1
Evolution of auroral asymmetries in the conjugate hemispheres
during two substorms
N. Østgaard1 , B. K. Humberset1 , K. M. Laundal1
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Short title: AURORAL ASYMMETRIES DURING SUBSTORMS
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Department of Physics and Technology, University of Bergen, Norway
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Abstract.
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Five hours of simultaneous global imaging data from the conjugate hemispheres
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are used to examine the dynamics of the auroral substorm. Earlier studies have
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demonstrated that substorm onset locations in the two hemispheres are systematically
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displaced due to the orientation of the interplanetary magnetic field. In this paper we
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present, for the first time, how the asymmetric auroras induced by the IMF orientation
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at substorm onset disappears during the expansion phase. We suggest that this is
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the large scale manifestation of auroral arcs as being the sites of magnetic stress
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release. Magnetic stress on field lines with asymmetric footpoints can lead to a net
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hemispherical difference in parallel electric field strength which implies that the auroras
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move with different speeds in the two hemispheres to release the magnetic stress. The
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twisted magnetic fields are rectified, bringing the closed magnetic field lines back to the
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configuration defined by the Earth’s interior.
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1. Introduction
We have previously reported that the locations of the auroral substorm onset in
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the conjugate hemispheres are usually not symmetric [Østgaard et al., 2004, 2005]. The
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degree of asymmetry is strongly correlated with the orientation of the Interplanetary
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Magnetic Field (IMF) or more precisely the IMF clock angle (θc ), that is, the angle
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between the IMF and the Z-axis in the YZ plane of the Geocentric Solar Magnetospheric
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(GSM) reference system. This IMF θc control can be understood as the magnetic stress
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imposed by the IMF on the Earth’s magnetic field from the moment the field lines are
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opened on the dayside, draped down the tail and until they eventually close through
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reconnection in the mid-tail before substorm onset. The result of this tension force on
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open field lines is that only field lines with asymmetric footpoints will reconnect in the
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mid-tail [Østgaard et al., 2005] forming closed field lines with asymmetric footpoints.
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One could also consider the asymmetric cross-tail pressure resulting from a non-zero
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IMF By to explain the partly penetration of IMF By into the closed magnetosphere
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[Khurana et al., 1996]. At the substorm onset energetic electrons travel from the source
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region in the magnetotail on a time scale (∼ 1 s) much shorter than any motion due to
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plasma convection. The auroral arcs can therefore be considered to be the illuminated
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footpoints of the magnetic field lines connecting the two hemispheres. Asymmetric
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footpoints means that these field lines are twisted. This strong IMF θc control of
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the asymmetry of the substorm onset locations was further supported by a statistical
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analysis [Østgaard et al., 2007]. Although, some studies have used By instead of θc to
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organize the substorm onset locations [e.g. Wang et al., 2007], we consider that the
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asymmetry of substorm onset locations, due to the magnetic stress on open field lines or
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the partly penetration of the IMF By into the magnetosphere, is fairly well documented.
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The observed asymmetry is also larger than predicted by the empirical magnetic field
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models [Østgaard et al., 2005].
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Conjugate auroral imaging data have been used to address the asymmetry of
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open-closed boundaries [Stubbs et al., 2005; Laundal et al., 2010] and auroral features
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[Stenbaek-Nielsen et al., 1972; Laundal and Østgaard , 2009] during substorms. In this
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paper we take the investigations of interhemispherical differences one step further, by
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studying, for the first time, the global evolution of the longitudinal asymmetries in the
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substorm auroras.
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2. Data
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On October 22, 2001, the Polar and IMAGE satellites recorded 5 hours of
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continuous global conjugate imaging data capturing two subsequent auroral substorms.
