ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus GmbHGöttingen, Germany10.5194/angeo-33-505-2015A quantitative study of magnetospheric magnetic field line
deformation by a two-loop substorm current wedgeNikolaevA. V.demosfen.spb@gmail.comhttps://orcid.org/0000-0001-5558-9615SergeevV. A.https://orcid.org/0000-0002-4569-9631TsyganenkoN. A.https://orcid.org/0000-0002-5938-1579KubyshkinaM. V.OpgenoorthH.https://orcid.org/0000-0001-7573-5165SingerH.AngelopoulosV.Department of Earth Physics, Saint Petersburg State
University, Petrodvoretz, RussiaUppsala Division, Swedish Institute of Space Physics,
Uppsala, SwedenSpace Weather Prediction Center, NOAA, Boulder, Colorado,
USADepartment of Earth, Planetary, and Space Sciences and
Institute of Geophysics and Space Physics, University of California, Los
Angeles, California, USAA. V. Nikolaev (demosfen.spb@gmail.com)29April201533450551724September20148March20152April2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/33/505/2015/angeo-33-505-2015.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/33/505/2015/angeo-33-505-2015.pdf
Substorm current wedge (SCW) formation is associated with global magnetic
field reconfiguration during substorm expansion. We combine a two-loop model
SCW (SCW2L) with a background magnetic field model to investigate distortion
of the ionospheric footpoint pattern in response to changes of different
SCW2L parameters. The SCW-related plasma sheet footprint shift results in
formation of a pattern resembling an auroral bulge, the poleward expansion
of which is controlled primarily by the total current in the region 1 sense
current loop (I1). The magnitude of the footprint latitudinal shift may
reach ∼ 10∘ corrected geomagnetic latitude (CGLat) during strong substorms (I1= 2 MA). A strong helical magnetic field around the field-aligned current
generates a surge-like region with embedded spiral structures, associated
with a westward traveling surge (WTS) at the western end of the SCW. The
helical field may also contribute to rotation of the ionospheric projection
of narrow plasma streams (auroral streamers). Other parameters, including
the total current in the second (region 2 sense) loop, were found to be of
secondary importance. Analyzing two consecutive dipolarizations on 17 March
2010, we used magnetic variation data obtained from a dense midlatitude
ground network and several magnetospheric spacecraft, as well as the
adaptive AM03 model, to specify SCW2L parameters, which allowed us to
predict the magnitude of poleward auroral expansion. Auroral observations
made during the two substorm activations demonstrate that the SCW2L combined
with the AM03 model nicely describes the azimuthal progression and the
observed magnitude of the auroral expansion. This finding indicates that the
SCW-related distortions are responsible for much of the observed global
development of bright auroras.
Magnetospheric physics (auroral phenomena; current systems; storms and substorms)Introduction
Electric currents flowing along the magnetic field lines (field-aligned
currents, FACs), known since K. Birkeland's studies in the early 1900s, are an
important part of the three-dimensional current system that is responsible
for the configuration of the dynamical magnetosphere. The most stable
well-known component of this current system, the large-scale double-layer
system of region 1 (R1) and region 2 (R2) FACs (Iijima and Potemra, 1976),
supports magnetospheric convection and the twin-vortex pattern of the
equivalent ionospheric current. Another well-known current system, the
substorm current wedge (SCW), is responsible for major magnetotail
reconfigurations during magnetospheric substorms. The SCW concept was first
introduced by McPherron et al. (1973), who described an SCW as a 3-D current
system, connecting the disrupted tail current with the ionosphere via the
downward/upward R1 type FACs (at the dawn/dusk sides, respectively). Their
single-loop SCW model not only qualitatively explained observed magnetotail
field dipolarizations, but also provided realistic magnitudes and polarity
of bay-like magnetic field variations at midlatitudes. Therefore, Horning et
al. (1974), Sergeev et al. (1996), and Chu et al. (2014) have suggested that
it be used as a tool to monitor the intensity and location of substorm
currents. Sergeev et al. (2011) proposed a corresponding single-wedge SCW
model with a realistic shape of the current-carrying magnetic field lines
and filamentary (rather than linear) currents suitable for magnetospheric
studies.
Theoretical and observational studies however, now require that the
single-wedge SCW model be updated by including an additional element, a loop
with oppositely directed current (in the R2 sense) spanning nearly the same
longitudinal sector as the primary R1 current loop, but located closer to
Earth. The single-wedge model thus becomes a two-loop (quadrupolar FAC) SCW
model (SCW2L) (Sergeev et al., 2014a). Magnetohydrodynamic simulations of
magnetotail reconnection (Birn and Hesse, 1999; Birn and Hesse, 2014), the
recent equilibrium Rice Convection Model (RCM-E), and flow burst simulations
(Yang et al., 2012) consistently show that a plasma pressure increase in front
of the earthward flow channel is responsible for generation of this
additional R2 loop. From observations, Liu et al. (2013) inferred quadrupolar
FACs by analyzing individual propagating flow bursts, while Sergeev et al. (2011) and Sergeev et al. (2014a) showed them to be consistent with
SCW-related magnetic perturbations by comparing multipoint observations in
the near magnetosphere and at ground midlatitudes during substorms.
