quan-lin fan et al- a possible interpretation of burst-like characteristics of explosive events

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Commun. Theor. Phys. (Beijing, China) 41 (2004) pp. 790–794c International Academic Publishers Vol. 41, No. 5, May 15, 2004

A Possible Interpretation of Burst-Like Characteristics of Explosive Events∗

FAN Quan-Lin,† FENG Xue-Shang, and XIANG Chang-QingLaboratory for Space Weather, Center for Space Science and Applied Research, the Chinese Academy of Sciences,P.O. Box 8701, Beijing 100080, China

(Received September 15, 2003)

Abstract Explosive events have been observed to occur consecutively in bursts at intermittent locations along the boundary near the opposite p olarity. The aim of the present paper is to explore a possible mechanism to interpret thisburst-like characteristic of explosive events. The 2D magnetohydrodynamic (MHD) numerical simulations with resistivity have been carried out to reproduce the intermittent spatial-temporal magnetic reconnection events taking place along the long, compressible current sheet. The observed density enhancements in previously published results have been verifiedto be associated to magnetic reconnection sites. Late observational evidences, which support present attempts, have alsobeen found, at least in morphological evolution of the consecutive explosive events.

PACS numbers: 96.60.Rd, 52.35.Vd, 95.30.Qd, 52.30.Cv, 02.60.CbKey words: explosive events, magnetic reconnection, magnetohydrodynamics, solar transition region, numer-

ical simulation

1 Introduction

Extreme ultraviolet (EUV) explosive events are a

prominent class of phenomena characterizing the solar

transition region. These highly energetic small-scale phe-

nomena have been frequently detected throughout the

quiet and active regions of the Sun for almost 20 years.[1−9]

High spectral, spatial, and temporal resolution UV obser-

vations report that most of the events are characterized by

strongly non-Gaussian line profiles formed at solar transi-

tion region temperature.[1] For a complete statistical de-

scription of explosive events, one can refer to Ref. [2]. The

main conclusions derived from these studies[1−10] can be

summarized as follows. Explosive events’ average size cov-

ers areas from one to a few arcsec squared, and observed

velocities range between ±250 km · s−1 and ±50 km · s−1

with lifetimes between 20 and 200 seconds and typical en-

ergies of the order of 1023 ∼1025 erg.

Explosive events have been considered to be a man-

ifestation of magnetic reconnection occurring in the

Sun.[3,5,6,11,12] Dere et al . noted that the Doppler veloci-

ties in explosive events are comparable to the local Alfven

speed, which would be expected if magnetic reconnection

played a significant role.[3,11] Innes et al . revealed that the

time variation and spatial structure of explosive eventsare consistent with bi-directional plasma jets produced

by magnetic reconnection.[5] Chae et al . found that they

are rather preferentially occurring in regions with weak

and mixed polarity fluxes, which display magnetic neu-

tral lines and are often associated with a cancellation of

photospheric magnetic flux.[6]

To date, there are also extensive numerical studies of

phenomena associated with explosive events. The asym-

metric interaction between a newly emerging intranetwork

magnetic flux and the pre-existing coronal field was nu-

merically studied by Jin et al . in a 2-dimensional mag-

netohydrodynamic (2D MHD) codes.[13] Innes and Toth

suggested that the ongoing magnetic reconnection has pro-

duced the blue- and red-shifted Doppler components ob-

served during explosive events.[14] Yet the effects due to

radiative losses, thermal conduction, and other heating

sources have been neglected under ad hoc assumptions.

In a series of related investigations, Roussev et al . have

explored the dynamical response of various transition re-

gion conditions to a magnetic reconnection event, involv-ing line synthesis of two resonance transition region lines,

namely C IV 1548.2 A and O VI 1031.9 A.[12,15,16] In

another series of recent numerical work, the effect of so-

lar gravity was taken into consideration to model mag-

netic reconnection in 2D stratified physical configurations,

considering non-equilibrium ionization.[17,18] On the other

hand, parallel progresses have been made in 1D hydrody-

namic (HD) models, also including a treatment of non-

ionization equilibrium to calculate the resulting spectra.

