Quan-Lin Fan et al- Simulation of small-scale coronal explosives due to magnetic reconnections

8/3/2019 Quan-Lin Fan et al- Simulation of small-scale coronal explosives due to magnetic reconnections

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Simulation of small-scale coronal explosives due to magnetic reconnections

Quan-Lin Fan, Xue-Shang Feng, Chang-Qing Xiang, and Ding-Kun ZhongSIGMA Weather Group, Laboratory for Space Weather, Center for Space Science and Applied Research,Chinese Academy of Sciences, P.O. Box 8701, Beijing 100080, China

Received 7 July 2003; accepted 29 August 2003

The dynamics of small-scale explosive phenomena in the lower corona have been simulated by

solving the compressible magnetohydrodynamic equations. Numerical results show that themagnetic reconnections in a long coronal current sheet consist of a series of discrete smallreconnection events, coalescence of magnetic islands, and plasmoid ejections, corresponding to theexplosive events occurring intermittently and as bursts in a mentioned observational case. Thegeneration of magnetic islands via multiple-X-point reconnection and their coalescence processes,to some extent, are qualitatively similar to the sequence of brightenings in the active region NOAA8668. The strong ejections are possibly related to the recorded extreme ultraviolet EUV emittingstructures. Morphological comparison and quantitative check of the plasma parameters support thiscandidate mechanism, and the idea that explosive events that appear to last long may not be singleevents, but a succession of explosive events either resolved or unresolved. The temporal energyconversion process is also examined. 2003 American Institute of Physics.DOI: 10.1063/1.1620999

Besides the large-scale eruptive phenomena occurring inthe solar atmosphere,1 namely coronal mass ejectionsCMEs, prominence eruptions, and large two-ribbon flares,there is a host of small-scale impulsive phenomena in thecorona and chromosphere,2 4 including small flares, x-raybright points, transition-region explosive events, surges, andsprays. These small-spatial events have gained much atten-tion, especially those in the solar transition region,5 8 sincethey are now widely believed to involve coronal heating,particle acceleration, etc. Accordingly, the main features ofthe small-scale explosive events derived from these studies

can be summarized to have an average size along the slitequal to 2 arcs 1500 km approximately, the observed ve-locities ranging between 250 and 50 km s1, and thelifetime distribution ranging between 20 and 200 s with anaverage value of 40 s.

Nowadays, solar explosive events are believed to be amanifestation of magnetic reconnection on the Sun and theconcept of the current sheet is a general recourse in explain-ing such phenomena. It is difficult to maintain a current sheetand thus store energy in it because a variety of magnetohy-drodynamic MHD and kinetic plasma instabilities can con-vert the stored magnetic energy to other types of energythrough magnetic reconnection, leading to a series of solar

explosive events ranging from nonresolvable eventsnanoflares up to the largest flares. For example, it issuggested that the ongoing magnetic reconnection has pro-duced the blue- and red-shifted Doppler components ob-served during explosive events, represented by the bi-directional outflow jets.2 The idea that the asymmetricreconnection between newly emerging intranetwork mag-netic field flux and pre-existing network flux causes the ex-plosive events in the solar atmosphere has been explored in atwo-dimensional 2D numerical experiment.5 In another se-ries of related investigations, explosive events in the solar

transition region in a 2D environment have been numericallystudied under the assumption of non-equilibriumionization.6 8 To date, several numerical work have success-fully predicted some signatures of violent flares in the co-rona, involving fast magnetic reconnection model with a cur-rent sheet.911 Attempts to associate a pulsating decimetriccontinuum solar flare radio burst event with a 2D MHD mag-netic reconnection model have proved to be successful,where the highly dynamic reconnection processes are consis-tent with the observed irregular or quasi-periodicemissions.12 However, MHD simulations without Ohmic

heating and other heat sources

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need improvements for un-derstanding the intrinsic nature of small explosives. The pre-vious related MHD studies6 8 would be more satisfactory ifa sufficiently realistic initial physical condition representingsolar transition region had been adopted. It should also bepointed out that the results on large two-ribbon flares or flar-ing loops cannot readily extended to the small-scale explo-sive events.9,10 It is worth exploring these small-scale explo-sions in depth, and thus giving a firm answer about their truenature.

