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Duncan H. Mackay

Publications and source records attributed to Duncan H. Mackay.

18 recordsLinked to original sources

Exploring the Solar Poles: The Last Great Frontier of the Sun

Despite investments in multiple space and ground-based solar observatories by the global community, the Sun's polar regions remain unchartered territory - the last great frontier for solar observations. Breaching this frontier is fundamental to understanding the solar cycle - the ultimate driver of short-to-long term solar activity that encompasses space weather and space climate. Magnetohydrodynamic dynamo models and empirically observed relationships have established that the polar field is the primary determinant of the future solar cycle amplitude. Models of solar surface evolution of tilted active regions indicate that the mid to high latitude surges of magnetic flux govern dynamics leading to the reversal and build-up of polar fields. Our theoretical understanding and numerical models of this high latitude magnetic field dynamics and plasma flows - that are a critical component of the sunspot cycle - lack precise observational constraints. This limitation compromises our ability to observe the enigmatic kilo Gauss polar flux patches and constrain the polar field distribution at high latitudes. The lack of these observations handicap our understanding of how high latitude magnetic fields power polar jets, plumes, and the fast solar wind that extend to the boundaries of the heliosphere and modulate solar open flux and cosmic ray flux within the solar system. Accurate observation of the Sun's polar regions, therefore, is the single most outstanding challenge that confronts Heliophysics. This paper argues the scientific case for novel out of ecliptic observations of the Sun's polar regions, in conjunction with existing, or future multi-vantage point heliospheric observatories. Such a mission concept can revolutionize the field of Heliophysics like no other mission concept has - with relevance that transcends spatial regimes from the solar interior to the heliosphere.

astro-ph.IM

A Statistical Comparison of EUV Brightenings Observed by SO/EUI with Simulated Brightenings in Non-potential Simulations

The High Resolution Imager (HRI_EUV) telescope of the Extreme Ultraviolet Imager (EUI) instrument onboard Solar Orbiter has observed EUV brightenings, so-called campfires, as fine-scale structures at coronal temperatures. The goal of this paper is to compare the basic geometrical (size, orientation) and physical (intensity, lifetime) properties of the EUV brightenings with regions of energy dissipation in a non-potential coronal magnetic field simulation. In the simulation, HMI line-of-sight magnetograms are used as input to drive the evolution of solar coronal magnetic fields and energy dissipation. We applied an automatic EUV brightening detection method to EUV images obtained on 30 May 2020 by the HRI_EUV telescope. We applied the same detection method to the simulated energy dissipation maps from the non-potential simulation to detect simulated brightenings. We detected EUV brightenings with density of 1.41x10^{-3} brightenings/Mm^2 in the EUI observations and simulated brightenings between 2.76x10^{-2} - 4.14x10^{-2} brightenings/Mm^2 in the simulation, for the same time range. Although significantly more brightenings were produced in the simulations, the results show similar distributions of the key geometrical and physical properties of the observed and simulated brightenings. We conclude that the non-potential simulation can successfully reproduce statistically the characteristic properties of the EUV brightenings (typically with more than 85% similarity); only the duration of the events is significantly different between observations and simulation. Further investigations based on high-cadence and high-resolution magnetograms from Solar Orbiter are under consideration to improve the agreement between observation and simulation.

astro-ph.SR

Eruptions from coronal bright points: A spectroscopic view by IRIS of a mini-filament eruption, QSL reconnection, and reconnection-driven outflows

The present study investigates a mini-filament eruption associated with cancelling magnetic fluxes. The eruption originates from a small-scale loop complex commonly known as a Coronal Bright Point (CBP). The event is uniquely recorded in both the imaging and spectroscopic data taken with IRIS. We analyse IRIS spectroscopic and slit-jaw imaging observations as well as images taken in the extreme-ultraviolet channels of AIA, and line-of-sight magnetic-field data from HMI onboard the SDO. We also employ an NLFFF relaxation approach based on the HMI magnetogram time series. We identify a strong small-scale brightening as a micro-flare in a CBP. The mini-eruption manifests with the ejection of hot (CBP loops) and cool (mini-filament) plasma recorded in both the imaging and spectroscopic data. The micro-flare is preceded by the appearance of an elongated bright feature in the IRIS slit-jaw 1400 A images located above the polarity inversion line. The micro-flare starts with an IRIS pixel size brightening and propagates bi-directionally along the elongated feature. We detect in both the spectral and imaging IRIS data and AIA data, strong flows along and at the edges of the elongated feature which we believe represent reconnection outflows. Both edges of the elongated feature that wrap around the edges of the erupting MF evolve into a J-type shape creating a sigmoid appearance. A quasi-separatrix layer (QSL) is identified in the vicinity of the polarity inversion line by computing the squashing factor Q in different horizontal planes of the NLFFF model. The QSL reconnection site has the same spectral appearance as the so-called explosive events identified by strong blue- and red-shifted emission, thus answering a long outstanding question about the true nature of this spectral phenomenon.