Attempts have been made, to some extent, in computing

the observable consequence, where observable quantities

of small-scale explosive events can be extracted from evo-

lutions of (E)UV emission line profiles or line-shifts simu-

lated numerically.[19,20]

An important feature of explosive events should be

mentioned. Both Dere et al .[3] and Chae et al .[6] have

observed explosive events occurring in bursts at intermit-

tent locations along the boundary separating opposite po-

larity elements. In the examples of explosive events listed

∗The project supported by National Natural Science Foundation of China under Grant Nos. 40104006, 40204010, 40374056, and 40336053†E-mail: [email protected]



No. 5 A Possible Interpretation of Burst-Like Characteristics of Explosive Events 791

by Perez et al .[21] either events located very closely or

consecutive events occurring in short time intervals have

been reported. Following the suggestion that the explosive

events might represent repetitive fast magnetic reconnec-

tions in solar transition region,[6] the present investiga-

tion is aimed at examining a possible interpretation of the

burst-like nature of explosive events, based on the simu-

lated results of consecutive magnetic reconnection events

in a current sheet. The next section contains our adopted

prescription and the choice of initial driver of magnetic re-

connection. Then we give our numerical results and some

conclusions.

2 Magnetohydrodynamic Simulations

In the present study we consider a transition re-

gion/lower coronal atmosphere represented by an inviscid

gas with a specific heat ratio of γ = 5/3 in the pres-

ence of magnetic field. The weakly ionized plasma is ap-

proximately described by the one-fluid model, which is justified when the coupling between ions and neutrals is

very strong.[22] Effects of non-equilibrium ionization have

not been involved. It would be reasonable to incorporate

the strong density stratification in the lower atmosphere.

However the unaffordable computational costs due to the

very fine grid system needed will make the present 2D sim-

ulation impractical. For simplicity, gravitational accelera-

tion is ignored. Then we solve numerically the nonlinear,

time-dependent, resistive compressible MHD equations in

conservative form in (x, y) 2D Cartesian coordinates. An

anomalous resistivity model is introduced, as described

below. Heat loss and gain are taken into account, in-

cluding Ohmic heating, the nonlinear field-aligned thermal

conduction, and radiative losses. The conduction coeffi-

cient is taken to be the classical Spitzer type, i.e., propor-

tional to T 5/2, where T is temperature. For the radiative

loss function, we choose the updated form presented by

Cook et al .,[23] which takes advantage of new estimates of

the coronal elemental abundances.

The initial magnetic configuration is in magneto-

hydrostatic equilibrium with anti-parallel magnetic fields

in the (x, y)-plane (positive in y > 0, and negative in

y < 0), between which there is a current sheet at y = 0

with a characteristic width L0, the half-thickness of the

initial current sheet. The units of the background plasmaare outlined in Table 1 from observations.[24,25] In this

initial condition, the density distribution is prescribed

uniform everywhere. Then, the so-called plasma beta

(the ratio of kinetic gas pressure to magnetic pressure)

at |y| L0 (far from the current sheet) is taken to be

β = 0.056.

Table 1 Characteristic values of the mentioned parameters.

Physical quantities‡ Values Physical quantities Values

Magnetic field B∞ 2.5

×10−3 Tesla Length L0 5.0

×106 m

Density ρ∞ 3.35 × 10−11 kg · m−3 Velocity V A∞ = B∞/√µ0ρ∞ 3.85 × 105 m · s−1

Temperature T ∞ 2.5 × 105 K Time t∞ = L0/V A∞ 13.0 s‡Observational values based on the TRACE EUV data and SOHO/MDI observations.