Here we consider a lower coronal atmosphere repre-sented by an inviscid perfect gas with a specific heat ratio of5/3 in the presence of magnetic field. The weakly ionized

plasma is approximately described by the one-fluid model,which is justified when the coupling between ions and neu-trals is very strong.13 For simplicity, gravitational accelera-tion is ignored. Then we numerically solve the nonlinear,time dependent, resistive compressible MHD equations inconservative form in (x,y) 2D Cartesian coordinates. TheOhmic heating has been added. The anisotropic heat conduc-tion effects working only in the direction along the magneticfield line are taken into account. The conduction coefficientis taken to be the classical Spitzer type, i.e., proportional toT5/2, where T is temperature.

PHYSICS OF PLASMAS VOLUME 10, NUMBER 11 NOVEMBER 2003

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The initial magnetic configuration has a current sheet aty0 with a characteristic width L0 . The field is parallel tothe x axis and varies only along the y axis. The backgroundplasma is in magneto-hydrostatic equilibrium and the initialdensity distribution is assumed to be uniform everywhere,0 . , T are the plasma density and temperature atx0 and y L0 far from the current sheet. The plasmabeta at yL0 is defined as P /(B

2/20), which isequal to 0.056 in our simulations based on theobservations.14 VA is the Alfven speed defined by VAB /

0

and the characteristic time tL0

/VA . Ananomalous resistivity model similar to that of Schumacheret al.15,16 is introduced into the current sheet, where an in-finite chain of spots of locally enhanced resistivity with scat-tered amplitudes are adopted as the initial driver of magneticreconnection. The anomalous resistivity is then determinedself-consistently from the local value of the current density ifa threshold for onset is exceeded. The background resistivity0 is set equal to 0.0005 in view of conditions in the lowercorona.

The simulations are performed on uniform grids with161321 points and x5y0.25L0 in a rectangularcomputation box of size 0x40L0 , 8L0y8L0 . The

improved high order LaxFriedrichs total variation dimin-ishing TVD finite difference model17 is used to solve theequations, which has the advantage of quick convergence aswell as robust ability of high resolution.18 A projectionscheme employing an iterative Poisson solver maintains theB0 constraint numerically.19 A fractional time-steppingtechnique is then adopted for the heat conduction part.Though the problem is assumed to be symmetrical about thex axis2,911 or y axis,15,16 calculation has been performed inthe whole region for the sake of avoiding nonphysical effectscaused by numerical symmetry boundary assumption in thetime-dependent process.20 Open boundary conditions arechosen at the four boundaries, where the normal derivative

of all variables vanishes, except for the normal component ofB, which is determined from the solenoidal condition. Inpractice, all the calculations are carried out in the nondimen-sional form based on several physical parameters listed inTable I.

The typical evolution of the magnetic field lines are de-scribed in Fig. 1, showing tearing, reconnection, and coales-cence in the current sheet, while Fig. 2 shows the corre-sponding images of the temporal development of plasmavelocity, temperature, and relative mass density changes.

The ad hoc localized resistivity causes current dissipa-tion and forces the magnetic field line in the diffusion regionto start reconnecting. An X-point topology can be found at

the point of largest resistivity value at t40 in the left part ofthe domain (5x15). The unequal amplitudes of the re-sistivity have induced different magnetic diffusion along thecurrent sheet, resulting in spatio-temporal reconnections oweto tearing instability, though the initial driver has beenswitched off after t03. As a dynamical consequence of this,a multi-X pattern has been developed at t55. While inanother point of view the close-up of the magnetic field linesof adjacent X-points reveals the formation of magnetic is-lands, or plasmoid, which could be attributed to the inducedtearing mechanism15,16 or a pitchfork bifurcation of themagnetic field line topology.21 However, the system is intrin-sically instable. At t80, the coalescence instability hasbeen initiated. The outflows in the x direction have trans-ported the leftright outer plasmoid out of the domain in Fig.2a. The magnetic island coalescence, or annihilation ofweak X-point has ended at t90 Fig. 1. Afterwards theplasmoid is accelerated to a substantial fraction of the Alfvenvelocity and ejected across the right-hand open boundary ofthe computation box see t105 in Fig. 2, leading to anasymmetric Petschek-type fast reconnection configuration.The role of anomalous resistivity model in the fast reconnec-tion mechanism and related parameter tests are beyond the