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IMAGE - WIC [Mende et al., 2000] (Lyman-Birge-Hopfield band: 140-180 nm) imaged
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the evolution of the auroral substorm in the northern hemisphere, while Polar VIS
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Earth camera [Frank et al., 1995] (124-149 nm and dominated by the atomic oxygen
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(O I) line at 130.4 nm) imaged the southern hemisphere. The OI-emissions measured by
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VIS Earth camera are slightly more scattered than the N2 and N emissions measured
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by WIC, and the emission intensity also varies with energy [Frey et al., 2003]. As
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we look at relatively large similar features in both hemispheres to determine if and
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how much they are displaced relative to each other in local time, we do not consider
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the different wavelengths of the two cameras to bias our results. Exposure times are
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10 s and 32.5 s and cadence is ∼2 min and 1 min for IMAGE WIC and VIS Earth
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camera, respectively. We assume the emission height to be 130 km and map the images
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onto magnetic apex coordinates [Richmond , 1995]. This coordinate system is based
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on the International Geomagnetic Reference Field and does not take into account any
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asymmetries imposed by external fields. The mapping accuracy is dependent on the
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pointing accuracy of the instruments. In addition to the usual star calibration, we have
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used available DMSP passes to confirm that we have a spatial accuracy of about 1◦ -2◦ .
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The IMF measurements are provided by WIND located at [34,1,2] RE GSM. In order to
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examine any IMF influence on the inner night-side magnetosphere we have assumed a
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planar propagation of the solar wind to -10 RE [Østgaard et al., 2004].
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3. Results
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In Figure 1A (southern hemisphere) and 1B (northern hemisphere) we show the
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5-hour time interval of simultaneous imaging observations as keograms of integrated
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emissions between 65◦ and 85◦ plotted every one (two) minute for VIS (WIC). Color
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bars are chosen to match peak intensity at substorm onset. As the tilt angle during
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these observations varied between -20◦ and -10◦ , there is more dayglow in the southern
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than in the northern hemisphere. Although most of this dayglow can be removed with
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a fairly robust method the dayglow removal may introduce some artificial differences in
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intensities. To avoid this we restrict our analysis to only compare features between 18
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MLT and 04 MLT from 07 UT until 1140 UT. This time interval contains one substorm
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at 0716 UT, a pseudo-breakup at 1044 UT and a new substorm at 1105 UT.
Figure 1.
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We apply three different methods to determine asymmetric features; visual
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inspection, 1D correlation and 2D correlation. The visual inspection is carried out by
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overlaying each image on a grid with 0.2 MLT resolution, normalizing the intensities and
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determining edges and peaks (of intensities) for all the images with overlapping exposure
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times. The 1D and 2D correlation methods were carried out in two steps. First, after
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dayglow removal, each image was converted onto a rectangular grid with 0.1 magnetic
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local time and 1◦ magnetic latitude resolution giving a matrix, 160 × 30, covering 18-4
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MLT and 50◦ -80◦ magnetic latitude. WIC and VIS images with no more than 1 minute
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time difference (center time of exposure) are compared. Two examples are shown in
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Figure 1C and 1D. For the 1D correlation method, all the counts between 50◦ and 80◦
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magnetic latitude are added and the two resulting vectors are cross correlated with
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shifts from -3 MLT to +3 MLT. For the 2D correlation method we calculated
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χ (i, j) =
P P
x
y
[W IC(x + i, y + j) − V IS(x, y)]2
P P
2
x
y W IC(x + i, y + j)
(1)
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where x and y have 0.1 MLT and 1◦ latitude resolution and we let i vary from -30 to
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+30 (±3 MLT) and j vary from -8 to +8 (±8◦ ). In Figure 1E and 1F we show the
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shifted (in i, j) WIC image that returned the smallest χ2 (i, j).
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Figure 2A, 2B and 2C show the result from applying the three different methods,
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as well as the IMF θc and By (Figure 2E and 2F). For the 1D and 2D correlations the
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grey diamonds are all the compared images with no more than 1 minute time difference.
Figure 2.
