quiet-Sun Corona Research Articles

Kelvin-Helmholtz instability and heating in oscillating loops perturbed by power-law transverse wave drivers

Context. Instabilities in oscillating loops are believed to be essential for dissipating the wave energy and heating the solar coronal plasma. Aims. Our aim is to study the development of the Kelvin-Helmholtz (KH) instability in an oscillating loop that is driven by random footpoint motions. Methods. Using the PLUTO code, we performed 3D simulations of a straight gravitationally stratified flux tube. The loop footpoints are embedded in chromospheric plasma, in the presence of thermal conduction and an artificially broadened transition region. Using drivers with a power-law spectrum, one with a red noise spectrum and one with the low-frequency part subtracted, we excited standing oscillations and the KH instability in our loops, after one-and-a-half periods of the oscillation. Results. We see that our broadband drivers lead to fully deformed, turbulent loop cross-sections over the entire coronal part of the loop due to the spatially extended KH instability. The low RMS velocity of our driver without the low-frequency components supports the working hypothesis that the KH instability can easily manifest in oscillating coronal loops. We report for the first time in driven transverse oscillations of loops the apparent propagation of density perturbations due to the onset of the KH instability, from the apex towards the footpoints. Both drivers input sufficient energy to drive enthalpy and mass flux fluctuations along the loop, while also causing heating near the driven footpoint of the oscillating loop, which becomes more prominent when a low-frequency component is included in the velocity driver. Finally, our power-law driver with the low-frequency component provides a RMS input Poynting flux of the same order as the radiative losses of the quiet-Sun corona, giving us promising prospects for the contribution of decayless oscillations in coronal heating.

Energy estimation of small-scale jets from the quiet-Sun region

Context. Solar jets play a role in coronal heating and the supply of solar wind. Aims. In this study, we calculate the energies of 23 small-scale jets emerging from a quiet-Sun region in order to investigate their contributions to coronal heating. Methods. We used data from the High-Resolution Imager (HRI) of the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter. Small-scale jets were observed by the HRIEUV 174 Å passband in the high cadence of 6 s. These events were identified by the time–distance stacks along the trajectories of jets. Using the simultaneous observation from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), we also performed a differential emission measure (DEM) analysis on these small-scale jets to obtain the physical parameters of plasma, which enabled us to estimate the kinetic and thermal energies of the jets. Results. We find that most of the jets exhibit common unidirectional or bidirectional motions, while some show more complex behaviors; namely, a mixture of unidirection and bidirection. A majority of jets also present repeated eruption blobs (plasmoids), which may be signatures of the quasi-periodic magnetic reconnection that has been observed in solar flares. The inverted Y-shaped structure can be recognized in several jets. These small-scale jets typically have a width of ∼0.3 Mm, a temperature of ∼1.7 MK, an electron number density of ≳109 cm−3, with speeds in a wide range from ∼20–170 km s−1. Most of these jets have an energy of 1023–1024 erg, which is marginally smaller than the energy of typical nanoflares. The thermal energy fluxes of 23 jets are estimated to be (0.74–2.96)×105 erg cm−2 s−1, which is almost on the same order of magnitude as the energy flow required to heat the quiet-Sun corona, although the kinetic energy fluxes vary over a wide range because of their strong dependence on velocity. Furthermore, the frequency distribution of thermal energy and kinetic energy both follow the power-law distribution N(E)∝E−α. Conclusions. Our observations suggest that although these jets cannot provide sufficient energy to heat the whole quiet-Sun coronal region, they are likely to account for a significant portion of the energy demand in the local regions where the jets occur.

Fleeting Small-scale Surface Magnetic Fields Build the Quiet-Sun Corona

Arch-like loop structures filled with million Kelvin hot plasma form the building blocks of the quiet-Sun corona. Both high-resolution observations and magnetoconvection simulations show the ubiquitous presence of magnetic fields on the solar surface on small spatial scales of ∼100 km. However, the question of how exactly these quiet-Sun coronal loops originate from the photosphere and how the magnetic energy from the surface is channeled to heat the overlying atmosphere is a long-standing puzzle. Here we report high-resolution photospheric magnetic field and coronal data acquired during the second science perihelion of Solar Orbiter that reveal a highly dynamic magnetic landscape underlying the observed quiet-Sun corona. We found that coronal loops often connect to surface regions that harbor fleeting weaker, mixed-polarity magnetic field patches structured on small spatial scales, and that coronal disturbances could emerge from these areas. We suggest that weaker magnetic fields with fluxes as low as 1015 Mx and/or those that evolve on timescales less than 5 minutes are crucial to understanding the coronal structuring and dynamics.