FIG. 1. Series of magnetic reconnection events occurred during the dynamiccurrent sheet evolution. Magnetic filed lines are shown at t40, 55, 80, 90,and 105, respectively from the top to the bottom.

TABLE I. Characteristic values of mentioned parameters.

Physical quantitiesa Notation Values Physical quantities Notation Values

Magnetic field B 2.5103 T Length L0 5.010

6 mDensity 3.3510

11 kg m3 Velocity VA 3.85105 m s1

Temperature T 2.5105 K Time t 13.0 s

aObservational values of physical quantities based on the TRACE EUV data and SOHO/MDI observations Ref.14.

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focus of present study, which can be referred to the formernumerical investigations.22,23

We have noticed that the simulated scenario above mightbe relevant and consistent with a recent observational case tosome extent. In August 1999, the active region NOAA 8668located at N22E54 was jointly observed by the Solar andHeliospheric Observatory SOHO, the Transition Regionand Coronal Explorer TRACE and the Big Bear Solar Ob-servatory for several days.14,24 Figure 3 illustrates the mor-phology and dynamics of a typical eruption at EUV 171 characteristic of emission from gas at 106 K), by TRACE in

the upper atmosphere above NOAA 8668. It displays manysmall-scale UV/EUV brightenings that are scattered both inspace and time. Specifically, a brightening was first seen atX1 which is a small site of magnetic reconnection 12:14:59UT. Within a few minutes before its full development, how-ever, a second jet-like brightening occurred at X2, anothersite of flux cancellation 12:16:29 UT. An EUV-emittingstructure possessing a huge amount of mass as indicated byO 12:25:29 UT is formed and lifted as a result of the nearlysimultaneous detachments of magnetic field lines at the twosites, X1 and X2 for more details see Refs. 14, 24, andrelated publications therein.

In respect of these observations the magnetic field con-figurations developed in Fig. 1 and the distributions ofplasma parameters in Fig. 2 are helpful for their possibleinterpretations. It might be reasonable to associate the bright-enings with the spatio-temporal establishment of theX-pattern in the current sheet. Plasma heating see Fig. 2band compressing see Fig. 2c take place at these sites fol-lowing the reconnection, which result in an increase in boththe plasma thermal energy and mass density. These X-points,or later the plasmoid, is possibly responsible for the occur-rence of the brightenings at X1 and X2 in Fig. 3. The nor-

malized temperature of the chief plasmoid formed at (10x20) at t55 is as high as 13.0 T , i.e., 3.210

6 K.Relative mass density variance is usually positive at the sitesof reconnections or magnetic islands, meaning that compres-sion happened there. As 40 computational time units passabout 520 s in dimension, where t13 s as listed in TableI, the large island formed by coalescence at t90 hasgained certain thermal energy due to heating relevant to thedynamics see Fig. 2b. It is corresponding to the structureO of EUV-emitting features. According to the TRACE EUVemission Chae14 concluded that the lifted materials eithermoving upward along the apparently open field lines as in-

dicated by U or falling down as indicated by D possess aspeed ranging between 80 and 250 km s1 see Fig. 3 at12:28:29 UT. Further checking the velocity vector at t55 and t90 in Fig. 2a we have found that the left-handplasma moved at a slower speed of about 0.32 VA whereasits counterpart in the right moved at a speed of 0.61 VApassing the boundary. They are rather acceptable if trans-formed into the dimensional ones with the conditions speci-fied above, 120.0 and 235.0 km s1, respectively. Thisproves the physical reasonableness of the present simula-tions.