During strong substorms, the total SCW current may exceed 1 MA and thus may
significantly change magnetospheric configuration and ionospheric mapping in
the near-Earth region. At the same time, intense FAC sheets (especially
upward FACs) accelerate precipitating electrons that cause bright auroras
(Waters et al., 2001). Therefore, substorm-related magnetic reconfiguration
and associated changes in field-line mapping from the magnetosphere to the
ionosphere should be reflected in an auroral pattern redistribution, which,
in turn, can provide information about these changes. An example is poleward
auroral expansion accompanied by formation of a bulge of bright auroras.
This basic signature of the substorm expansion phase has been traditionally
related to electric current disruption and magnetic reconnection in the
magnetotail (e.g., Roux et al., 1991; Yahnin et al., 2006; Kubyshkina et al.
2011). The relationship is based on rather limited evidence however (see,
e.g., summary by Keiling et al., 2012). The quantitative evaluation of the role
of FACs in variable patterns of field-line mapping during substorm-related
dipolarization and auroral expansion, an interesting exercise, has been
addressed in a few previous papers. Those studies, however, utilized highly
idealized SCW models with infinitely thin line currents flowing along either
dipolar or early empirical model field lines (Vasilyev et al., 1986;
Kaufmann and Larson, 1989; Tsyganenko, 1997), or used dipolarization effects to
represent a global tail reconfiguration (Kubyshkina et al., 2011). Because
SCW effects on the magnetotail configuration and mapping by applying the
upgraded (quadrupolar) SCW2L model is an promising approach, we do so in
this paper.
In Sect. 2, we quantitatively investigate SCW-related deformations,
emphasizing mapping from the equatorial magnetosphere to the ionosphere;
determine the impact of adding the SCW2L model on the deformation magnitude;
and discuss expected manifestations in the auroral observations. In Sect. 3,
we evaluate the expected poleward expansion based on time-varying,
data-adaptive magnetospheric models (using the SCW2L and the AM03 adaptive
model) and compare their results with observed magnitude of poleward
expansion for the isolated substorm event, taking the advantage of excellent
spacecraft coverage in the magnetosphere.
Modeling of the ionospheric footprint displacement produced by the substorm
current wedgeBrief description of the SCW2L model
Here we use the SCW2L model, which was presented, tested, and extensively
discussed by Sergeev et al. (2014a) (hereafter referred to as Paper 1). It
includes two pairs of field-aligned currents: the high-latitude R1 loop and
the more earthward/equatorward R2 loop (see Fig. 1a). When combined, these
loops form a quadrupolar FAC source near the ionosphere. The model was
developed for substorm case studies to quantitatively evaluate the
intensities of both R1 (I1) and R2 (I2) currents, based on
observations. Its input includes the dipolarization amplitude (ΔBZ) in the magnetosphere, measured by a few spacecraft, and the
amplitudes of ΔX and ΔY components of bay-like variations,
measured at several ground midlatitude observatories. As discussed in Paper 1
and illustrated in Fig. 1c, the magnitude ΔBZ in the
magnetosphere is rather uniform over most of the dipolarized region, that
is, in the area between the R1 and R2 loops (red hatching in Fig. 1d). Here
ΔBZ is mostly sensitive to the magnitude of R1 current
(I1) and allows one to evaluate its magnitude, whereas the midlatitude
ground variations respond to the net current (I1+I2), so the
combination of two (magnetospheric and ground-based) inputs is necessary to
evaluate both I1 and I2 parameters.
(a) Illustration of the two-loop SCW model (SCW2L); (b) magnetic
field-line topology when the background (T89 + IGRF) magnetic field (shown by
current-carrying red/green lines) is compared to field lines (black lines)
after the addition of SCW2L; (c) partial contribution to ΔBZ
perturbations of R1 (red) and R2 (green) SCW components and their sum (black
line); (d)ΔBZ distribution in the equatorial plane in the
SCW2L model (adapted from Sergeev et al., 2014a). All illustrations are done
for a 60∘ wide wedge with I1= 1 MA and I2= 0.5 MA.
Because of the scarcity of magnetospheric spacecraft observations, the model
should be as simple as possible. In particular, both R1 and R2 loops are
assumed to occupy the same azimuthal sector, which is roughly consistent
with simulation results presented by Yang et al. (2012) and Birn and Hesse (2013).
In our case, we use the filamentary current model with the current
transverse spread specified as D0∼R3/2, which
amounts to 1 to 2 Re in the region of interest, with the FACs flowing
along the realistic magnetic field lines of the T89 model (Tsyganenko et
al., 1989). The stretch of the background magnetic field (used to trace the
FACs) is controlled by the RCF parameter, which varies between 0 (for a
quiet dipolar-like configuration) and 8 (for a very stretched tail-like
configuration) in the T89 code. With RCF = 0, an equatorial point at
XGSM=- 15 RE, YGSM= 0 in the neutral sheet maps to
geomagnetic latitude of ∼ 70∘ GLat in the ionosphere, while
setting RCF = 6 moves the footprint down to ∼ 63∘ GLat (see
also Sergeev et al. (2011) for the detailed description of RCF parameter).