Systems with a single initially prescribed region

of anomalous resistivity, usually located at the center

of a current sheet, have been studied systematically

in 2D (mostly symmetrical) simulations[26,27] and 3D

performance.[28] In the present model, the resistivity is

introduced into the domain in an ad hoc manner. Three

spots of locally enhanced resistivity are introduced into

the current sheet for 0 ≤ t ≤ t0 as initial driver of magnetic reconnection (with t0 = 3 in all cases below):

η(x, y, t ≤ t0) = max{η0; Ai exp[−(ri/r0)3] (i = 1, 2, 3)},

where ri is the distance to the i-th spot at position

[(i · 40L0)/4, 0]. The parameter r0, taken equal to L0,

characterizes the width of the spots, and Ai denote their

amplitudes. Some scatter of the amplitudes can be ex-

pected in natural systems due to variation of plasma pa-

rameters along the current sheet. Therefore, the ampli-

tudes are assumed to be 0.0010, 0.0025, 0.0055, respec-

tively (1:2.5:5.5), arranged symmetrically about the center

of the computational box, contrast to the amplitudes of

1.2:1:1.2 in a perfectly symmetrical manner in the simula-

tions of Schumacher and Kliem.[29] For t ≥ t0, the anoma-

lous resistivity is determined self-consistently from the lo-

cal value of the current density, j, for every time step: an

anomalous resistivity is set,

η(x, y, t ≥ t0

) = η0 , j ≤ jcr ,

C 1(| j| − jcr) + C 2η0 , j ≥ jcr ,

if a threshold jcr is exceeded, where C 1 = 0.005 and

C 2 = 5.0. The background resistivity η0 is set equal to

0.0005 in view of conditions in the lower coronal zone.

The improved high order Lax–Friedrichs TVD finite

difference model[30] is used to solve the one-fluid MHD

equations, which has been proved possessing the advan-

tage of quick convergence as well as robust ability of high

resolution in a simulation on a formation mechanism of in-

terplanetary magnetic cloud boundaries.[31] A projection



792 FAN Quan-Lin, FENG Xue-Shang, and XIANG Chang-Qing Vol. 41

scheme employing an iterative Poisson solver maintains

the·B = 0 constraint numerically.[32] A fractional time-

stepping technique is adopted for the heat conduction

part. Open boundary conditions are chosen at the four

boundaries, where the normal derivatives of all variables

vanish, except for the normal component of B, which is

determined from the solenoidal condition. A rectangular

computation box of size 0 ≤ x ≤ 40L0, −8L0 ≤ y ≤ 8L0

is assumed. A uniform grid system, 161 × 321, is used

with ∆x = 5∆y = 0.25L0. Such a choice guarantees a

sufficiently high numerical resolution needed in the dif-

fusion region width in the y direction while a reasonable

cost-effectiveness is maintained. In contrast to the various

2D MHD experiments by Roussev et al .[12] and Galsgaard

and Roussev,[17] where the simulations are focused on a

few initial Alfven-crossing time units, the numerical model

adopted here can run reasonably for a long time about

hundred Alfven units. This is essential for our investiga-

tion of the bursty nature of explosive events. In practice,all the calculations are carried out in the non-dimensional

form based on several physical parameters listed in Ta-

ble 1.

3 Numerical Results and Discussions

3.1 Intermittent Spatial-Temporal Magnetic

Reconnection Events

Five snapshots of the morphological evolution of the

magnetic field lines are presented in Fig. 1, showing tear-

ing, reconnection, coalescence, and plasmoid ejection in

the dynamic current sheet at t = 40, 55, 80, 95, and 115.The ad hoc localized resistivity causes current dissipa-

tion and forces the magnetic field line in the diffusion re-

gion to start reconnection. A magnetic reconnection event

can be found at the point of largest resistivity value at t =

40 in the left part of the domain (5 < x < 15) represent-

ing by an X -point topology. One usually attributes this

development phase to the MHD tearing instabilities.[29]

However, we conjecture that thermal instabilities may also

contribute to this evolution. The present initial state does

not have thermal equilibrium in the ambient background

plasma, since it has not included the background coronalheating rate as Roussev’s,[15] which is in reality a compli-

cated function of the other plasma variables and devoid

of an explicit suitable expression till now. Therefore, de-

spite the fact that the system does start with a mechanical

equilibrium between the gas and magnetic pressures, the

evolution is also thermally driven.[33]

