE condensation and evaporation cycles. On the other hand, many intensity pulsation events observed by Froment et al. show little to no coronal rain forma…
We investigate the evolution of coronal loop emission in the context of the coronal magnetic field topology. New modeling techniques allow us to investigate the magnetic field structure and energy release in active regions. Using these models and high resolution multi-wavelength coronal observations from the Transition Region and Coronal Explorer (TRACE) and the X-ray Telescope (XRT) on Hinode, we are able to establish a relationship between the light curves of coronal loops and their associated magnetic topologies for NOAA Active Region 10963. We examine loops that show both transient and ste…
Empirically, the X-ray luminosity LX from M dwarfs has been found to have an upper limit of about 0.2% of the bolometric flux Lbol. In the limit where magnetic fields in M dwarfs are generated in equipartition with convective motions, we use stellar models to calculate the energy flux of Alfven waves FA as a function of depth in the sub-surface convection zone. Since Alfven waves have the optimal opportunity for wave modes to reach the corona, we suggest that FA sets an upper limit on the mechanical flux Fmech which causes coronal heating. This suggestion accounts quantitatively for the satura…
The effect of the numerical spatial resolution in models of the solar corona and corona / chromosphere interface is examined for impulsive heating over a range of magnitudes using one dimensional hydrodynamic simulations. It is demonstrated that the principle effect of inadequate resolution is on the coronal density. An underresolved loop typically has a peak density of at least a factor of two lower than a resolved loop subject to the same heating, with larger discrepencies in the decay phase. The temperature for under-resolved loops is also lower indicating that lack of resolution does not "…
We present a new global model of the solar corona, including the low corona, the transition region and the top of chromosphere. The realistic 3D magnetic field is simulated using the data from the photospheric magnetic field measurements. The distinctive feature of the new model is incorporating the MHD Alfven wave turbulence. We assume this turbulence and its non-linear dissipation to be the only momentum and energy source for heating the coronal plasma and driving the solar wind. The difference between the turbulence dissipation efficiency in coronal holes and that in closed field regions is…
Increasing evidence for coronal heating contributions from cooler solar atmospheric layers, notably quiet Sun (QS) conditions, challenges standard solar atmospheric descriptions of bright transition region (TR) emission. As such, questions to the role of dynamic QS transients in contributing to the total coronal energy budget are elevated. Using observations from the {\it Atmospheric Imaging Assembly} and {\it Heliosemic Magnetic Imager} on board the {\it Solar Dynamics Observatory}, and numerical model extrapolations of coronal magnetic fields, we investigate a dynamic QS transient energetica…
Thermal non-equilibrium (TNE) is believed to be a potentially important process in understanding some properties of the magnetically closed solar corona. Through one-dimensional hydrodynamic models, this paper addresses the importance of the numerical spatial resolution, footpoint heating timescales and background heating on TNE. Inadequate transition region (TR) resolution can lead to significant discrepancies in TNE cycle behaviour, with TNE being suppressed in under-resolved loops. A convergence on the periodicity and plasma properties associated with TNE required spatial resolutions of les…
The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. We study the area response with a time-dependent 2D MHD loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal co…
Parker (1983) suggested a mechanism for the formation of current sheets (CSs) in the solar atmosphere. His main idea was that the tangling of coronal magnetic field lines by photospheric random flows facilitates the continuous formation of CSs in the solar atmosphere. This part of his idea represents one of the many ways by which the turbulent convection zone drives the formation of coherent structures and CSs in the solar atmosphere. Other mechanisms include emerging magnetic flux, interaction of current filaments, and explosive magnetic structures. However, there are two unproven assumptions…
Context. The solar corona is heated to high temperatures of the order of 10^{6} K. The coronal energy budget and specifically possible mechanisms of coronal heating (wave, DC-electric fields, ..) are poorly understood. This is particularly true as far as the formation of X-ray bright points (BPs) is concerned. Aims. Investigation of the energy budget with emphasis on the relative role and contribution of adiabatic compression versus current dissipation to the formation of coronal BPs. Methods. Three-dimensional resistive MHD simulation starts with the extrapolation of the observed magnetic fie…
