Download Electric current neutralization in solar active regions

Electric current neutralization in solar active regions
K. Dalmasse1, G. Aulanier2, P. Démoulin2, B. Kliem3, T. Török4 & E. Pariat2
2 LESIA,
1 CISL/HAO,
NCAR, P.O. Box 3000, Boulder, CO 80307-3000, USA; [email protected]
Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, F-92195, Meudon, France
3 Institut für Physik und Astrnonmie, Universität Postdam, Karl Liebknecht-Str. 24-25, D-14476 Postdam, Germany
4 Predictive Science, Inc., 9990 Mesa Rim Road, Suite 170, San Diego, CA 92121, USA
Abstract
A recurring question in solar physics concerns the neutralization of electric currents in active regions (ARs), i.e., whether or not the total electric current integrated over a single magnetic polarity of an AR vanishes. This question was recently revisited using three-dimensional (3D) magnetohydrodynamic
(MHD) numerical simulations of magnetic flux emergence into the solar atmosphere. Such simulations showed that flux emergence can generate a substantial net current in ARs. Another source of AR currents are photospheric horizontal flows. Regarding the latter, our present aim is to determine the
conditions for the occurrence of net vs. neutralized currents. Using 3D MHD simulations, we impose line-tied, quasi-static, photospheric twisting and shearing motions to a bipolar potential magnetic field. We find that such flows: (1) produce both direct and return currents, and (2) can generate force free
magnetic fields with a net current. We demonstrate that neutralized currents are in general produced only in the absence of magnetic shear at the photospheric polarity inversion line - a special condition rarely observed in ARs that produce eruptive flares. Our results thus predict that mostly net currents
should be derived from observations of eruptive ARs obtained, e.g., with the high-sensitivity Spectro-Polarimeter of the Hinode/Solar Optical Telescope.
1. Current-neutralization predictions in confined magnetic flux tubes
Active region (AR) currents are believed to be formed by two main mechanisms: (1) the emergence of
confined, current-carrying magnetic flux tubes from the convection zone (CZ) into the corona (e.g.,
Leka et al. 1996), and (2) the stressing of the coronal magnetic field by sub-photospheric and
photospheric horizontal flows (e.g., Klimchuck & Sturrock 1992).
2.5D considerations predict that confined (current-carrying) magnetic flux tubes should possess
neutralized currents (e.g., Melrose 1991, Parker 1996), meaning that the total current, I, integrated
over a single magnetic polarity of the flux tube vanishes. This requires that the main (or direct)
current connecting the flux tube polarities is surrounded by a shielding (or return) current of equal
total strength and opposite direction (see Fig. 1).
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Figure 1: Expected distribution of electric currents for a
confined, twisted magnetic flux tube in cylindrical
geometry. The direct (respectively return) current is in
red (respectively blue). The green and black lines are
twisted magnetic field lines.
Direction of
current density
4. Proposed method for studying current-neutralization in observations
2. Three main issues with predictions of current-neutralization
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Such predictions are based on simplified geometries that do not consider the possible effects that
become relevant in a fully 3D geometry (e.g., partial magnetic flux emergence).
Early observational studies using vector-magnetograms indicate that ARs with neutralized currents
may be as numerous as ARs possessing a net current (e.g., Wheatland 2000, Georgoulis et al. 2012).
The Torus Instability (TI) –believed to be one of the main drivers of coronal mass ejections (CMEs)–
requires the existence of a net coronal electric current in ARs (e.g., Kliem & Török 2006, Démoulin &
Aulanier 2010, Forbes 2010).
These issues bring the following questions:
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Can a net current exist in ARs?
What would be the origin of such a net current?
Such simplified considerations have been used to argue that both magnetic flux emergence and
photospheric horizontal flows should in principle produce current-neutralized ARs.
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In earlier observational studies seemingly finding current-neutralized ARs, the neutralization of
current was assumed to occur because the total current integrated over each magnetic polarity was of
the order of the noise level, i.e., 1011 A. This criterion alone is not suited for analyzing the
neutralization of currents since it is the ratio of the return to the direct current, i.e., the neutralization
ratio (Eq. (1)), that really quantifies the degree of current-neutralization. In addition, the existence of
net currents is inevitably related to magnetically sheared PILs (see Eq. (2)). We therefore suggest the
four following key steps for observational studies of current-neutralization in ARs:
1.  identifying the dominant sign of magnetic twist/shear to identify the sign of the direct and
return currents;
2.  computing Izdirect, Izreturn, and their sum (= total current) in each magnetic polarity of a given
AR to highlight and remove the possible contributions from connection with surrounding
ARs. Note that these currents should be computed using the method of Gosain et al.