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The black diamonds in Figure 2B are data where the images are overlapping in time
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(center times differ < 21 s) and correlation coefficient > 0.4. The black diamonds in
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Figure 2C are data where the images are overlapping in time and χ2 < 0.4, normalized
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value, as marked by horizontal grey dashed line in 2D. For both substorms the first
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brightening is asymmetric consistent with earlier findings. Then, all the methods show
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that the asymmetry disappears during the expansion phase. The 2D method also
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indicates that the asymmetry is slowly reproduced during the weak precipitation before
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the pseudo-breakup (1044 UT).
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4. Discussion and Summary
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Neither the IMF By or θc can account for the asymmetry changes. The variations in
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IMF By are small, and during the first 10 minutes of the first substorm ∆MLT changes
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∼1 hour while By stays constant. During the second substorm the IMF By turns
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positive without inducing an opposite asymmetry. The correlation coefficient between
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IMF By and ∆MLT is only 0.5 and 0.4 for the 1D and 2D method, respectively, when
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the ’good’ data (black diamonds) are used. The θc stays fairly constant for the first
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substorm except after 9 UT when both By and Bz (not shown) are very close to zero.
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Haerendel [2007] has suggested that the the immediate source of auroral energy
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is the magnetic shear stresses, which ’are set up by longitudinal convection driven by
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pressure forces in the outer magnetosphere against the frictional forces in the lower
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ionosphere’. Furthermore, that the ’release of these stresses are enabled by the ”cutting”
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of field lines’ [Haerendel , 2007], often described as the decoupling of the magnetosphere
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from the ionosphere due to parallel potential drops. In this scenario the auroral arcs
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will move in the direction of releasing magnetic stress. We suggest that our observations
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are a large scale manifestation of this effect. A simple sketch of this scenario is depicted
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in Figure 3A. Due to the stress imposed on the open field lines by the negative IMF
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By (θc = 240◦ ) the closed magnetic field lines before substorm onset have asymmetric
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footpoints (Figure 3A - i). The resulting magnetic stress on this closed field line (black
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arrows) is balanced by ionospheric friction (blue arrows). At substorm onset (Figure 3A
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- ii) the field lines are dipolarized, which increases the magnetic field strength and the
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tension force in the tail (larger black arrows) and, if overcoming the frictional force in
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the ionosphere, this will act to decrease the asymmetry. However, parallel electric fields
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are also created which will decouple the magnetic field in the ionosphere, allowing the
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field lines to ’slip’ back to the symmetric configuration defined by the Earth’s interior
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field (Figure 3A - iii).
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A simple theoretical argument can be made. First, due to Ampere’s law
∇ × B = µ0 (j + ǫ0
dE
)
dt
Figure 3.
(2)
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a twisted magnetic field can produce a parallel electric field if the current between
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the hemispheres cannot balance the magnetic stress. A similar idea was suggested by
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Stenbaek-Nielsen and Otto [1997]. The twist in By contributing in the z-direction is
(
∂By
∂Ez
)z ∼ (
)z
∂x
∂t
(3)
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Considering that the twist is produced in the tail decreasing steadily towards the Earth,
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as depicted in Figure 3B, the left term in Eq. 3 is negative, which implies a net parallel
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138
electric field (∆Ek ) pointing southward (along m1 ). There are of course parallel electric
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fields in the acceleration regions in both hemispheres, but for simplicity we only consider
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the net difference between the two hemispheres. Along m2 there is no ∆Ek as
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Now, we apply Faraday’s law along a loop of the two closed magnetic field lines (m1
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and m2 ) and the two small segments (in and is ) in the ionosphere connecting them, as
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shown in Figure 3C.
I
(E + u × B) · dl = −
∂By
∂x
= 0.
d Z
B · dA
dt
(4)
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where u is the speed of the loop. This approach was originally proposed by Vasyliunas
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[1984] choosing a loop along field lines at the separatrix to estimate the reconnection
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electric field. Laundal et al. [2010] extended this approach to show that parallel electric
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fields could lead to relative motion of of magnetic footpoints in the two hemispheres.