Once the reconnection process starts to take place, the

unequal amplitudes of the resistivity are expected to play

crucial roles in the following nonlinear evolutions. Fig-

ure 1 shows that they have induced different magnetic

diffusion along the current sheet, resulting in consecutive

spatial-temporal reconnection events, though the initial

driver has been switched off after t0 = 3. As a dynami-

cal consequence of both tearing and thermal instabilities,

two additional reconnection events, around x = 20, and

x = 30, respectively, can be identified successively at in-

termittent positions of the initial current sheet. A multi-X pattern has been developed at t = 55. While from

another point of view the close-up of the magnetic field

lines of adjacent X -points reveals the formation of mag-

netic islands, or plasmoid, which could be attributed to a

pitchfork bifurcation of the magnetic field line topology [34]

or the “induced tearing” mechanism.[29]

Fig. 1 Two-dimensional distributions of magnetic fieldlines at t = 40, 55, 80, 95, and 115, respectively (fromthe top to the bottom). Series of magnetic reconnectionevents occurred during the dynamic current sheet evolu-tion.

However, the system is intrinsically instable. At t =

80, the coalescence instability has been initiated. The out-flows in the x-direction, i.e. the bi-directional reconnection

jets,[14] have transported the left/right outer plasmoid out

of the domain. New magnetic reconnection event due to

magnetic island coalescence, or annihilation of weak X -

point, has almost ended at t = 95, driven primarily by

the effects of small difference between the initial anoma-

lous resistivity spots and the jet-like flows toward the box

center. Afterwards the plasmoid is accelerated to a sub-

stantial fraction of the Alfven velocity and ejected across



No. 5 A Possible Interpretation of Burst-Like Characteristics of Explosive Events 793

the right-hand open boundary of the computation box

(t = 115), leading to an asymmetric Petschek-like fast re-

connection configuration. Since we are mainly interested

in the magnetic reconnection events occurring at intermit-

tent locations, we will not go further into the complicated

physics involved. The role of radiative losses, thermal con-

duction, etc. and related parameter study are not the fo-

cus of the present study either, which can be referred to

the former numerical investigations by Roussev et al .,[15]

Forbes and Malherbe,[33] Yokoyama and Shibata.[35]

3.2 Density Enhancements in Explosive Events

Simulated

The observed density enhancements of explosive events

have been associated with magnetic reconnection sites,

where such density variations can be as large as a factor

of two.[24] The present MHD simulations discover simi-

lar density enhancement features, which reveal the burst-

like nature of explosive events in another more evidential

manner. Figure 2 presents the time series of plasma rela-

tive mass density (ρ − ρ∞)/ρ∞ with respect to the initial

density distribution ρ∞ in x-direction at the same time

corresponding to Fig. 1. In order to display the density

variation impressively, the data sampling is carried out by

passing along the outer edge of the diffusion region, i.e.

y = 0.5 for t = 40 and 55, and y = 0.8 for t = 80, 95, and

115, respectively.

Fig. 2 One-dimensional distributions of plasma relativemass density (ρ−ρ∞)/ρ∞. The adjacent panels from topto bottom are corresponding to those in Fig. 1 at the fivetimes.

The plasma density variations presented in Fig. 2

show several characteristics. The burst-like occurrences of

plasma density enhancements develop temporally at inter-

mittent locations. On the other hand, the enhancement

amplitude is multiplied in a positive way as the reconnec-

tion events take place repetitively along the current sheet.

One possible explanation of this phenomenon suggested by

Perez and Doyle[24] is that the energy deposition by mag-

netic reconnection events caused compression and, there-

fore, density enhancements. The one-dimensional results

display that the density enhancement regions are located

in the proximity of the X -topological structures, especially

confined at the O-points, or plasmoid positions. If we ex-

tend the concept of magnetic reconnection site from the

reconnected x-point to a region including the compressive

areas nearby, the outcomes illustrated by the profiles in

Fig. 2 are strongly supported by the effort of associating

the observed density enhancements to magnetic reconnec-

tion sites.[24] The two peaks of the relative density profile

at t = 115 and the drop-like configuration of the magnetic

field lines in the last panel of Fig. 1 is due to the upcom-

ing reconnection events resulting from the recurrence of

anomalous resistivity, which has been discussed by Schu-

macher and Kliem.[29] This evolutionary feature appears

repeatedly as the local current density exceeds the thresh-old of kinetic instability.

