Flux emergence and coronal eruption
aa r X i v : . [ a s t r o - ph . S R ] M a r Astronomy&Astrophysicsmanuscript no. 13502 c (cid:13)
ESO 2018October 29, 2018
Flux emergence and coronal eruption
V. Archontis and A. W. Hood School of Mathematics and Statistics, University of St. Andrews, North Haugh, St. Andrews, Fife, KY16 9SS, UKe-mail: [email protected] e-mail: [email protected] Received ...; accepted ...
ABSTRACT
Aims.
Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also reporton the eruption of a new flux rope when the emerging tube rises into a pre-existing magnetic field in the corona.
Methods.
To study the evolution, we use 3D numerical simulations by solving the time-dependent and resistive MHD equations. Wequalitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface.
Results.
We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetictails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initialfield strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are inqualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twistof the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases,we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on thestrength of the ambient field.
Key words.
Magnetohydrodynamics (MHD) – Methods: numerical – Sun: activity – Sun: corona – Sun: magnetic fields
1. Introduction
Active regions are often associated with episodes of magneticflux emergence from the solar interior (Zwaan (1985) and refer-ences therein). An important question then is, what is the evolu-tion of the magnetic field configuration at the photosphere dur-ing emergence? Observations of emerging flux regions (EFRs)as recorded at the photospheric level, show that they consist oftwo main flux bundles of opposite magnetic polarity that may bethe manifestation of an emerging flux tube. There is strong evi-dence that, in many EFRs, the rising magnetic fields are twisted.The idea of a flux rope configuration has been supported byphotospheric measurements and observations of emerging fieldsin normal and complex (the so-called δ sunspot) ARs (Tanaka1991; Lites et al. 1995; Leka et al. 1996; Canou et al. 2009).A common feature in EFRs is the presence of magnetic tongues or tails , which are connected with the main polarities on the twosides of the PIL of the AR (Li et al. 2007; Canou et al. 2009;Chandra et al. 2009). The appearance of magnetic tails is inter-preted as the result of the emergence of twisted magnetic fieldlines at the photosphere (L´opez Fuentes et al. 2000). However,a study of how the formation and evolution of the tails dependon the physical properties of the emerging field is still missing.Canou et al. (2009) used SOHO / MDI magnetograms and theyreported on the existence of tails , which formed along the PILand accompanied the emergence of magnetic flux in the regionNOAA AR 1808. The shape of the tails was deformed duringthe evolution of the system. They also used the THEMIS vectormagnetogram to reconstruct the coronal field (via a nonlinearforce-free model) and found evidence for a pre-eruptive twistedflux tube above the emerging field.In this paper, for the first time, we focus on the photosphericdistribution of an emerging flux tube and the formation of the tails , showing the relationship between the topology of the tails and the initial tube parameters. We compare some of the nu-merical results with the observations by Canou et al. (2009) andwe find a preliminary, qualitative agreement. Secondly, we re-port on the emergence of the tube into a magnetized coronaand the subsequent coronal eruption of a flux rope. Similarto previous experiments (Magara 2001; Manchester et al. 2004;Archontis & Hood 2008; Archontis & T¨or¨ok 2008; Hood et al.2009), we find that the emerging twisted flux tube and the coro-nal rope are two distinct structures. More importantly, we findthat the evolution of the erupting rope (ejective vs confined erup-tion) depends on the strength of the ambient field.
2. Model
The results in our experiments are obtained from a 3D MHDsimulation. The basic setup of the experiment follows the sim-ulation by Archontis et al. (2005) and consists of a hydrostaticatmosphere and a horizontal twisted magnetic flux tube. Allvariables are made dimensionless by choosing photospheric val-ues of density, ρ ph = × − g cm − , pressure, p ph = . × ergs cm − , and pressure scale height, H ph =
170 km, andby derived units (e.g., magnetic field strength B ph = V ph = . − and time t ph =
25 s). The atmo-sphere includes a subsurface layer ( − ≤ z < ≤ z < ≤ z < ≤ z ≤ − , × [ − , × [ − , x ), transverse ( y ) and vertical ( z ) directions, respectively. Themagnetic flux tube is imposed 1 . Mm below the surface alongthe y -axis. The radius of the tube is 425 Km . The axial field isdefined by B y = B exp( − r / R ) and B φ = α r B y , where r isthe radial distance from the tube axis and α is the twist per unit V. Archontis and A. W. Hood: Flux emergence and coronal eruption
Fig. 1. Top:
SOHO / MDI magnetograms during flux emergence in NOAA AR 10808.