It is of interest to examine the temporal behavior of thekinetic, magnetic, thermal, and total energy, normalized by

FIG. 2. Temporal development of plasma velocity, temperature, and relative changes in mass density, ( 0)/0 , are shown. The adjacent panels from topto bottom in each column are corresponding to those in Fig. 1 at the five times. a Velocity vector field; b plasma temperature distribution; c relative massdensity, (0)/0 .

FIG. 3. The 16 August 1999 eruptions observed at EUV Fe IX/X 171 byTRACE.

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the total energy at t0 after being integrated over the wholesimulation box shown in Fig. 4. The generation of series ofmagnetic islands in the current sheet mainly results in theplasma heating before t75, when only small kinetic energyenhancement has fulfilled. The obvious monotonous increaseof the kinetic energy during t80 110 is due to the enhanc-ing reconnection driven by the coalescence instability.25 Theconversion of magnetic energy into kinetic energy is stron-gest, exceeding the Ohmic heating and resulting in the strongbulk acceleration of the plasmoid. Note that the magneticenergy is continuously decreasing, which reveals that the re-organization of the magnetic field lines is associated with aseries of magnetic reconnection events, including multiplereconnection, coalescence of magnetic islands, and accelera-tion of the ejections. The facts simulated contribute to under-standing the observations of nearly simultaneous, multi-sitemagnetic reconnection in the transition zone in Fig. 3. It isnot surprising that almost constant total energy is destroyed

after t

75 when the free outflows or persistent inflowsacross the open boundaries also take or bring certain thermaland magnetic energies.

Our numerical results prove that a series of many dis-crete small magnetic reconnection events along the long,compressible current sheet might correspond to the explosiveevents occurring intermittently and as brightenings or burstsin the mentioned observational case. This candidate mecha-nism can principally explain some observational features ofNOAA 8668 discovered by TRACE. The generation of mag-netic islands via multiple-X-point reconnection and theircoalescence processes may be regarded to constitute the se-quence of brightenings in the upper atmosphere at the region

of canceling magnetic features. The strong ejections are pos-sibly related to the recorded EUV-emitting structures. Mor-phological comparison and quantitative check of the plasmavelocity, temperature, and density support the idea that ex-plosive events that appear to last long may not be singleevents, but a succession of explosive events that are eitherresolved or unresolved. Meanwhile, the temporal energyconversion process is also examined.

It should be mentioned that our model situation involvedonly an unstratified atmosphere without the inclusion ofgravity, which might have a nontrivial role in constructingthe initial magneto-hydrostatic configuration.26 On the otherhand our purely 2D MHD modeling could not discriminate

the variations along the solar radius, while the bi-directionaloutflow jet velocities of the observations are derived from aprojection component. Conventionally, the emission measurefrom related observations represents the integrated densitysquare along the line of sight. In this context, there are somedifferences between parameters of the plasmoid simulatedand the observed structures although the results provide es-sential information about the fine structure of the reconnec-

tion event. With these in mind, the three-dimensional 3Deffects of magnetic reconnection analyzed by former MHDnumerical investigations of linkage induced reconnection oftwo magnetic flux tubes,27 spontaneous reconnection modelwith strongly anisotropic initial perturbation28,29 might alle-viate the above discrepancies, which are beyond the scopeand intention of the present study.

ACKNOWLEDGMENTS

We gratefully acknowledge suggestion and assistance byDr. J. Chae and the valuable comments by the anonymousreferees.

This work is jointly supported by the National NaturalScience Foundation of China Grant Nos. 40104006,40204010, and 49925412. The open data policy from theTRACE team is acknowledged.

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FIG. 4. Temporal evolution of the total energy, Etotal , kinetic energy, Ekin ,magnetic energy, Emag , and plasma thermal energy, Etherm , in the computa-tional domain. Normalized by the total energy at t0.

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Quan-Lin Fan et al- Simulation of small-scale coronal explosives due to magnetic reconnections

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