3.3 Further Observational Support

The burst-like nature of explosive events has been men-

tioned in several observational examples.[3,6,21] Recently,

Perez and Doyle[24] have attempted to associate the ob-

served density enhancements to magnetic reconnection

sites, on the basis of analyzing the proximity in time and

co-spatial location of the explosive events and their ob-

served burst-like occurrences. Besides, we have noticed

that the above simulated scenario might bear relevant andconsistent characteristics of a late observational case to

some extent.

In August, 1999, the active region NOAA 8668 located

at N22E54 was jointly observed by the Solar and Helio-

spheric Observatory (SOHO), the Transition Region and

Coronal Explorer (TRACE) and the Big Bear Solar Ob-

servatory for several days.[25] Figures 4 and 5 in the paper

of Chae[25] display many small-scale UV/EUV brighten-

ings that scattered both in space and time. Specifically, a

brightening was first seen at R1, which is a small site of

magnetic reconnection (12:14:59 UT). Within a few min-

utes before its full development, however, a second jet-like

brightening occurred at R2, another site of flux cancella-

tion (12:16:29 UT). An EUV-emitting structure possessing

a huge amount of mass as indicated by H (12:25:29 UT)

is formed and lifted as a result of the nearly simultane-

ous detachments of magnetic field lines at the two sites,

R1 and R2 (for more details see Ref. [25], and a related

numerical simulation work by Fan et al .[36]). In respect

of these observations the magnetic field configurations in

Fig. 1 are helpful for their possible interpretations. It



794 FAN Quan-Lin, FENG Xue-Shang, and XIANG Chang-Qing Vol. 41

might be reasonable to associate the brightenings with

the spatial-temporal burst of the explosive events in the

current sheet. A more detailed comparison between distri-

butions of plasma parameters, including velocity, temper-

ature, and density simulated and the observed quantities,

and their underlying correlation are beyond the scope of

the present paper and will be elucidated elsewhere. There-

fore, at least in the morphologic evolution of the consec-

utive explosive events, this observation reasonably proves

the physical reasonableness of the present simulations.

4 Summary

We numerically examined a possible interpretation of

the burst-like nature of explosive events, by associating

the repetitive occurrence of explosive events to a series of

many discrete small magnetic reconnection events. The

simulations are carried out in terms of several key physi-

cal parameters adopted from previously published obser-

vations. The initial state is in magneto-hydrostatic equi-librium but not in thermal equilibrium. Magnetic recon-

nection is initiated through ad hoc enhanced resistivity in

the current structure during the early phase of the recon-

nection process. Inclusion of anomalous resistivity is then

introduced when some critical state in the current sheet

is reached after the initial driver is turned off.

Here we have attributed the origin of explosive events

to magnetic reconnection, which has been believed by

other authors. The present 2D MHD model has repro-

duced the bursty features of explosive events through sim-ulating intermittent spatial-temporal magnetic reconnec-

tion events taking place along the long, compressible cur-

rent sheet. The observed plasma density enhancements

are verified in our simulations. Results of density vari-

ations at magnetic positions including the X -point and

compressive regions nearby support the former attempts

to connect the observed density enhancements to magnetic

reconnection sites.

In conclusion we believe that our efforts shed further

light into the physics and modeling of the complexity of

explosive events, though additional comparisons betweenmodels and observations are needed. A full 2D MHD sim-

ulation, taking account into stratified physical configura-

tion and the non-equilibrium ionization, is underway.

References

[1] G.E. Brueckner and J.-D.F. Bartoe, Ap. J. 272 (1983)329

[2] K.P. Dere, J.-D.F. Bartoe, and G.E. Brueckner, Sol. Phys.123 (1989) 41.