Bottom : Magnetograms produced in thenumerical experiments, at z =
21 and t = t =
125 and t =
175 for the panels 1d-1f respectively. Arrows show the horizontalcomponent of the magnetic field, B hor (panels 1d and 1e, black) and velocity field, V hor (panel 1f, red).length. The twist of the fieldlines around the axis of the tube isuniform. The tube is made buoyant by applying a density pertur-bation ∆ ρ = [ p t ( r ) / p ( z )] ρ ( z ) exp ( − y /λ ), where p t is the pres-sure within the flux tube and λ is the buoyant part of the tube.We perform four experiments: E1 ( B = , α = . , λ = B = , α = . , λ = B = , α = . , λ =
20) andE4 ( B = , α = . , λ =
3. Results
Figure 1 (panels 1a-1c) shows the evolution of the emerging fieldin the NOAA AR 10808. At the beginning (panel 1a) there isa clear appearance of a bipolar region at the photosphere witha North-South orientation. The two polarities progressively di-verge from each other in an approximate East-West direction(panels 1b, 1c). During the evolution of the system, two elon-gated tails or tongues are formed in the wake of the two polari-ties (panel 1b). Initially, the tails possess an apparently coherentshape but as time goes on their structure appears to be more frag-mented on the two sides of the PIL (panel 1c).Panels 1d-1f show the photospheric distribution of theemerging field in our numerical experiments. Panel 1d showsthe bipolar appearance of the emerging field, shortly after itintersects the photosphere. The North-South orientation of thebipolar field is due to the strong initial twist of the flux tube.Eventually (panel 1e), the two main polarities drift apart towardan East-West orientation. Similar to the observations, they arefollowed by magnetic tails that develop an intricate geometricalshape. The projection of the horizontal component of the mag-netic field (arrows) is overplotted onto the magnetograms of pan-els 1d and 1e. At t =
40, the direction of the horizontal magneticfield vectors shows a normal configuration, i.e. from the positiveto the negative polarity, at the PIL. Later on, as more magneticflux emerges from the solar interior, the direction of the mag-netic field reveals a dominant inverse configuration along the PIL. This is due to the rise of the original axis of the twisted fluxtube above this height ( z = not emerge above 2 − tails develop fingers seperated by dips along the curved PIL. Inthe fingers, the magnetic field remains strong (around 70% of themaximum value of B z at this height). At the dips, the magneticfield is weak and the plasma density is relatively small. In fact,we find that there is a good correlation between the location ofthe dips and sites where plasma is moving in the transverse direc-tion. There, the converging flows may reach values up to 3 Km / s and the kinetic energy density becomes larger than the magneticenergy of the field. Thus, it seems that the shape of the magnetic tails is deformed due to inflows that are able to compress andadvect the magnetic field. The origin of the inflows depends onthe evolution of the total pressure ( P tot = magnetic + gas pres-sure) at photospheric heights. Panel 2a shows the distribution of P tot at z =
25, when the outer magnetic field has expanded intothe corona. Due to the rapid expansion, a total pressure deficithas developed at the central area of the EFR and so the plasmamoves towards the small pressure, and deforms the tails .The link between the appearance of the tails and the topologyof the fieldlines is shown in panel 2b. The yellow fieldlines havebeen traced from a far edge of the fingers (at x = − y = tails that are closer to the PIL. They make afull turn around the main axis of the emerging tube connectingthe central area of the two tails. The red fieldlines have beentraced from the region closer to the main positive polarity ofthe field. They are very weakly twisted, possessing an arch-likebundle of fieldlines, joining the two sunspots. These fieldlines donot go through the tails . The above configuration shows that theappearance of the tails is due to the projection of the azimuthalcomponent of the magnetic field at the photosphere. . Archontis and A. W. Hood: Flux emergence and coronal eruption 3 Fig. 2. Top:
The colour-scaled maps correspond to the P tot (2a) and B z (2b, 2c). Contours show B z and arrows the horizontal velocity.Time is t =
165 and z =
25, all for experiment E1.