Using the filamentary model rather than the azimuthally distributed
field-aligned currents does not significantly affect ΔBZ in the
dipolarized region, except in the immediate vicinity of the FAC filament
(see Fig. 3 and supplementary plots S1–S3 in Sergeev et al., 2014a). Also,
in our analyses below we set the distance to the equatorial current of the
R1 loop to RT1= 15 Re (see also parameter descriptions in Fig. S1 in the Supplement).
Figure 1b illustrates the applicability domain of the SCW2L model, limited
primarily to the inner magnetosphere, where the model is intended to
faithfully describe the dipolarization effects. Close to the filamentary
equatorial R1 current and beyond it, the model cannot provide a realistic
description of electric currents flowing in the reconnecting plasma sheet.
Nevertheless, as shown in Paper 1, the amplitude and distribution of the
dipolarization amplitude ΔBZ in the inner region (earthward of
12 Re) depends only slightly on the exact location and radial distribution
of the equatorial R1 current. If the peak perturbation from the equatorial
filament exceeds the background BZ value, a closed field line loop is
formed around the filament (Fig. 1b). In addition, a region with southward
total BZ that is topologically disconnected from the ionosphere is
formed tailward of the R1 filament. These two model artifacts should be kept
in mind when analyzing SCW2L-related deformation and magnetic field-lines
mapping.
Magnetospheric pattern of neutral sheet footprint geocentric
angular displacement (color coded) caused by addition of the SCW2L model to
the T89 + IGRF models. The SCW2L model parameters were set as follows:
I1= 1 MA, I2= 0.5 MA, RT1= 15 Re, RT2= 6 Re,
RCF = 6, and the wedge azimuthal width 50∘.
SCW2L-related deformations
Both the background magnetic field (IGRF + T89) and SCW2L perturbations
are three-dimensional vector fields with complex distribution and geometry.
To quantitatively characterize magnetic field deformations associated with
SCW onset, we use a method in which a regular set of contours in the
nightside equatorial plane is mapped along field lines onto the ionosphere.
We then evaluate changes in the mapping patterns caused by the adding of the SCW
model contribution to the background field. More specifically, the reference
contours are chosen as a family of equatorial arcs, i.e., geocentric
circular segments in the Z= 0 plane (with the geodipole tilt angle
assumed to be zero), distributed between 4 and 20 Re, as shown in Fig. 2.
Each point on the arc is mapped to the ionosphere (R= 1.02 Re) twice:
first, using only the background IGRF + T89 field, and then using the IGRF
+ T89 + SCW2L model with the substorm wedge contribution added. The
azimuthal and longitudinal shift between the footpoints
α=cos-1x1x2+y1y2+z1z2R2,
serves as a quantitative measure of the SCW mapping effect. Here R= 1.02
Re, and [x1, y1, z1] and [x2, y2, z2] are
footprint Cartesian coordinates, obtained from the two tracings. An example
of the footprint shift distribution in the equatorial plane is shown in Fig. 2; each point on the arc is colored according to its α value. As
mentioned above, the valid area in our analysis is the region earthward of
the R1 equatorial current between the upward and downward FACs and colored
in green and red lines. No ionospheric footpoints exist tailward of that area
(grey color) because the corresponding field lines either belong to the
magnetic “island” inside the loop or map tailward.
The equatorial diagram of the footpoint shifts should be viewed with the
ionospheric mapping pattern shown in Fig. 3 aimed to characterize its
geometry. At the ionospheric level, we show two families of reference
equatorial equidistant arcs mapped to the ionosphere using only the
background model field (red contours) as well as the background and the
SCW2L field (green curves). Such a representation, which helps to show different
types of magnetic field deformation; it is especially useful when discussing
possible auroral implications.
Ionospheric mapping of equatorial geocentric circle arcs
(equatorial distance is labeled for selected circles). The red lines show
neutral sheet mapping using the T89 + IGRF model; the green lines show
mapping of the same points using the SCW2L + T89 + IGRF model.
Ionospheric locations of upward (downward) FACs are indicated by diamond
(cross) symbols. The SCW2L model is the same as in Fig. 2.
Comparing Figs. 2 and 3 reveals three specific regions of footprint
deformation. The first, the most important region inside the dipolarized
region, lies between the equatorial R1 and R2 currents. Here the
SCW2L-related ΔBZ perturbations are significantly larger than
the background BZ component (BZ0): the traced field lines pass at
larger distances from the neutral sheet plane (see Fig. 1b) and hence land
at higher latitudes. At the ionospheric level, the dipolarization region
corresponds to the area of significant poleward shift of the footpoints. In
the example illustrated in Figs. 2 and 3, this shift can reach up to
8∘ corrected geomagnetic latitude (CGLat) at the center of the SCW. Because of an increase in the
ΔBZ/BZ0 ratio, the magnitude of the poleward expansion
increases as the equatorial point approaches the R1 filament.
The second region corresponds to the field-line twisting area around the
intense R1 field-aligned current filament, which is well represented by the
spiral-like shapes in Fig. 3. Initially located within the wedge close to
the filament axis, the points are significantly twisted, but their resulting
footpoint displacements appear to be small, forming the blue areas near the
FACs (between 8 and 14 Re along the x axis) in Fig. 2. Contradictions
between the amount of footprint movement and small α values appear
in the cases when footpoints rotate around FACs and return close
to the original location. The combination of type 1 and type 2 deformations
produces a large-scale poleward bulge-like structure in the ionospheric
projection of the magnetospheric dipolarization region, which may be
associated with the auroral bulge.