Beyond small-scale transients: A closer look at the diffuse quiet solar corona

Aims. Within the quiet Sun corona imaged at 1 MK, much of the field of view consists of diffuse emission that appears to lack the spatial structuring that is so evident in coronal loops or bright points. Our aim is to determine if these diffuse regions are categorically different in terms of their intensity fluctuations and spatial configuration from the better-studied dynamic coronal features. Methods. We analyzed a time series of observations from Solar Orbiter’s High Resolution Imager in the extreme ultraviolet to quantify the characterization of the diffuse corona at high spatial and temporal resolutions. We then compared this to the dynamic features within the field of view, mainly a coronal bright point. Results. We find that the diffuse corona lacks visible structuring, such as small embedded loops, and that this is persistent over the 25 min duration of the observation. The intensity fluctuations of the diffuse corona, which are within ±5%, are significantly smaller in comparison to the coronal bright point; however, the total intensity observed in the diffuse corona is on the same order as the bright point. Conclusions. It seems inconsistent with our data that the diffuse corona is a composition of small loops or jets or that it is driven by discrete small heating events that follow a power-law-like distribution. We speculate that small-scale processes such as magnetohydrodynamic turbulence might be energizing the diffuse regions, but at this point we cannot offer a conclusive explanation for the nature of this feature.

Propagating brightenings in small loop-like structures in the quiet-Sun corona: Observations from Solar Orbiter/EUI

Brightenings observed in solar extreme-ultraviolet images are generally interpreted as signatures of micro- or nanoflares occurring in the transition region or at coronal temperatures. Recent observations with the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter have revealed the smallest of such brightenings (called campfires) in the quiet-Sun corona. Analyzing EUI 174 Å data obtained at a resolution of about 400 km on the Sun with a cadence of 5 s on 30 May 2020, we report here a number of cases in which these campfires exhibit propagating signatures along their apparently small (3–5 Mm) loop-like structures. The measured propagation speeds are generally between 25 km s−1and 60 km s−1. If the loop plasma is assumed to be at a million Kelvin, these apparent motions would be slower than the local sound speed. Furthermore, these brightenings exhibit nontrivial propagation characteristics such as bifurcation, merging, reflection, and repeated plasma ejections. We suggest that these features are manifestations of the internal dynamics of these small-scale magnetic structures and could provide important insights into the dynamic response (∼40 s) of the loop plasma to the heating events and also into the locations of the heating events themselves.

On the Impulsive Heating of Quiet Solar Corona

Abstract The solar corona consists of a million degree Kelvin plasma. A complete understanding of this phenomenon demands the study of quiet Sun (QS) regions. In this work, we study QS regions in the 171 Å, 193 Å, and 211 Å passbands of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory, by combining the empirical impulsive heating forward model of Pauluhn & Solanki with a machine-learning inversion model that allows uncertainty quantification. We find that there are ≈2–3 impulsive events per minute, with a lifetime of about 10–20 minutes. Moreover, for all the three passbands, the distribution of power-law slope α peaks above 2. Our exploration of correlations among the frequency of impulsive events and their timescales and peak energy suggests that conduction losses dominate over radiative cooling losses. All these findings suggest that impulsive heating is a viable heating mechanism in QS corona.

Extreme-ultraviolet bursts and nanoflares in the quiet-Sun transition region and corona