[3] K.P. Dere, J.-D. F. Bartoe, G.E. Brueckner, J. Ewing,and P. Lund, J. Geophys. Res. 96 (1991) 9399.

[4] D.E. Innes, P. Brekke, D. Germerott, and K. Wilhelm,Sol. Phys. 175 (1997a) 341.

[5] D.E. Innes, B. Inhester, W.I. Axford, and K. Wilhelm,Nature 386 (1997b) 811.

[6] J. Chae, H. Wang, C.-Y. Lee, P.R. Goode, and U.Schuehle, Ap. J. 497 (1998) L109.

[7] L. Teriaca, M.S. Madjarska, and J.G. Doyle, Sol. Phys.200 (2001) 91.

[8] L. Teriaca, M.S. Madjarska, and J.G. Doyle, A & A 392

(2002) 309.

[9] M.S. Madjarska and J.G. Doyle, A & A 382 (2002) 319.

[10] A.R. Winebarger, A.G. Emslie, J.T. Mariska, and H.P.Warren, Ap. J. 565 (2002) 1298.

[11] K.P. Dere, Adv. Space Res. 14 (1994) 13.

[12] I. Roussev, K. Galsgaard, R. Erdelyi, and J.G. Doyle, A& A 370 (2001a) 298.

[13] S.P. Jin, B. Inhester, and D.E. Innes, Sol. Phys. 168

(1996) 279.

[14] D.E. Innes and G. Toth, Sol. Phys. 185 (1999) 127.

[15] I. Roussev, K. Galsgaard, R. Erdlyi, and J.G. Doyle, A& A 375 (2001b) 228.

[16] I. Roussev, J.G. Doyle, K. Galsgaard, and R. Erdelyi, A& A 380 (2001c) 719.

[17] K. Galsgaard and I. Roussev, A & A 383 (2002) 685.

[18] I. Roussev and K. Galsgaard, A & A 383 (2002) 697.

[19] L.M. Sarro, R. Erdelyi, J.G. Doyle, and M.E. Perez, A &A 351 (1999) 721.

[20] L. Teriaca, J.G. Doyle, R. Erdelyi, and L.M. Sarro, A &

A352

(1999) L99.[21] M.E. Perez, J.G. Doyle, R. Erdelyi, and L.M. Sarro, A &A 342 (1999) 279.

[22] E.G. Zweibel, Ap. J. 340 (1989) 550.

[23] J.W. Cook, C.-C. Cheng, V.L. Jacobs, and S.K. Antio-chos, Ap. J. 338 (1989) 1176.

[24] M.E.Perez and J.G. Doyle, A & A 360 (2000) 331.

[25] J. Chae, Ap. J. 584 (2003) 1084.

[26] M. Scholer, J. Geophys. Res. 94 (1989) 8805.

[27] M. Ugai, Phys. Plasmas 2 (1995) 388.

[28] M. Hesse and J. Birn, J. Geophys. Res. 99 (1994) 8565.

[29] J. Schumacher and B. Kliem, Phys. Plasmas 4 (1997)3533.

[30] X.S. Feng, S.T. Wu, Q.L. Fan, and F. S. Wei, Chin. J. of Space Sci. 22 (2002) 300.

[31] Q.L. Fan, F.S. Wei, and X.S. Feng, Commun. Theor.Phys. (Beijing, China) 40 (2003) 247.

[32] G. Toth, J. Comput. Phys. 161 (2000) 605.

[33] T.G. Forbes and J.M. Malherbe, Sol. Phys. 135 (1991)361.

[34] E.R. Priest, D.P. Lonie, and V.S. Titov, J. Plasma Phys.56 (1996) 507.

[35] T. Yokoyama and K. Shibata, Ap. J. 474 (1997) L61.

[36] Q.L. Fan, X.S. Feng, C.Q. Xiang, and D.K. Zhong, Phys.

Plasmas 10 (2003) 4575.

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