The third deformation region is co-located with the footprint equatorward
shift near the R2 equatorial current (here we placed it at the distance
RT2= 6 Re). The effect of the footpoint twisting around the
corresponding FACs results in an equatorward bulge-like ionospheric pattern.
This bulge is several times smaller than the poleward bulge for two reasons:
(1) a much stronger background field in the inner magnetosphere, where the
R2 loop is formed and (2) an R2 current that is smaller than the R1 current.
(a) Equatorial locations of three hypothetical narrow plasma
streams; (b) their ionospheric footprints. The black strips indicate stream
mapping using the background IGRF + T89 model; the colored strips represent
stream mapping in the IGRF + T89 + SCW2L model (I1= 1 MA,
I2= 0.5 MA, R1 = 15 Re, RT2= 6 Re and RCF = 6). Color
coding indicates the streamers, spatial orientation or movement direction.
For auroral research, it is also instructive to map another type of neutral
sheet contour. Rather than arc-like segments, one may consider rectilinear
strips oriented along the x axis plasma flow geometry (Fig. 4a) and created
as azimuthally localized partitions of the neutral sheet described in Sect. 2.2. The distorted ionospheric projections of these strips can be likened to
elementary structures associated with auroral arcs or other features
observed at low altitudes. One such structure can be an ionospheric
projection of narrow (2–3 Re wide across the tail), fast plasma streams,
also known as “bursty bulk flows” (BBFs) (Baumjohann et al., 1990; Angelopoulos et al., 1992),
which are associated with a family of approximately north–south aligned
auroral arcs (or auroral streamers, or poleward boundary intensifications,
PBIs) (e.g., Elphinstone et al., 1996; Henderson et al., 1998; Lyons et al.,
1999; Nakamura et al., 2001; Henderson, 2012, and references
therein). Figure 4a shows an equatorial view of three line segments (I and
II contours) in the dipolarized region, which simulate three hypothetical
fast earthward plasma streams. Although their mapped images look similar, if
mapped along the background magnetic field (Fig. 4b, black contours), adding
the SCW2L contribution causes a significant deformation of the image.
Although it is shifted poleward and somewhat elongated, the shape of the
stream located at the central wedge meridian (Y= 0, contour I) does not
change much. The shape of the off-center contours (II), however, changes
considerably, including a significant rotation of the mapped structure.
Although the general features of the deformation are recognizable with the
help of Fig. 3, the amount of rotation and the scale of the crescent-like
structure depend on many details of structure location relative to the wedge
field-aligned currents. In particular, the footpoints of the dawnside stream
that crosses the equatorial projection of the wedge (but does not intersect
the FAC flux tube) are subject to stronger rotation than those of a
non-crossing duskside stream. In addition, the latitude of the stream
endpoint (the most earthward) is roughly 4∘ CGLat southward of the
non-crossing stream's endpoint. Investigation of corresponding auroral
patterns may have interesting implications for studies of the FAC strength
and distribution.
Poleward footpoint expansion as a function of SCW parameters
In this section, we investigate poleward shifts of ionospheric footpoints
traced from the neutral sheet at the central wedge meridian (here Y= 0,
Z= 0) using different SCW2L parameter values. Values of the SCW2L spatial
parameters, such as PW, PE, RT1, and RT2, are similar to
those used in the previous section. Characterizing the event strength by a
combination of R1 current intensity (I1) and field-line stretching
amplitude (RCF), we select combinations corresponding to different magnetic
disturbance levels as follows: weak substorms I1= 0.5 MA, RCF = 3
(Fig. 5c); moderate substorms I1= 1 MA, RCF = 6 (Fig. 5d); and
strong substorms I1= 2 MA, RCF = 8 (Fig. 5e). To set the RCF
dependence on I1, we relied on Fig. 10 in Sergeev et al. (2014a), which
demonstrated a statistical relationship between dipolarization amplitudes
and BZ0 at geosynchronous distance prior to the dipolarization onset
and suggested I2/I1=0.5.
As seen from Fig. 5c, d, and e, the parameter that effectively controls
magnitude of poleward expansion is the intensity of the R1 current. The
computed maximal poleward shift of ionospheric footpoints at the wedge
central meridian is rather small in the case of weak substorm (ΔLat
∼ 2–3∘ CGLat). It increases under moderate substorm
conditions (ΔLat ∼ 5–6∘ CGLat) and can reach
ΔLat ∼ 10∘ CGLat during highly disturbed events.
Such values look quite realistic when compared to the known magnitudes of
the auroral poleward expansion during substorms (Akasofu, 1976).