Bottom:
Distribution of B z for E2 (2d), E3 (2e) and E4 (2f).Panels 2c-2f show the magnetic flux distribution at the pho-tosphere for the experiments E1-E4 respectively. We take as areference case the E1 and we examine the e ff ect of varying theinitial field strength B , λ and α on the appearance of the tails .For comparison, we consider the configuration of the field at acertain time for all experiments. The increase of B (in E2) re-sults in keeping a coherent shape of the tails for a longer timeperiod: at t = tails in E2 are less fragmented than inE1. This is due to the fact that the total pressure within the EFRis large enough for the tails to be distinctively deformed by theinflows. However, we should emphasize that the shape of the tails is altered at a later time, when the two sunspots have seper-ated enough and the magnetic field in the EFR becomes weak.The increase of λ (panel 2e) a ff ects the downward tension of thefieldlines upon the buoyant part of the emerging field. The ten-sion is less in the E3 and the field is emerging at the photosphererelatively faster. Thus, at a certain time, the magnetic field at thephotosphere appears stronger in E3 than in E2. As we mentionedabove, the stronger the magnetic field the less e ff ective is the de-formation of the tails’ shape. This is clearly shown in panel 2e,compared to the E2 (panel 2d). Also, the appearance of the tails critically depends on the initial twist of the emerging field. InE4, the twist parameter α is equal to 0.1 and the emerging fieldis almost horizontal and parallel to the E-W direction, shortlyafter its arrival to the photosphere. We find that there is no tail formation when the emerging field has α < .
2. In this case, theEFR consists of the two sunspots and patches of magnetic fluxwith mixed polarity on the two sides of the PIL. Some of thesephotospheric flux segments are connected with the same field-lines, possessing an overall undulating magnetic system. Thisis reminiscent of the “sea-serpent” configuration, which is pro-duced during the emergence of a magnetic flux sheet. The latter develops undulations when it becomes unstable to the Parker in-stability (Archontis & Hood 2009).
In Section 3.1, we showed that the photospheric fingerprints ofthe EFR in E1 consist of features (e.g. tails ) with a similar con-figuration to observed ARs (e.g. the AR 10808). In addition, theactivity in the region NOAA AR 10808 is known to lead to fila-ment and CME eruption (Canou et al. 2009). Thus, an importantquestion is whether our twisted flux tube model can produce acoronal eruption. Our experiment shows that a new flux rope isformed above the original axis of the emerging flux tube due toreconnection of sheared fieldlines. The reconnection occurs inthe higher photosphere / lower chromosphere in a similar mannerto the model by van Ballegooijen & Martens (1989). A key is-sue is whether this eruption is confined (and, thus, the flux ropecannot fully escape into the outer atmosphere) or ejective . In pre-vious experiments, Archontis & T¨or¨ok (2008) found that the in-clusion of a pre-existing magnetic field in the corona may inducea runaway situation, via reconnection, during which the new fluxrope fully erupts into the outer solar atmosphere. Here, we per-form a similar experiment but using di ff erent initial parametersfor the pre-existing coronal field. Our aim is to study whetherthe field strength of the ambient field a ff ects the rising motion ofthe erupting flux rope.The observed magnetogram in the AR 10808 shows that theemerging flux is rising into a pre-existing field oriented in the E-W direction. The emerging field has a N-S orientation and, thus,the relative orientation of the two fields is about 90 degrees. Tosimulate this, we include a horizontal and uniform magnetic fieldin the corona along the y-axis, parallel to the main axis of the V. Archontis and A. W. Hood: Flux emergence and coronal eruption
Fig. 3.
Height-time profiles of the apex of the emerging field(solid) and the flux rope (dashed) in experiments B1 (black), B2(red) and B3 (green).twisted tube (for example, see Archontis et al. (2005)). To a firstapproximation, this field may correspond to the upper part of theobserved AR’s field, which is likely to be anchored in the sur-rounded di ff use polarities. We find that the field strength of theambient field ( B amb ) plays a critical role in the eruptive motionof the new flux rope. Figure 3 shows the height-time profile ofthe front of the emerging field (solid lines) and the center of thenew flux rope (dashed lines) for three experiments (B1, B2 andB3) where: B amb = .