astro-ph.SR

Determining the source and eruption dynamics of a stealth CME using NLFFF modelling and MHD simulations

Coronal mass ejections (CMEs) that exhibit weak or no eruption signatures in the low corona, known as stealth CMEs, are problematic as upon arrival at Earth they can lead to geomagnetic disturbances that were not predicted by space weather forecasters. We investigate the origin and eruption of a stealth event that occurred on 2015 January 3 that was responsible for a strong geomagnetic storm upon its arrival at Earth. To simulate the coronal magnetic field and plasma parameters of the eruption we use a coupled approach. This approach combines an evolutionary nonlinear force-free field model of the global corona with a MHD simulation. The combined simulation approach accurately reproduces the stealth event and suggests that sympathetic eruptions occur. In the combined simulation we found that three flux ropes form and then erupt. The first two flux ropes, which are connected to a large AR complex behind the east limb, erupt first producing two near-simultaneous CMEs. These CMEs are closely followed by a third, weaker flux rope eruption in the simulation that originated between the periphery of AR 12252 and the southern polar coronal hole. The third eruption coincides with a faint coronal dimming, which appears in the SDO/AIA 211 A observations, that is attributed as the source responsible for the stealth event and later the geomagnetic disturbance at 1 AU. The incorrect interpretation of the stealth event being linked to the occurrence of a single partial halo CME observed by LASCO/C2 is mainly due to the lack of STEREO observations being available at the time of the CMEs. The simulation also shows that the LASCO CME is not a single event but rather two near-simultaneous CMEs. These results show the significance of the coupled data-driven simulation approach in interpreting the eruption and that an operational L5 mission is crucial for space weather forecasting.

astro-ph.SR

Simulating the Coronal Evolution of Bipolar Active Regions to Investigate the Formation of Flux Ropes

The coronal magnetic field evolution of 20 bipolar active regions (ARs) is simulated from their emergence to decay using the time-dependent nonlinear force-free field method of Mackay et al. A time sequence of cleaned photospheric line-of-sight magnetograms, that covers the entire evolution of each AR, is used to drive the simulation. A comparison of the simulated coronal magnetic field with the 171 and 193 A observations obtained by the Solar Dynamics Observatory (SDO)/ Atmospheric Imaging Assembly (AIA), is made for each AR by manual inspection. The results show that it is possible to reproduce the evolution of the main coronal features such as small- and large-scale coronal loops, filaments and sheared structures for 80% of the ARs. Varying the boundary and initial conditions, along with the addition of physical effects such as Ohmic diffusion, hyperdiffusion and a horizontal magnetic field injection at the photosphere, improves the match between the observations and simulated coronal evolution by 20%. The simulations were able to reproduce the build-up to eruption for 50% of the observed eruptions associated with the ARs. The mean unsigned time difference between the eruptions occurring in the observations compared to the time of eruption onset in the simulations was found to be ~5 hrs. The simulations were particularly successful in capturing the build-up to eruption for all four eruptions that originated from the internal polarity inversion line of the ARs. The technique was less successful in reproducing the onset of eruptions that originated from the periphery of ARs and large-scale coronal structures. For these cases global, rather than local, nonlinear force-free field models must be used. While the technique has shown some success, eruptions that occur in quick succession are difficult to reproduce by this method and future iterations of the model need to address this.

astro-ph.SR

Identifying solar-like magnetic cycles with Zeeman-Doppler-Imaging (ZDI)

We are reaching the point where spectropolarimetric surveys have run for long enough to reveal solar-like magnetic activity cycles. In this paper we investigate what would be the best strategy to identify solar-like magnetic cycles and ask which large-scale magnetic field parameters best follow a solar-type magnetic cycle and are observable with the Zeeman-Doppler-Imaging (ZDI) technique. We approach these questions using the 3D non-potential flux transport simulations of \cite{Yeates2012} modelling the solar vector magnetic field over 15 years (centred on solar cycle 23). The flux emergence profile was extracted from solar synoptic maps and used as input for a photospheric flux transport model in combination with a non-potential coronal evolution model. We synthesise spectropolarimetric data from the simulated maps and reconstruct them using ZDI. The ZDI observed solar cycle is set into the context of other cool star observations and we present observable trends of the magnetic field topology with time, sunspot number and S-index. We find that the axisymmetric energy fraction is the best parameter of the ZDI detectable large-scale field to trace solar-like cycles. Neither the surface averaged large-scale field or the total magnetic energy is appropriate. ZDI seems also to be able to recover the increase of the toroidal energy with S-index. We see further that ZDI might unveil hints of the dynamo modes that are operating and of the global properties of the small-scale flux emergence like active latitudes.