Parameter dependence of footprint displacement. (a) The X0Z plane
projection of SCW2L FACs (dashed lines) and magnetic field line traced from
X=-10 Re; (b)ΔBZ generated by SCW2L (I1= 1 MA)
along the T89 magnetic field line starting at X=-10 Re; (c) latitudinal
shifts for weak substorms (I1= 0.5 MA, RCF = 3); (d) same panel for
strong events with two different magnetotail stretches (I1= 1 MA,
RCF = 0 and 6); (e) same as (c) and (d) but calculated for extremely strong
substorms (I1= 2 MA, RCF = 8). Different colors in panels
(c–e) correspond to the same I1 but with two values of the I2/I1
current ratio, shown in green for I2/I1= 0.3 and in red for
I2/I1= 0.8. All calculations are done for the fixed RT1= 15 Re, RT2= 6 Re, wedge azimuthal width of 50∘.
Surprisingly, the growth of the R2 current (increase in the I2/I1 ratio under a fixed value of I1), which enhances the
dipolarization in the equatorial plane (see Fig. 1c, d, and e), actually
decreases footprint shifts, resulting in a ∼ 20 % smaller
latitudinal expansion. This is explained by Fig. 5b, which shows the
wedge-related ΔBZ at locations along the magnetic field line,
corresponding to the T89 + IGRF model and starting in the middle of the
wedge from X=-10 Re, Z= 0. Figure 5b shows that the increase in
I2 actually suppresses ΔBZ in the high-latitude part of
the field line (at small radial distances, R < 6 Re), without a
substantial increase in ΔBZ at its near-equatorial (R > 6 Re) part. The configuration of such a distorted field line is
illustrated in Fig. 5a. According to Fig. 5c, d, and e, the equatorial bulge
caused by the R2 current is virtually absent when I2/I1 is small
(= 0.3) and has a relatively small magnitude (<∼ 1∘ΔLat) when I2/I1= 0.8.
As shown in Fig. 5d, the role of background field line stretching is also
very modest. The stretch increase from RCF = 3 to 6 reduces the
ionospheric shift in the region of strong magnetic gradients (near the R1
and R2 type currents) by ΔLat ∼ 1–2∘ CGLat.
This can be partly due to changing magnitudes of the background BZ0 at
different RCF, which resulted in an equatorward shift of the field-line
footpoints.
SCW and poleward auroral expansion during the 17 March 2010 substorm
Realistic modeling of magnetospheric field deformation is an important step
to validate the SCW2L model itself and quantitatively testing its prediction
of the poleward expansion during substorms. Here we conduct such testing for
the isolated substorm event on 17 March 2010, with excellent coverage of the
magnetosphere by four Geostationary Operational Satellites (GOES), which
monitored the nightside part of the synchronous orbit, and by four Time
History of Events and Macroscale Interaction during Substorms spacecraft
(Angelopoulos, 2008) in the tail. The event itself and its spacecraft-based
modeling (including SCW2L runs) are described in detail in a companion paper
by Sergeev et al. (2014b). Here we briefly restate some of their results and
concentrate on the mapping issues.
The inversion modeling was performed in two stages. In the first, we used
the well-known magnetogram inversion algorithm (Sergeev et al., 1996) with a
simple (based on dipolar field lines) SCW model and with input from 20
midlatitude magnetic observations, to infer the parameters of the SCW,
symmetric (DR), and partial (DRP) ring current systems (the latter two
systems changed little during that event, and their effect is not discussed
here). In the second, we used values of westward (PW) and eastward (PE) SCW
longitudes, obtained in the previous step, and ran the inversion procedure
based on a combination of midlatitude ground-based data, spacecraft
observations, and the advanced SCW2L model (see also Fig. S1 in the Supplement).
The inversion algorithm usually searched for and found a global minimum of a
fit function σ:
σ=KST∑ΔXOBSKIND-ΔXMOD2+ΔYOBSKIND-ΔYMOD2+KSC∑ΔBZobs-ΔBZmod2,
where the indices “obs” and “mod” stand for the observed and modeled
fields, respectively, and KIND= 1.5 is the induction correction
coefficient. The summation is carried out over the NST stations and
NSC spacecraft, and KST and KSC are the weight coefficients
needed to balance the contributions to the minimized target function (i.e.,
KST×NST=KSC×NSC) from a large number of stations
(NST= 19) and a small number of spacecraft located inside the
dipolarized region (NSC= 1 or 2). Throughout that run, we kept some
parameters fixed, including RT1= 15 Re, RTDRP= 13 Re, and
RDR= 4 Re. We made equatorial distance to R2 current free and
varied RT2 parameter between 5.5 and 6 Re.
As a result, we evaluated the I1, I2, and I3 (DRP) currents
for two consecutive dipolarizations with the activity starting at T= 04:56 UT (reference level, start time of activation no. 1) and T= 05:36 UT (start time of activation no. 2). The reference level for
both activations was chosen at T0= 04:56 UT because the second
activation started during the recovery from the first activation. The observed
and modeled field perturbations during the peaks of two activations are
compared in Fig. 6. This figure demonstrates good agreement between the
observed and predicted dipolarization magnitudes, namely ΔBZ
in the bottom right panels for spacecraft dipolarization and ΔX and
ΔY components in the left panels for ground stations. We also ran
the adaptive model AM03 (see also Sergeev et al. (2014b) for more details),
which uses the T96 model equations but adjusts their parameters to provide a
best fit to the magnetic field observed during the event of interest.