The quiet solar corona consists of myriads of loop-like features, with magnetic fields originating from network and internetwork regions on the solar surface. The continuous interaction between these different magnetic patches leads to transient brightenings or bursts that might contribute to the heating of the solar atmosphere. The literature on a variety of such burst phenomena in the solar atmosphere is rich. However, it remains unclear whether such transients, which are mostly observed in the extreme ultraviolet (EUV), play a significant role in atmospheric heating. We revisit the open question of these bursts as a prelude to the new high-resolution EUV imagery expected from the recently launched Solar Orbiter. We use EUV image sequences recorded by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) to investigate statistical properties of the bursts. We detect the bursts in the 171 Å filter images of AIA in an automated way through a pixel-wise analysis by imposing different intensity thresholds. By exploiting the high cadence (12 s) of the AIA observations, we find that the distribution of lifetimes of these events peaks at about 120 s. However, a significant number of events also have lifetimes shorter than 60 s. The sizes of the detected bursts are limited by the spatial resolution, which indicates that a larger number of events might be hidden in the AIA data. We estimate that about 100 new bursts appear per second on the whole Sun. The detected bursts have nanoflare-like energies of 1024 erg per event. Based on this, we estimate that at least 100 times more events of a similar nature would be required to account for the energy that is required to heat the corona. When AIA observations are considered alone, the EUV bursts discussed here therefore play no significant role in the coronal heating of the quiet Sun. If the coronal heating of the quiet Sun is mainly bursty, then the high-resolution EUV observations from Solar Orbiter may be able to reduce the deficit in the number of EUV bursts seen with SDO/AIA at least partly by detecting more such events.

An Observational Test of Solar Plasma Heating by Magnetic Flux Cancellation

Abstract Recent observations suggest that magnetic flux cancellation may play a crucial role in heating the Sun’s upper atmosphere (chromosphere, transition region, corona). Here, we intended to validate an analytic model for magnetic reconnection and consequent coronal heating, driven by a pair of converging and canceling magnetic flux sources of opposite polarities. For this test, we analyzed photospheric magnetic field and multiwavelength ultraviolet/extreme ultraviolet (EUV) observations of a small-scale flux cancellation event in a quiet-Sun internetwork region over a target interval of 5.2 hr. The observed cancellation event exhibits a converging motion of two opposite-polarity magnetic patches on the photosphere and redshifted Doppler velocities (downflows) therein consistently over the target interval, with a decrease in magnetic flux of both polarities at a rate of 1015 Mx s−1. Several impulsive EUV brightenings, with differential emission measure values peaked at 1.6–2.0 MK, are also observed in the shape of arcades with their two footpoints anchored in the two patches. The rate of magnetic energy released as heat at the flux cancellation region is estimated to be in the range of (0.2–1) × 1024 erg s−1 over the target interval, which can satisfy the requirement of previously reported heating rates for the quiet-Sun corona. Finally, both short-term (a few to several tens of minutes) variations and long-term (a few hours) trends in the magnetic energy release rate are clearly shown in the estimated rate of radiative energy loss of electrons at temperatures above 2.0 MK. All these observational findings support the validity of the investigated reconnection model for plasma heating in the upper solar atmosphere by flux cancellation.

First Radio Evidence for Impulsive Heating Contribution to the Quiet Solar Corona

Abstract This Letter explores the relevance of nanoflare-based models for heating the quiet Sun corona. Using meterwave data from the Murchison Widefield Array, we present the first successful detection of impulsive emissions down to flux densities of ∼mSFU, about two orders of magnitude weaker than earlier attempts. These impulsive emissions have durations ≲1 s and are present throughout the quiet solar corona. The fractional time occupancy of these impulsive emissions at a given region is ≲10%. The histograms of these impulsive emissions follow a power-law distribution and show signs of clustering at small timescales. Our estimate of the energy that must be dumped in the corona to generate these impulsive emissions is consistent with the coronal heating requirements. Additionally, the statistical properties of these impulsive emissions are very similar to those recently determined for magnetic switchbacks by the Parker Solar Probe (PSP). We hope that this work will lead to a renewed interest in relating these weak impulsive emissions to the energy deposited in the corona, the quantity of physical interest from a coronal heating perspective, and explore their relationship with the magnetic switchbacks observed by the PSP.

Turbulence in a Coronal Loop Excited by Photospheric Motions

Photospheric motions are believed to be the source of coronal heating and of velocity fluctuations detected in the solar corona. A numerical model, based on the shell technique applied on reduced magnetohydrodynamics equations, is used to represent energy injection due to footpoint motions, storage and dissipation of energy in a coronal loop. Motions at the loop bases are simulated by random signals whose frequency-wavenumber spectrum reproduces features of photospheric motions: the p-mode peak and the low-frequency continuum. Results indicate that a turbulent state develops, dominated by magnetic energy, where dissipation takes place in an intermittent fashion. The nonlinear cascade is mainly controlled by velocity fluctuations, where resonant modes are dominant at high frequencies. Low frequency fluctuations present a power-law spectra and a bump at p-mode frequency; similar features are observed in velocity spectra detected in the corona. For typical loop parameters the energy input flux is comparable with that necessary to heat the quiet-Sun corona.