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Following Vasyliunas [1984] we let the loop move with the magnetic field line, which
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implies that no magnetic field lines cross the surface encircled by the loop and the right
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side of Eq. 4 equals zero. We let the ionospheric segments be at altitudes where the
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MHD approximation
E+v×B≈0
(5)
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holds. This altitude has to be below the acceleration region (1-2RE ) and above the
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altitude where the ratio of electron-neutral collision frequency and gyro-frequency is
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small. Considering also the segment l with parallel electric field (along m1 ) Eq. 4
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becomes
Z
m1
[Ek + (u − v) × B] · dl +
Z
in ,m2 ,is
[(u − v) × B] · dl = 0
(6)
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As the integration path is along the magnetic field lines the only contribution along m1
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comes from the net parallel electric field and the integral along m2 is zero. By defining
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(u − v) positive eastward in both hemispheres and taking into account that the magnetic
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field is upward (downward) in the South (North) we get
−Ek l − (un − vn ) B⊥n in + 0 + (us − vs ) B⊥s is = 0
(7)
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Following Laundal et al. [2010] we assume the convection speed in the two hemispheres
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to be equal (vn = vs ) as well as the length of the two ionospheric segments (in = is = L)
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and the magnetic field strength in the two ionospheres (B⊥n = B⊥s = B⊥ ). Then, we
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get
us − un =
Ek l
B⊥ L
(8)
This result shows that the motion of the magnetic footpoints in southern hemisphere
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will be faster than in the northern hemisphere as long as there is a ∆Ek pointing
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southward. Eventually, this relative speed difference will re-establish symmetric
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y
footpoints by rectifying the field line and release the magnetic stress ( ∂B
6= 0) that
∂x
168
created ∆Ek in the first place. Thus, during the expansion phase of the substorm the
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closed magnetic field lines are brought back to the configuration the Earth’s interior
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determines. This result applies to the region where
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∂By
∂x
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the onset region and assuming that
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along the two segments would cancel in the integration and us = un .
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∂By
∂x
6= 0 at the outer field line and
= 0 at the inner field line. If we had chosen a loop along a field line tailward of
∂By
∂x
is constant at m1 and m0 (Figure 3b), the ∆Ek
Another implication of this result is that the aurora should be brighter in the
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northern hemisphere (in our case) if the strength of the ∆Ek is comparable to, or at
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least a substantial fraction of the potential drops in the acceleration regions. As we are
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looking at different wavelengths with different cameras we are not able to address this.
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However, this could explain the brightness differences reported by Frank and Sigwarth
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[2003]. With the southern onset being dawnward of the northern, the twist was opposite
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of what we see, resulting in a ∆Ek pointing northward. Thus, a brighter aurora should
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be seen in the South, which is what they did.
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To summarize, in this paper we have reported the following:
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1) Both substorm onsets are asymmetric - due to the magnetic stress imposed by
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the IMF on opened magnetic field or the partial penetration of IMF By .
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2) During the expansion phase of both substorms the asymmetry disappears
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Our findings can be explained by the decoupling of the magnetosphere and
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ionosphere due to parallel electric fields that are produced in the substorm process
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allowing the field lines to ’slip’ back to the symmetric configuration defined by the
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Earth’s interior.
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We have also presented a theoretical argument:
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1) The magnetic stress on field lines with asymmetric footpoints can set up a net
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difference in parallel electric field in the two hemispheres.
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2) This net electric field difference will lead to a different speed of the auroral arcs
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in the two hemispheres rectifying the magnetic field lines and releasing magnetic stress.
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The overall results is that the auroral substorm expansion phase brings the magnetic
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configuration of closed field lines back to what the Earth’s interior demands.
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Acknowledgments.
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We are indebted to the IMAGE and Polar teams for the design and successful operations
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of the two missions. We thank S. B. Mende for the use of IMAGE FUV WIC data, J.