Using the inversion results, we can now predict the mapping using realistic
parameters of the SCW2L model current system as we did in Sect. 2.2 (Figs. 7 and 8). The AM03 + IGRF model at 04:56 UT is used here as the
background field model. Colored patterns in Fig. 7 illustrate the degree of
footprint distortion (similarly to Fig. 2) for two dipolarization maxima
epochs at 05:13 UT (left panel, event no. 1) and 05:50 UT (right
panel, event no. 2).
Figure 8b (colored lines) complements the previous figure by showing the
time-varying latitude locations of GOES-12 and 14 and THEMIS-A spacecraft
footprints predicted by the SCW2L-based model. These footprints are compared
to those predicted by the time-varying AM03 model (Fig. 8c, thin lines). To
monitor the longitudinal location of these spacecraft relative to the SCW
location, they are plotted in Fig. 8a. The mapping from a fixed neutral
sheet location at X=-11 Re , Y= 3 Re, and Z=-1.56 Re through both
events is shown for reference (black lines in Fig. 8a and b). This location
(also plotted as a black square in Fig. 7) entered the SCW sector
temporarily during both activations. At these times the poleward shifts of
this location footpoint (relative to the background location at 04:56 UT)
were about 3.5 and 5∘, respectively, for the SCW2L model. The
maximal poleward shifts near the central meridians of corresponding SCW
sectors are about 8 and 11∘, according to the diagrams in Fig. 7a and b. Note, that we do not take into account DRP current in our analysis
because (1) we actually have no magnetospheric data to evaluate accurately
its parameters, (2) its magnitude is three times smaller compared to SCW and
(3) we compare observed and predicted expansion by an order of magnitude.
According to the data-based time-varying AM03 model, the maximal poleward
shifts were predicted to be smaller, about 1.6 and 4.5∘,
respectively (see red notches in Fig. 8b). The spatial distribution of the predicted shifts is
rather smooth in this case, reflecting the large-scale nature of the model
functions in the T96 model. Accordingly, it predicts similar footpoint
variations for all GOES spacecraft, irrespective of whether they actually
observed the dipolarization. An example is the variation of footpoints of
GOES-12 and 14, which entered the SCW sector and registered the
dipolarization at different times.
Another detail to be noted is that the SCW2L and AM03 models predict
different footpoint variations during the recovery phase. According to the
time-varying adaptive model, the latitude locations of the spacecraft
continue to grow when the R1 current starts to drop (regardless of whether
the spacecraft stayed inside the dipolarized region). In contrast, the
spacecraft footprints calculated using the SCW2L-based model undergo an equatorward
shift. Another notable feature is a sharp negative footpoint shift at times
when the spacecraft exit from the model SCW (see GOES-14 at around the onset
and at ∼ 05:25 UT).
Inversion results for two dipolarization peaks at 05:13 UT
(activation no. 1, top) and 05:50 UT (activation no. 2, bottom). The left panels show
observed (red) and predicted (blue) ground ΔX and ΔY
variation amplitudes; I1, I2, I3, and I4 indicate R1, R2, DRP, and ring
current intensities, repsectively. The right bottom panel shows the same
for spacecraft ΔBZ data. The upper right panel illustrates the
SCW2L configuration projected onto the X0Y plane.
Same as in Fig. 2, but predicted for the peak epochs of two SCW
activations, shown in Fig. 6. The black square points indicate dummy
spacecraft location relative to the SCW (in the neutral sheet, X=-11 Re,
Y= 3 Re and Z=-1.56 Re).
Also, even though GOES-12 observed a strong dipolarization (ΔBZ
up to ∼ 20 nT) during the first activation, its footpoint
latitude varied only slightly (∼ 0.5∘ CGLat) for two
reasons. The first is that GOES operates in a region of a strong background
magnetic field, which is why the magnitude of spacecraft footprints
displacement remains almost unchanged (e.g., Figs. 2 and 7). The
situation is different for THEMIS-A, which was located tailward (closer to
the R1 current) in a region of a weaker magnetic field (and stronger
SCW-related ΔBZ) and, correspondingly, in an area of increased
mapping distortion. The second is that GOES-12 was located closer to the
central SCW meridian, where the effects of FACs are weaker than in regions
closer to the edges of the SCW. For this reason, the footprint of GOES-14,
which operates in vicinity of upward FACs, has bigger latitudinal variations.
During this substorm, several THEMIS all-sky imagers (ASI) provided useful
auroral observations. Although limited by bad weather and moonlight,
observations made at post-midnight stations KUUJ and SNKQ distinctly
recorded auroral brightening after 04:56 UT (top of Fig. 9). These
stations had to be inside the SCW sector according to Fig. 8a. Poleward
expansion is clearly limited, and the latitudinal interval of intensified
auroras (boundaries of green color in Fig. 9 KUUJ keogram, see white
vertical bin) is estimated to be roughly about ∼ 3∘
during the first activation. This is comparable to the ∼ 3.5∘ poleward expansion predicted by SCW2L the model (see Fig. 8b,
vertical bin compared with black line maximum).