Scaling laws of quiet-Sun coronal loops

We study a series of relations between physical parameters in coronal loops of the quiet Sun reconstructed by combining tomographic techniques and modeling of the coronal magnetic field. We use differential emission measure tomography (DEMT) to determine the three-dimensional distribution of the electron density and temperature in the corona, and we model the magnetic field with a potential-field source-surface (PFSS) extrapolation of a synoptic magnetogram. By tracing the DEMT products along the extrapolated magnetic field lines, we obtain loop-averaged electron density and temperature. Also, loop-integrated energy-related quantities are computed for each closed magnetic field line. We apply the procedure to Carrington rotation 2082, during the activity minimum between Solar Cycles 23 and 24, using data from the Extreme Ultraviolet Imager on board the Solar Terrestrial Relations Observatory (STEREO) spacecraft. We find a scaling law between the loop-average density N and loop length L,Nm∼L-0.35, but we do not find a significant relation between loop-average temperature and loop length. We confirm though the previously found result that loop-average temperatures at the equatorial latitudes are lower than at higher latitudes. We associate this behavior with the presence at the equatorial latitudes of loops with decreasing temperatures along their length (“down” loops), which are in general colder than loops with increasing temperatures (“up” loops). We also discuss the role of “down” loops in the obtained scaling laws of heating flux versus loop length for different heliographic latitudes. We find that the obtained scalings for quiet-Sun loops do not generally agree with those found in the case of AR loops from previous observational and theoretical studies. We suggest that to better understand the relations found, it is necessary to forward model the reconstructed loops using hydrodynamic codes working under the physical conditions of the quiet-Sun corona.

Phase mixing of nonlinear Alfvén waves

Aims. This paper presents 2.5D numerical experiments of Alfvén wave phase mixing and aims to assess the effects of nonlinearities on wave behaviour and dissipation. In addition, this paper aims to quantify how effective the model presented in this work is at providing energy to the coronal volume.Methods. The model is presented and explored through the use of several numerical experiments which were carried out using the Lare2D code. The experiments study footpoint driven Alfvén waves in the neighbourhood of a two-dimensional x-type null point with initially uniform density and plasma pressure. A continuous sinusoidal driver with a constant frequency is used. Each experiment uses different driver amplitudes to compare weakly nonlinear experiments with linear experiments.Results. We find that the wave trains phase-mix owing to variations in the length of each field line and variations in the field strength. The nonlinearities reduce the amount of energy entering the domain, as they reduce the effectiveness of the driver, but they have relatively little effect on the damping rate (for the range of amplitudes studied). The nonlinearities produce density structures which change the natural frequencies of the field lines and hence cause the resonant locations to move. The shifting of the resonant location causes the Poynting flux associated with the driver to decrease. Reducing the magnetic diffusivity increases the energy build-up on the resonant field lines, however, it has little effect on the total amount of energy entering the system. From an order of magnitude estimate, we show that the Poynting flux in our experiments is comparable to the energy requirements of the quiet Sun corona. However a (possibly unphysically) large amount of magnetic diffusion was used however and it remains unclear if the model is able to provide enough energy under actual coronal conditions.

Coronal Elemental Abundances in Solar Emerging Flux Regions

Abstract The chemical composition of solar and stellar atmospheres differs from the composition of their photospheres. Abundances of elements with low first ionization potential (FIP) are enhanced in the corona relative to high-FIP elements with respect to the photosphere. This is known as the FIP effect and it is important for understanding the flow of mass and energy through solar and stellar atmospheres. We used spectroscopic observations from the Extreme-ultraviolet Imaging Spectrometer on board the Hinode observatory to investigate the spatial distribution and temporal evolution of coronal plasma composition within solar emerging flux regions inside a coronal hole. Plasma evolved to values exceeding those of the quiet-Sun corona during the emergence/early-decay phase at a similar rate for two orders of magnitude in magnetic flux, a rate comparable to that observed in large active regions (ARs) containing an order of magnitude more flux. During the late-decay phase, the rate of change was significantly faster than what is observed in large, decaying ARs. Our results suggest that the rate of increase during the emergence/early-decay phase is linked to the fractionation mechanism that leads to the FIP effect, whereas the rate of decrease during the later decay phase depends on the rate of reconnection with the surrounding magnetic field and its plasma composition.