astro-ph.SR

Eruptions from coronal hole bright points: observations and non-potential modelling

A single case study of a CBP in an equatorial coronal hole with an exceptionally large size is investigated to extend our understanding of the formation of mini-filaments, their destabilisation and the origin of the eruption triggering the formation of jet-like features recorded in the extreme-ultraviolet (EUV) and X-ray emission. We aim to explore the nature of the so-called micro-flares in CBPs associated with jets in coronal holes and mini coronal mass ejections in the quiet Sun. Co-observations from the Atmospheric Imaging Assembly (AIA) and Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory, and GONG Halpha images are used together with a Non-Linear Force Free Field (NLFFF) relaxation approach, where the latter is based on a time series of HMI line-of-sight magnetograms. A mini-filament (MF) that formed beneath the CBP arcade around 3-4 h before the eruption is seen in the Halpha and EUV AIA images to lift up and erupt triggering the formation of an X-ray jet. No significant photospheric magnetic flux concentration displacement (convergence) is observed and neither is magnetic flux cancellation between the two main magnetic polarities forming the CBP in the time period leading to the MF liftoff. The CBP micro-flare is associated with three flare kernels that formed shortly after the MF liftoff. No observational signature is found for reconnection beneath the erupting MF. The applied NLFFF modelling successfully reproduces both the CBP loop complex as well as the magnetic flux rope that hosts the MF during the build-up to the eruption.

astro-ph.SR

Investigation of the Middle Corona with SWAP and a Data-Driven Non-Potential Coronal Magnetic Field Model

The large field-of-view of the Sun Watcher using Active Pixel System detector and Image Processing (SWAP) instrument on board the PRoject for Onboard Autonomy 2 (PROBA2) spacecraft provides a unique opportunity to study extended coronal structures observed in EUV in conjunction with global coronal magnetic field simulations. A global non-potential magnetic field model is used to simulate the evolution of the global corona from 1 September 2014 to 31 March 2015, driven by newly emerging bipolar active regions determined from Helioseismic and Magnetic Imager (HMI) magnetograms. We compare the large-scale structure of the simulated magnetic field with structures seen off-limb in SWAP EUV observations. In particular, we investigate how successful the model is in reproducing regions of closed and open structures; the scale of structures; and compare the evolution of a coronal fan observed over several rotations. The model is found to accurately reproduce observed large-scale off-limb structures. When discrepancies do arise they mainly occur off the east solar limb due to active regions emerging on the far side of the Sun, which cannot be incorporated into the model until they are observed on the Earth-facing side. When such ``late'' active region emergences are incorporated into the model, we find that the simulated corona self-corrects within a few days, so that simulated structures off the west limb more closely match what is observed. Where the model is less successful, we consider how this may be addressed, through model developments or additional observational products.

astro-ph.SR

Understanding the plasma and magnetic field evolution of a filament using observations and Nonlinear force-free field modelling

We present observations and magnetic field models of an intermediate filament present on the Sun in August 2012, associated with a polarity inversion line that extends from AR 11541 in the east into the quiet sun at its western end. A combination of SDO/AIA, SDO/HMI, and GONG H alpha data allow us to analyse the structure and evolution of the filament from 2012 August 4 23:00 UT to 2012 August 6 08:00 UT when the filament was in equilibrium. By applying the flux rope insertion method, nonlinear force-free field models of the filament are constructed using SDO/HMI line-of-sight magnetograms as the boundary condition at the two times given above. Guided by observed filament barbs, both modelled flux ropes are split into three sections each with a different value of axial flux to represent the non-uniform photospheric field distribution. The flux in the eastern section of the rope increases by 4$\times$10$^{20}$ Mx between the two models, which is in good agreement with the amount of flux cancelled along the internal PIL of AR 11541, calculated to be 3.2$\times$10$^{20}$ Mx. This suggests that flux cancellation builds flux into the filament's magnetic structure. Additionally, the number of field line dips increases between the two models in the locations where flux cancellation, the formation of new filament threads and growth of the filament is observed. This suggests that flux cancellation associated with magnetic reconnection forms concave-up magnetic field that lifts plasma into the filament. During this time, the free magnetic energy in the models increases by 0.2$\times$10$^{31}$ ergs.