At the same time the pre-midnight stations FSMI and SNAP were duskward of
the SCW and recorded no active auroras, but they entered the SCW during
second activation according to Fig. 8a. Beginning at 05:36 UT, these
stations observed auroral breakup and subsequent extended poleward
expansion under good viewing conditions. The breakup started ∼ 50 km south of FSMI station zenith at 67.4∘ CGLat. It is also seen at
the equatorward horizon, ∼ 4∘ CGLat south of SNAP station
located at 71.0∘ CGLat at the same meridian. The bright auroras
expanded poleward to the northern horizon, suggesting a roughly
∼ 8∘ CGLat poleward shift during the second activation.
This number is slightly larger than in our SCW2L predictions, which give
∼ 5∘ CGLat. The AM03 model provides an even smaller value of
∼ 4.5∘. Our modeling indicates that the deformation of
magnetic configuration by SCW currents provides more than half of the
observed poleward expansion. The remaining part can be ascribed to tailward
motion of the magnetic reconnection region (and of the current disruption
region), that is, to an effect that could not be taken into account in our
data-based modeling.
Discussion and concluding remarks
A few previous studies concluded that field-aligned currents, having
realistic strength and distribution, may considerably affect ionospheric
mapping of equatorial magnetospheric points and ionospheric images of
magnetospheric structures (e.g., Vasilyev et al., 1986; Kaufmann and Larson,
1989; Donovan, 1993; Tsyganenko, 1997). These examples utilized simplified
models of filamentary and/or distributed currents. Kaufmann and Larson
(1989) constructed FAC models as a combination of a number of current wires
and used this model to map magnetic field lines, electric fields, and
equipotentials throughout the magnetosphere. Near intense region 1 and
region 2 Birkeland currents, they found large magnetic footpoint
displacements and discussed the importance of twisting the magnetic field
lines to form spiral patterns in the regions co-located with the WTS and at
the eastward end of the substorm current system. By modeling finite
thickness field-aligned current sheets connected via radial or azimuthal
currents in the magnetosphere, Donovan (1993) emphasized the large amplitude
of footpoint distortions and the crucial dependence of distortion type and
mapping on the character of FAC closure in the magnetosphere (of which very
little is known). Tsyganenko (1997) developed a mathematical approach to
construct electric current flow lines, the prototype of which was based on
two inclined, tailward-shifted circular loops. Using this model, the author
mapped a set of equatorial circular contours to the ionosphere,
equidistantly distributed in the equatorial plane between 5 and 20 Re. A
conspicuous bulge-like form was shown to emerge in the nightside ionosphere
inside the SCW sector, where the magnetic field lines collapsed towards a
more dipole-like configuration.
(a) THEMIS and GOES spacecraft, KUUJ and SNAP station locations
relative to SCW; (b) CGLat variations of spacecraft ionospheric footpoints
caused by SCW2L (colored solid lines) during activations no. 1 and no. 2;
(c) comparison of CGLat footprints variations predicted by the SCW2L (thick
lines) and time-varying adaptive AM03 models (thin lines). The black line in panel (b) indicates the ionospheric position of dummy spacecraft at X=-11 Re,
Y= 3 Re, and Z=-1.56 Re (neutral sheet, see also black square in
Fig. 7a and b). Vertical bars illustrate the amplitude of the auroral
poleward expansion observed by FSMI and SNAP ground magnetometers. The
ginger notches show AM03 predictions (at dipolarization peaks) for the dummy
spacecraft located at R= 11 Re. The footprint calculation time covers
both dipolarizations from T= 04:30 to 05:58 UT.
THEMIS ground-based all sky imager (ASI) observations. From top to
bottom: Keograms of post-midnight stations KUUJ and SNKQ and pre-midnight
stations SNAP and FSMI.
Specific magnetic field line distortions resulting from the growth an
SCW-like current system were addressed by Vasilyev et al. (1986), who
calculated the current system's magnetic effects using a wire-type SCW model
with currents flowing along stretched field lines described by the empirical
T87 magnetospheric model (Tsyganenko, 1987). Their results are most relevant
to the results of our study. In particular these authors mapped neutral
sheet locations to the ionosphere, identified mapping patterns that are
similar to the auroral bulge (like those shown in our Fig. 3), and found
that the magnitude of footprint poleward shift due to the R1 type current of
I1= 1 MA may reach 7∘ CGLat. According to their results,
FAC-related magnetic field distortions are strong enough to potentially
explain poleward auroral expansion and shape of the auroral bulge, including
the WTS formation. Our investigation includes a more accurate finite-size
filamentary model for the field-aligned currents, that is, a better (more
accurate) empirical model to describe both the background and the FAC
field-line skeleton (see Paper 1), and more sophisticated and realistic
(two-loop) construction of the SCW model. With its model flexibility and
spacecraft data coverage, our approach has a greater chance of validating the
model. Because of these improvements, we can confirm the main findings of
Vasilyev et al. (1986) and particularly confirm that the intensity of R1
current plays the main role in magnetospheric magnetic field and mapping
distortions.
The mapping problem was addressed differently by Kubyshkina et al. (2011).
As in our effort described in Sect. 3, they fit the time-varying AM03
model to observations during a substorm made with good spacecraft coverage.