The Slowly Varying Corona. I. Daily Differential Emission Measure Distributions Derived from EVE Spectra

Abstract Daily differential emission measure (DEM) distributions of the solar corona are derived from spectra obtained by the Extreme-ultraviolet Variability Experiment (EVE) over a 4 yr period starting in 2010 near solar minimum and continuing through the maximum of solar cycle 24. The DEMs are calculated using six strong emission features dominated by Fe lines of charge states viii, ix, xi, xii, xiv, and xvi that sample the nonflaring coronal temperature range 0.3–5 MK. A proxy for the non-Fe xviii emission in the wavelength band around the 93.9 Å line is demonstrated. There is little variability in the cool component of the corona (T < 1.3 MK) over the 4 yr, suggesting that the quiet-Sun corona does not respond strongly to the solar cycle, whereas the hotter component (T > 2.0 MK) varies by more than an order of magnitude. A discontinuity in the behavior of coronal diagnostics in 2011 February–March, around the time of the first X-class flare of cycle 24, suggests fundamentally different behavior in the corona under solar minimum and maximum conditions. This global state transition occurs over a period of several months. The DEMs are used to estimate the thermal energy of the visible solar corona (of order 1031 erg), its radiative energy loss rate ((2.5–8) erg s−1), and the corresponding energy turnover timescale (about an hour). The uncertainties associated with the DEMs and these derived values are mostly due to the coronal Fe abundance and density and the CHIANTI atomic line database.

Spectroscopic Evidence of Alfvén Wave Damping in the Off-limb Solar Corona

Abstract We investigate the off-limb active-region and quiet-Sun corona using spectroscopic data. The active region is clearly visible in several spectral lines formed in the temperature range of 1.1–2.8 MK. We derive the electron number density using the line ratio method, and the nonthermal velocity in the off-limb region up to the distance of 140 Mm. We compare density scale heights derived from several spectral line pairs with expected scale heights per the hydrostatic equilibrium model. Using several isolated and unblended spectral line profiles, we estimate nonthermal velocities in the active region and quiet Sun. Nonthermal velocities obtained from warm lines in the active region first show an increase and then later either a decrease or remain almost constant with height in the far off-limb region, whereas nonthermal velocities obtained from hot lines show consistent decrease. However, in the quiet-Sun region, nonthermal velocities obtained from various spectral lines show either a gradual decrease or remain almost constant with height. Using these obtained parameters, we further calculate Alfvén wave energy flux in both active and quiet-Sun regions. We find a significant decrease in wave energy fluxes with height, and hence provide evidence of Alfvén wave damping. Furthermore, we derive damping lengths of Alfvén waves in the both regions and find them to be in the range of 25–170 Mm. Different damping lengths obtained at different temperatures may be explained as either possible temperature-dependent damping or by measurements obtained in different coronal structures formed at different temperatures along the line of sight. Temperature-dependent damping may suggest some role of thermal conduction in the damping of Alfvén waves in the lower corona.

The Characteristics of Solar X-Class Flares and CMEs: A Paradigm for Stellar Superflares and Eruptions?

This paper explores the characteristics of 42 solar X-class flares that were observed between February 2011 and November 2014, with data from the Solar Dynamics Observatory (SDO) and other sources. This flare list includes nine X-class flares that had no associated CMEs. In particular our aim was to determine whether a clear signature could be identified to differentiate powerful flares that have coronal mass ejections (CMEs) from those that do not. Part of the motivation for this study is the characterization of the solar paradigm for flare/CME occurrence as a possible guide to the stellar observations; hence we emphasize spectroscopic signatures. To do this we ask the following questions: Do all eruptive flares have long durations? Do CME-related flares stand out in terms of active-region size vs. flare duration? Do flare magnitudes correlate with sunspot areas, and, if so, are eruptive events distinguished? Is the occurrence of CMEs related to the fraction of the active-region area involved? Do X-class flares with no eruptions have weaker non-thermal signatures? Is the temperature dependence of evaporation different in eruptive and non-eruptive flares? Is EUV dimming only seen in eruptive flares? We find only one feature consistently associated with CME-related flares specifically: coronal dimming in lines characteristic of the quiet-Sun corona, i.e. 1 – 2 MK. We do not find a correlation between flare magnitude and sunspot areas. Although challenging, it will be of importance to model dimming for stellar cases and make suitable future plans for observations in the appropriate wavelength range in order to identify stellar CMEs consistently.