003 (B1, black lines) , B amb = .
015 (B2,red lines) and B amb = .
03 (B3, green lines) respectively. Theheights are calculated at the vertical midplane after the emerg-ing field enters the transition region.In B1, the front of the expanding tube rises slowly withinthe magnetized corona and eventually it saturates at a height of z ≈
96. The new flux rope is formed at the low atmosphere at t ≈
95 and, thereafter, it follows a similar evolution to the enve-lope field of the expanding tube. Firstly, it rises almost linearlywith time but then it reaches an equilibrium where the magneticpressure force is balanced by the tension of the fieldlines. In thiscase, the eruption is confined: the flux rope is trapped withinthe envelope field. In B2, the apex of the emerging field reacheslower heights during its rising motion. This is because it comesinto contact with an ambient field that is stronger and able todelay the emergence. At the same time, a considerable amountof the rising magnetic flux is removed from the envelope fielddue to reconnection. As a result, the distance between the newflux rope and the front of the envelope field is reduced. As moremagnetic layers above the flux rope are peeled o ff , the down-ward tension of the envelope fieldlines decreases. Eventually,the flux rope experiences an ejective eruption reaching the up-per boundary of the domain very quickly. Due to the short dis-tance between the erupting rope and the closed top boundary, thevelocity of the center of the flux rope is restricted to 197 Km / s .However, the plasma underneath the flux rope is rising with evenhigher velocity at ≈ Km / sec . This is a reconnection jet thatis formed due to internal (i.e. within the EFR) reconnection offieldlines and helps the flux rope to accelerate during its erup-tion. According to these calculations, it is possible that the riseof the flux rope might account for a CME-like eruption. In B3, the eruption of the flux rope is triggered earlier. Again,this is because the stronger ambient field reconnects more e ff ec-tively with the flux above the rope and removes more magneticlayers from the emerging system. However, for the same rea-son, the front of the envelope field rises with a slower rate andthe distance between the new flux rope and the front decreases.As a result, soon after the triggering of the ejective eruption, theerupting rope collides with the front and loses its distinct circularshape, possibly due to reconnection with the ambient field. Afterthe collision, the leading edge of the emerging system is liftedup for a few pressure scale heights. However, it does not recon-nect e ff ectively with the magnetic flux above it, and eventuallyreaches a quasi-static state at a height of z ≈
80. Thus, in B3, theejective flux rope is trapped by the dominant ambient field andnot by the envelope field.
4. Summary and Discussion
In this paper, we have presented a 3D model to study the emer-gence of a twisted flux tube throughout the solar atmosphere.Our model gives new insights into the photospheric distributionof the emerging magnetic field: it consists of a bipolar regionand tails on the two sides of the PIL. The appearance of tails re-veal that the emerging magnetic field is twisted. For small twist,the emerging field possess undulations. Our results predict thatthe irregular structure of the tails is due to the interplay betweenthe flows and the dynamical evolution of the magnetic field. Theconfiguration of the emerging field at the photosphere is in qual-itative agreement with observations (Canou et al. 2009).In agreement with previous simulations, our experimentsshow the eruption of a flux rope, which is formed above the orig-inal axis of the emerging tube. For the first time, we find that thefield strength of a pre-existing coronal magnetic field is a crucialparameter a ff ecting the eruptive phase of the rope. Under thespecific conditions of the present experiments, we found that theeruption is ejective when 0 . < B amb < .
02. For other values,the eruption is confined within the envelope field.The aim of these experiments is not a direct comparison withthe observations, but rather to suggest possible mechanisms thatdrive the dynamical behaviour of the system. Further experi-ments are required to verify the e ff ect of the initial parameters(e.g. field strength, radius, initial atmospheric height and twist,etc.) of the twisted flux tube and the pre-existing field on (a)the characteristics of its photospheric appearance (formation andevolution of the tails , shear and transverse flows, etc.) and (b) thedynamics of the associated eruption. Acknowledgements.
Financial support by the European Comission throughthe SOLAIRE network (MTRM-CT-2006-035484) is gratefully acknowledged.Simulations were performed on the UKMHD consortium cluster, funded bySTFC and a SRIF grant to the University of St Andrews.
References
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