Based on that model, they found that locations of the spacecraft footprints
undergo changes from magnetic field distortion and are similar to variations
in the poleward edge of bright auroras. However, as with our case, the
AM03-based technique, which uses large-scale current distributions, is not
capable of reproducing localized dipolarization and the azimuthally confined
auroral-bulge shape of footpoint distortions. The Kubyshkina et al. (2011)
result also crucially depends on spacecraft coverage and details of the
spacecraft location with respect to the location and evolution of
magnetospheric activity. The hypothesis that magnetic field distortions are
capable of producing significant bulge-like mapping displacement is also
consistent with first-principle-based simulations of fast-flow intrusion
into the inner magnetosphere (Yang et al. 2012, Birn and Hesse 2013). These
simulations also confirm the quadrupolar (combination of R1 and R2 like
loops) field-aligned current distributions associated with localized
dipolarizations.
Our investigation explored the effects of the substorm current wedge
parameters on the geometry of ionospheric mapping from the magnetospheric
equatorial plane using the advanced substorm current wedge model (SCW2L). It
provides a few conclusions important for understanding mapping distortions
and their implications for dynamics and structure of bright auroras during
the substorms.
The mapping from the dipolarized region provides evidence for the poleward shift of
ionospheric footpoints (see Figs. 2, 3 and 5). The magnitude of the latitudinal shift depends
primarily on the R1 loop current intensity (I1), which controls the
dipolarization magnitude in the magnetosphere. The footpoint displacement,
which may reach 10∘ CGLat during extremely strong substorms (I1= 2 MA)
and is minimized (< 3∘) during weak disturbances
(I1 < 0.5 MA), gives a realistic range of auroral expansion
sizes during substorms (Akasofu, 1976; Yahnin, 2006). Modeling of a substorm
event on 17 March 2010 confirms that poleward shift values (∼ 3.5 and ∼ 5∘ CGLat) predicted from data-based SCW2L
modeling results are comparable to (or are somewhat less than) the poleward
auroral expansion observed by the ground ASI network during two consecutive
activations (∼ 3 and ∼ 7…8∘ CGLat). The difference is ascribed to tailward propagation of the
reconnection/disruption region during the final substorm stage (e.g.,
Baumjohann et al., 1999).
The helical magnetic field twists magnetic field lines near FAC
filaments and forms medium-size surges at the dusk and dawn side boundaries
of the current wedge (of the azimuthally localized dipolarization region).
The surge size is comparable to the magnitude of the abovementioned poleward
expansion (Fig. 3). The surge around intense upward FACs, where electrons are
expected to be accelerated into the ionosphere by the intense field-aligned
electric field, explains the bright westward travelling surge, a remarkable
substorm-related mesoscale auroral structure. It should also be noted that
we do not consider the spiral structure at the eastward bulge termination,
because in reality it corresponds to diffuse auroras (region of active
proton precipitation) and downward FACs, which are azimuthally wider than upward FACs and
cannot be represented by a current filament. The spiral form of the aurora
is usually observed near the upward FACs, but rarely near the downward FACs.
Images of straight-shaped magnetospheric flow channels or structures can
be significantly distorted (twisted, rotated) near intense field-aligned
currents with large-scale geometry (see also Vasilyev et al., 1986; Kaufmann
and Larson, 1989; Donovan, 1993). The effect strongly depends on the
relative location of the structures with respect to the filamentary FACs.
Magnetic field twisting effect may partly cause azimuthal deflection of
auroral streamers approaching diffuse auroras (Nakamura et al., 1993;
Nishimura et al., 2010), although true flow deflection in the azimuthal
direction may also contribute to this effect (Lyons et al., 2012). An
illustration of the spiral structure around upward FACs was provided by
FREJA satellite measurements of multiple spiral arcs and the associated rotating electric fields
in the WTS region were published in Marklund et al. (1998).
In the near-Earth part of the azimuthal sector occupied by the SCW
earthward of the inner edge of the dipolarized region (where particle
injection also takes place), footpoint poleward expansion is largely
suppressed by the counter-effect of the R2 current loop. In cases with
strong R2 current (e.g., with I2/I1= 0.8 in Fig. 4, or
larger), the R2 loop field-aligned current may even produce the equatorward
shift and rotation of ionospheric footpoints, causing a small equatorward
footpoint bulge (see, e.g., Fig. 3). It is not clear the R2 current may be
this strong; more study is required. If this effect exists, it may
contribute to the modest (∼ 1–2∘ CGLat)
equatorward expansion of diffuse structured auroras that has been observed
(e.g., Nakamura et al., 1993; Keiling et al., 2012), but has not been
extensively studied.
The Supplement related to this article is available online at doi:10.5194/angeo-33-505-2015-supplement.
Acknowledgements
This study was supported by the EU FP7 grant 263325 (ECLAT) and RFBR grant
no. 14-05-31472. We thank J. Hohl (Department of Earth, Planetary, and
Space Sciences, UCLA) for help with editing of the manuscript. We also thank
INTERMAGNET project (http://intermagnet.org) for providing ground
magnetometer data and CDAWeb (http://cdaweb.gsfc.nasa.gov) data base for
providing spacecraft and auroral observations. The topical editor E. Roussos thanks the two anonymous referees for help in evaluating this paper.
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