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B. Sigwarth for the use of Polar VIS Earth Camera data and R. Lepping for the WIND
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magnetic field data. This study was supported by the Norwegian Research Council, through
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the IPY-ICESTAR project 176045/S30
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203
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Figure Captions
Figure 1. A) Keogram of the emissions in the southern hemisphere from 7 UT to 12 UT
on October 22, 2001 (VIS). Emissions are integrated between 65◦ and 85◦ and plotted
every minute. B) Keogram from the northern hemisphere every two minutes (WIC).
C, E and D, F) Two examples of how the determination of the relative displacement of
auroral features are determined using the 2D correlation method.
Figure 2. The relative displacement, ∆MLT, of substorm auroral features based on A)
Visual inspection, B) 1D cross correlation, C) 2D correlation. Grey diamonds are all
data, black diamonds are valid data. D) Normalized total counts in WIC (solid line) and
VIS (dashed line) images and minimum χ2 (grey line). E) IMF θc and F) IMF By from
WIND at [34,1,2] RE GSM, planar propagated to -10 RE .
Figure 3. A) How the field line is rectified due to magnetic stress (black arrows) on
field lines with asymmetric footpoints. Blue arrows indicate ionospheric friction and red
arrows parallel electric fields. B) How the magnetic fields are twisted from the tail and
inward with a non-twisted field line earthward of the onset region. C) A loop of the
twisted field line m1 with asymmetric footpoints and the non-twisted inner field line, m2
with symmetric footpoints. ∆Ek is the net difference between the two hemispheres on
the twisted field line. The two ionospheric segments, in and is , are completing the loop,
and u and v are the speeds of the loop and the plasma, respectively, defined positive
eastward.
17
Figures
A) 12
MLT
6
0
18
12
B)
7
8
7
8
9
10
11
10
11
12
12
6
MLT
257
0
18
12
70
C)
9
12
E)
0720:19
Moved: - 1.4 MLT
60
50
0719:58
-70
-60
-50
18
70
20
22
0
2
18
20
22
0
20
22
0
F)
0813:31
D)
2
4
Moved: - 0.6 MLT
60
50
0813:29
-70
-60
-50
18
20
22
0
2
18
2
4
Figure 1. A) Keogram of the emissions in the southern hemisphere from 7 UT to 12 UT
on October 22, 2001 (VIS). Emissions are integrated between 65◦ and 85◦ and plotted
every minute. B) Keogram from the northern hemisphere every two minutes (WIC).
C, E and D, F) Two examples of how the determination of the relative displacement of
auroral features are determined using the 2D correlation method.
18
South dawnward of North
A)
South duskward of North
B)
C)
D)
E)
F)
Figure 2. The relative displacement, ∆MLT, of substorm auroral features based on A)
Visual inspection, B) 1D cross correlation, C) 2D correlation. Grey diamonds are all
data, black diamonds are valid data. D) Normalized total counts in WIC (solid line) and
VIS (dashed line) images and minimum χ2 (grey line). E) IMF θc and F) IMF By from
WIND at [34,1,2] RE GSM, planar propagated to -10 RE .
19
a)
Northern
ionosphere
i
ii
iii
Magnetosphere
Southern
ionosphere
b)
z
m1
x
m0
m2
∆E ||
y
c)
un-vn
in
+
m1
m2
∆ E ||
is
us-vs
Figure 3. A) How the field line is rectified due to magnetic stress (black arrows) on
field lines with asymmetric footpoints. Blue arrows indicate ionospheric friction and red
arrows parallel electric fields. B) How the magnetic fields are twisted from the tail and
inward with a non-twisted field line earthward of the onset region. C) A loop of the
twisted field line m1 with asymmetric footpoints and the non-twisted inner field line, m2
with symmetric footpoints. ∆Ek is the net difference between the two hemispheres on
the twisted field line. The two ionospheric segments, in and is , are completing the loop,
and u and v are the speeds of the loop and the plasma, respectively, defined positive
eastward.