astro-ph.SR

Eruptions from Quiet Sun Coronal Bright Points. II. Non-Potential Modeling

Our recent observational study shows that the majority of coronal bright points (CBPs) in the quiet Sun are sources of one or more eruptions during their lifetime. Here, we investigate the non-potential time dependent structure of the magnetic field of the CBP regions with special emphasis on the time evolving magnetic structure at the spatial locations where the eruptions are initiated. The magnetic structure is evolved in time using a Non-Linear Force Free Field (NLFFF) relaxation approach, based on a time series of Helioseismic and Magnetic Imager (HMI) longitudinal magnetograms. This results in a continuous time series of NLFFFs. The time series is initiated with a potential field extrapolation based on a magnetogram taken well before the time of the eruptions. This initial field is then evolved in time in response to the observed changes in the magnetic field distribution at the photosphere. The local and global magnetic field structures from the time series of NLFFF field solutions are analysed in the vicinity of the eruption sites at the approximate times of the eruptions. The analysis shows that many of the CBP eruptions reported in Mou etl. (2018) contain twisted flux tube located at the sites of eruptions. The presence of flux ropes at these locations provides in many cases a direct link between the magnetic field structure, their eruption and the observation of mini coronal mass ejections (mini-CMEs). It is found that all repetitive eruptions are homologous. The NLFFF simulations show that twisted magnetic field structures are created at the locations hosting eruptions in CBPs. These twisted structures are produced by footpoint motions imposed by changes in the photospheric magnetic field observations. The true nature of the micro-flares remains unknown. Further 3D data-driven MHD modelling is required to show how these twisted regions become unstable and erupt.

astro-ph.SR

Photospheric observations of surface and body modes in solar magnetic pores

Over the past number of years, great strides have been made in identifying the various low-order magnetohydrodynamic wave modes observable in a number of magnetic structures found within the solar atmosphere. However, one aspect of these modes that has remained elusive, until now, is their designation as either surface or body modes. This property has significant implications on how these modes transfer energy from the waveguide to the surrounding plasma. Here, for the first time to our knowledge, we present conclusive, direct evidence of these wave characteristics in numerous pores which were observed to support sausage modes. As well as outlining methods to detect these modes in observations, we make estimates of the energies associated with each mode. We find surface modes more frequently in the data, and also that surface modes appear to carry more energy than those displaying signatures of body modes. We find frequencies in the range of ~2 to 12 mHz with body modes as high as 11 mHz, but we do not find surface modes above 10 mHz. It is expected that the techniques we have applied will help researchers search for surface and body signatures in other modes and in differing structures to those presented here.

astro-ph.SR

Simulating the Coronal Evolution of AR 11437 using SDO/HMI Magnetograms

The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. (2011). A sequence of photospheric line-of-sight magnetograms produced by SDO/HMI are used to drive the simulation and continuously evolve the coronal magnetic field of the active region through a series of non-linear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/AIA observations show that many aspects of the active region's observed coronal evolution are reproduced. In particular, it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occur on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at 14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and 10 hours before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.

astro-ph.SR

Simulating AIA observations of a flux rope ejection

Extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) are providing new insights into the early phase of CME evolution. Observations now show the ejection of magnetic flux ropes from the solar corona and how they evolve into CMEs. These observations are difficult to interpret in terms of basic physical mechanisms and quantities. To fully understand CMEs we need to compare equivalent quantities derived from both observations and theoretical models. To this end we aim to produce synthesised AIA observations from simluations of a flux rope ejection. To carry this out we include the role of thermal conduction and radiative losses, both of which are important for determining the temperature distribution of the solar corona during a CME. We perform a simulation where a flux rope is ejected from the solar corona. From the density and temperature of the plasma in the simulation we synthesise AIA observations. The emission is then integrated along the line of sight using the instrumental response function of AIA. We sythesise observations of AIA in the channels at 304 A, 171 A, 335 A, and 94 A. The synthesised observations show a number of features similar to actual observations and in particular reproduce the general development of CMEs in the low corona as observed by AIA. In particular we reproduce an erupting and expanding arcade in the 304 A and 171 A channels with a high density core. The ejection of a flux rope reproduces many of the features found in the AIA observations. This work is therefore a step forward in bridging the gap between observations and models, and can lead to more direct interpretations of EUV observations in terms of flux rope ejections. We plan to improve the model in future studies in order to perform a more quantitative comparison.