THE DETECTION OF UPWARDLY PROPAGATING WAVES CHANNELING ENERGY FROM THE CHROMOSPHERE TO THE LOW CORONA

There have been ubiquitous observations of wave-like motions in the solar atmosphere for decades. Recent improvements to space- and ground-based observatories have allowed the focus to shift to smaller magnetic structures on the solar surface. In this paper, high-resolution ground-based data taken using the Swedish 1 m Solar Telescope is combined with co-spatial and co-temporal data from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) satellite to analyze running penumbral waves (RPWs). RPWs have always been thought to be radial wave propagation that occurs within sunspots. Recent research has suggested that they are in fact upwardly propagating field-aligned waves (UPWs). Here, RPWs within a solar pore are observed for the first time and are interpreted as UPWs due to the lack of a penumbra that is required to support RPWs. These UPWs are also observed co-spatially and co-temporally within several SDO/AIA elemental lines that sample the transition region and low corona. The observed UPWs are traveling at a horizontal velocity of around 17 +- 0.5 km s-1 and a minimum vertical velocity of 42 +- 21 km s-1. The estimated energy of the waves is around 150 W m-2, which is on the lower bound required to heat the quiet-Sun corona. This is a new, yet unconsidered source of wave energy within the solar chromosphere and low corona.

OUTFLOW STRUCTURE OF THE QUIET SUN CORONA PROBED BY SPACECRAFT RADIO SCINTILLATIONS IN STRONG SCATTERING

Radio scintillation observations have been unable to probe flow speeds in the low corona where the scattering of radio waves is exceedingly strong. Here we estimate outflow speeds continuously from the vicinity of the Sun to the outer corona (heliocentric distances of 1.5-20.5 solar radii) by applying the strong scattering theory to radio scintillations for the first time, using the Akatsuki spacecraft as the radio source. Small, nonzero outflow speeds were observed over a wide latitudinal range in the quiet-Sun low corona, suggesting that the supply of plasma from closed loops to the solar wind occurs over an extended area. The existence of power-law density fluctuations down to the scale of 100 m was suggested, which is indicative of well-developed turbulence which can play a key role in heating the corona. At higher altitudes, a rapid acceleration typical of radial open fields is observed, and the temperatures derived from the speed profile show a distinct maximum in the outer corona. This study opened up a possibility of observing detailed flow structures near the Sun from a vast amount of existing interplanetary scintillation data.

Low‐frequency heliographic observations of the quiet Sun corona

AbstractWe present new results of heliographic observations of quiet‐Sun radio emission fulfilled by the UTR‐2 radio telescope. The solar corona investigations have been made close to the last solar minimum (Cycle 23) in the late August and early September of 2010 by means of the two‐dimensional heliograph within 16.5–33 MHz. Moreover, the UTR‐2 radio telescope was used also as an 1‐D heliograph for one‐dimensional scanning of the Sun at the beginning of September 2010 as well as in short‐time observational campaigns in April and August of 2012. The average values of integral flux density of the undisturbed Sun continuum emission at different frequencies have been found. Using the data, we have determined the spectral index of quiet‐Sun radio emission in the range 16.5–200 MHz. It is equal to –2.1±0.1. The brightness distribution maps of outer solar corona at frequencies 20.0 MHz and 26.0 MHz have been obtained. The angular sizes of radio Sun were estimated. It is found that the solar corona at these frequencies is stretched‐out along equatorial direction. The coefficient of corona ellipticity varies slightly during above period. Its mean magnitudes are equal to ≈ 0.75 and ≈ 0.73 at 20.0 MHz and 26.0 MHz, respectively. The presented results for continuum emission of solar corona conform with being ones at higher frequencies. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5 – 0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.