(2014) to remove the parasitic contributions from the fibrils;
3.  computing the neutralization ratio (Eq. (1)) averaged over all magnetic polarities;
4.  quantifying the mean (signed and unsigned) magnetic shear along the PIL (e.g., Bobra &
Couvidat 2015).
3. Net currents in 3D MHD simulations of photospheric horizontal flows
We address the question of current-neutralization in ARs by means of 3D, zero-β, MHD simulations of photospheric twisting motions imposed on a bipolar potential field (Fig. 2), using the Observationally-driven
High-order scheme MHD code (OHM; Aulanier et al. 2005).
We consider four twisting runs, T{1;2;3;4}, such T3
that w(T1) < w(T2) < w(T3)S2< w(T4), where w is the vortex
SP2 width (further details on the twisting profiles can be found in Section 2 of Dalmasse et al. 2015).
Each run induces the generation of a core of strong and compact negative-direct currents surrounded by a shell of weaker and diffuse positive-return currents (e.g., as reported by Török & Kliem 2003 for
similar models), as shown in Fig. 3 where the photospheric vertical current density for T2 and T4 before each simulation terminated is displayed.
The right panel of Fig. 3 presents the evolution of the neutralization ratio, Ineut., computed in the positive magnetic polarity for each twisting simulation
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y
y
y
Twist ing mot ions
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x
Twist
4 cases
x
Shear
4 cases
ing profiles
Twist
Figure 2: Left:
Initial
potential magnetic field. The synthetic magnetogram is
represented at the z=0 plane with superposed ±[0.25; 0.5; 0.75] isocontours of Bz
(solid purple and dashed cyan lines) and selected field lines (red). Right: 3D views of
the magnetic field generated by the photospheric twisting motions for the T3 run.
Current-carrying (respectively potential)
u /cfield lines are in color (respectiveley black).
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x
T1
T2
T3
T4
x
Shear PIL
2 cases
t/tA
Figure 3: Left and Center: Photospheric (z=0) current maps, jz, at the end of the simulations T{2;4}. White and black
coloring display positive and negative currents, respectively. The solid purple and dashed cyan lines represent ±0.25 isocontours
of Bz. From the positive magnetic polarity, the direct current is negative while the return current is positive. Right: Evolution
of the neutralization ratio, Ineut., at z=0 in the positive magnetic polarity for each twisting simulation.
Bt(PIL) T2 T4 Figure 4: Photospheric transverse magnetic field at the PIL, Bt(PIL) (green
arrows), plotted over the photospheric Bz (gray shading), for a currentneutralized (T2; left) and a net current (T4; right) simulation. The solid
purple and dashed cyan lines represent ±0.25 isocontours of Bz.
A
Bz
T1
T2
T3
T4
These results are also supported by photospheric shearing simulations (see Section 4 of Dalmasse et al. 2015). In fact, using Ampère’s law and decomposing the magnetic field of our simulations into a potential, Bp,
and a current-carrying component, Bj, one can show –after some algebra (see Section 5.2 of Dalmasse et al. 2015 for further details)– that the total current in the positive magnetic polarity is
y
Shearing profiles
Bz
S1
S2
S3
S4
SP1
SP2
(2)
where dl is the line element along C, C being a closed curve defined such that (i) C includes the PIL, and (ii) the surface enclosed by C is much larger than the surface where the currents are generated by the
These
two choices ensure that all the currents that are transferred to the magnetic field are fully enclosed by C.
A
Bz photospheric motions.ux/c
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Eq. (2) is non-zero only in the presence of a net magnetic shear at the PIL. This shows that force-free net currents naturally arise from the build up of magnetic shear at PILs.
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Can a net current exist in ARs?
Yes, 3D MHD simulations show that photospheric motions and magnetic flux emergence (see Török et
al. 2014 for the latter) can dynamically produce force-free net currents in ARs.
What would be the origin of such a net current?
Such a net current arise from the development of magnetic shear along PILs.
ARs producing eruptive flares are mostly associated with (strongly) sheared PILs (e.g., Falconer et al.
2002, Georgoulis et al. 2012). We thus predict that mostly net currents should be derived from
observations of eruptive ARs. This would be relatively easy to estimate from systematic analyses as
proposed in Section 4, using the high-sensitivity Spectro-Polarimeter of the Hinode/Solar Optical
Telescope.
Ineut.
y
Bz
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Izreturn
Bz
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(1)
where Izdirect and Izreturn respectively refer to the total direct and return currents. It shows that photospheric horizontal flows can generate force-free net currents.
T1
T2 is induced for simulations generating a stronger magnetic shear
As summarized in Fig. 4, we find that (1) a net current develops simultaneously with magnetic shear at the PIL,Iand
(2)
a
stronger
net
current
z
T3
at the PIL.
T4
x
x
x
x
Contain neutralized currents
Contain a net current
Izdirect
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5. Conclusions
References
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