astro-ph.SR

The Solar Cycle Variation of Topological Structures in the Global Solar Corona

The distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the separatrix surfaces that divide the field into topologically distinct regions, allowing open-field regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections (separators) are important likely energy release sites. This paper investigates, throughout the solar cycle, the nature of coronal magnetic-field topologies that arise under the potential-field source-surface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potential-field source-surface model. Hence, variations in the coronal skeleton are studied over three solar cycles. Key building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes. Many open-field regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar dipole. A strong dipole results in a simple large-scale structure involving just two large polar open-field regions, but, at short radial distances between plus or minus 60 deg latitude, the small-scale topology is complex. If the solar dipole if weak, as in the recent minimum, then the low-latitude quiet-sun magnetic fields may be globally significant enough to create many disconnected open-field regions at low latitudes, in addition to the two polar open-field regions.

astro-ph.SR

Dynamic properties of bright points in an active region

Context. Bright points (BPs) are small-scale, magnetic features ubiquitous across the solar surface. Previously, we have observed and noted their properties for quiet Sun regions. Here, we determine the dynamic properties of BPs using simultaneous quiet Sun and active region data. Methods. High spatial and temporal resolution G-band observations of active region AR11372 were obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope. Three subfields of varying polarity and magnetic flux density were selected with the aid of magnetograms obtained from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Bright points within these subfields were subsequently tracked and analysed. Results. It is found that BPs within active regions display attenuated velocity distributions with an average horizontal velocity of ~0.6 km/s, compared to the quiet region which had an average velocity of 0.9 km/s. Active region BPs are also ~21% larger than quiet region BPs and have longer average lifetimes (~132s) than their quiet region counterparts (88 s). No preferential flow directions are observed within the active region subfields. The diffusion index (gamma) is estimated at ~1.2 for the three regions. Conclusions. We confirm that the dynamic properties of BPs arise predominately from convective motions. The presence of stronger field strengths within active regions is the likely reason behind the varying properties observed. We believe that larger amounts of magnetic flux will attenuate BP velocities by a combination of restricting motion within the intergranular lanes and by increasing the number of stagnation points produced by inhibited convection. Larger BPs are found in regions of higher magnetic flux density and we believe that lifetimes increase in active regions as the magnetic flux stabilises the BPs.

astro-ph.SR

Effect of gravitational stratification on the propagation of a CME

Our aim is to study the role of gravitational stratification on the propagation of CMEs. In particular, we assess how it influences the speed and shape of CMEs and under what conditions the flux rope ejection becomes a CME or when it is quenched. We ran a set of MHD simulations that adopt an eruptive initial magnetic configuration that has already been shown to be suitable for a flux rope ejection. We varied the temperature of the backgroud corona and the intensity of the initial magnetic field to tune the gravitational stratification and the amount of ejected magnetic flux. We used an automatic technique to track the expansion and the propagation of the magnetic flux rope in the MHD simulations. From the analysis of the parameter space, we evaluate the role of gravitational stratification on the CME speed and expansion. Our study shows that gravitational stratification plays a significant role in determining whether the flux rope ejection will turn into a full CME or whether the magnetic flux rope will stop in the corona. The CME speed is affected by the background corona where it travels faster when the corona is colder and when the initial magnetic field is more intense. The fastest CME we reproduce in our parameter space travels at 850 km/s. Moreover, the background gravitational stratification plays a role in the side expansion of the CME, and we find that when the background temperature is higher, the resulting shape of the CME is flattened more. Our study shows that although the initiation mechanisms of the CME are purely magnetic, the background coronal plasma plays a key role in the CME propagation, and full MHD models should be applied when one focusses especially on the production of a CME from a flux rope ejection.

physics.space-ph

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4e16 - 1e19 Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4e16 Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.

astro-ph.SR

Modeling the Dispersal of an Active Region: Quantifying Energy Input into the Corona

In this paper a new technique for modeling non-linear force-free fields directly from line of sight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive force-free equilibria over long periods of time. It is illustrated by applying it to MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a 4 day period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to small scale convective cells. Through studying the build up of magnetic energy in the model, it is found that such small scale motions may inject anywhere from $2.5-3 \times 10^{25}$ erg s$^{-1}$ of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After 4 days the build-up of free energy is 10% that of the corresponding potential field. This energy buildup, is sufficient to explain the radiative losses at coronal temperatures within the active region. Small scale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new high resolution, high cadence observations from the SDO:HMI and SDO:AIA instruments.

astro-ph.SR