Introduction
The solar wind plasma outflow from the Sun carries the interplanetary
magnetic field (IMF) outward into the solar system, where it interacts with
the Earth's magnetic field. When the IMF is oriented southward, reconnection
of the geomagnetic field with the IMF at the outer magnetopause boundary of
the planetary field efficiently produces open magnetic field lines which map
from the polar regions of the planet into the solar wind. These open-field
lines are dragged anti-sunward by the solar wind flow and are stretched into
a long magnetic tail, in which the field lines eventually reconnect and
return toward the Earth, back to the dayside (Dungey, 1961). This sequence
of processes broadly governs the interaction between the solar wind and the
Earth's magnetosphere–ionosphere-coupled system, including the overall
convection (Cowley and Lockwood, 1992, and references therein). This
interaction constrains the evolution of the magnetospheric system that is
known to be able to produce several possible responses, the most important
of which being the auroral substorm cycle, which classically consists of a
growth phase, a substorm onset, an expansion phase and finally a recovery
phase (Akasofu, 1964; McPherron, 1970). During the growth phase, the
interplanetary magnetic field (IMF) carried by the solar wind is usually
oriented southward so that it efficiently reconnects with the geomagnetic
field, producing new open flux. This phase ends in a substorm onset
characterized by a sudden localized brightening of the polar aurora near
midnight, which announces the expansion phase during which accumulated open
flux is closed by intense magnetic reconnection in the magnetotail (Milan et
al., 2004, 2007, and references therein). The magnetosphere then returns to
a less active state during the recovery phase, and the flux closure rate
decreases. During the substorm cycle, the open magnetic flux in the
magnetosphere, i.e. the flux of field lines that close in the interplanetary
medium (the magnetic field remains divergenceless), is often found to lie
between ∼ 0.6 and 0.7 GWb. It can also reach ∼ 0.8 GWb and sometimes more, while the reconnection rate can become as large
as ∼ 120 kV (Hubert et al., 2006a; Milan et al., 2009; Boakes
et al., 2009).
However, when the merging rate of the IMF and the geomagnetic field becomes
very large, the evolution of the magnetosphere can depart from the pattern
of the substorm cycle. The magnetosphere then exhibits another response and
enters an interval of “sawtooth” events. During a sawtooth interval,
vigorous magnetic reconnection on the dayside causes the magnetosphere to
accumulate up to ∼ 1.2 GWb of open magnetic flux and sometimes
more (De Jong et al., 2007; Hubert et al., 2008), while the reconnection rate
can easily exceed 130–150 kV (Hubert et al., 2008), whereas during the
substorm cycle, the open magnetic flux rarely exceeds 1 GWb with generally
lower reconnection rates. The other extreme situation happens at quiet
times, generally when the IMF is oriented northward so that dayside magnetic
reconnection relies on the By component of the IMF (instead of
Bz when the IMF is southward), producing a much lower merging
rate. During such quiet times, the open magnetic flux becomes smaller but
nevertheless remains non-zero (∼ 0.4–0.5 GWb and less) and
still depends on the competing opening and closure rates of magnetic flux by
dayside and nightside reconnection (respectively) that typically amount to
less than ∼ 40 kV (Hubert et al., 2006a).
Steady magnetospheric convection (SMC) intervals represent a fourth distinct
situation in which the solar wind interaction produces near-steady
conditions. They are considered representative of the steady state of the
magnetosphere interacting with the solar wind. SMCs have moderate
reconnection rates; they differ from the classical substorm cycle and from
the quiet-time situation during which the IMF-magnetosphere interaction is
reduced. The properties of SMC intervals have been thoroughly reviewed by
Sergeev et al. (1996), and we will only give a short summary in this
paragraph. During SMC intervals, the magnetospheric convection is stable,
governed by magnetic reconnection that produces open magnetic flux along the
dayside magnetopause and closes previously opened magnetic flux in the
magnetotail. Anti-sunward transport carries open-field lines to a
reconnection site located as far as, probably, ∼ 50–100 Earth radii downtail (Sergeev et al., 1996, and references therein). The tail
configuration is then intermediate between a growth phase configuration near
the Earth within ∼ 12 RE downtail and a recovery phase
configuration farther downtail. Open magnetic flux is introduced in
the system on the dayside and transported downtail like during a growth
phase. However, sustained flux closure takes place in the more distant tail
that prevents a large accumulation of open magnetic flux, unlike during a
growth phase. This can give the tail a configuration similar to what can be
found at the end of a substorm expansion and during the recovery phase, when
flux closure still takes place while the amount of open magnetic flux is not
as large as prior to the substorm onset. Indeed, detailed analysis of
in situ tail data and modelling indicate a very tail-like magnetic field
configuration and a very intense and thin current sheet in the near-Earth
tail reminiscent of substorm growth phase, whereas large magnetic field
values are found in the mid-tail along with an expanded plasma sheet, which
resembles recovery phase conditions (Sergeev et al., 1996). In addition, the
convection has a component towards the tail flanks in the plasma sheet and
transient activations, possibly reminiscent of “bursty bulk flows” (BBF),
can also take place (Sergeev et al., 1996, and references therein). It is
generally expected that the open magnetic flux content of the magnetosphere
should not vary by more than 10–20 % during SMCs and that this state
should last for more than ∼ 4–6 h, i.e. significantly
longer than the characteristic timescale of the substorm cycle. During such
an interval, the energy input from the solar wind into the magnetosphere is
rather large and fairly constant. In principle, there is no obvious physical
reason to assume that there would be a lower limit to the cross-polar cap
potential for SMCs to occur; i.e. in principle, a steady state could be
achieved by the magnetosphere whatever the value of the IMF
Bz. However, Sergeev et al. (1996, and references therein)
reported that SMCs are sometimes recorded during intervals when the
cross-polar cap potential drop, which can differ from the reconnection rate,
ranges between 60 and 90 kV, i.e. values compatible with the development of
substorm growth and expansion phases that mostly take place when the IMF is
oriented southward with a large Bz component (although
magnetic merging can also take place due to the presence of an IMF
By
component, as already mentioned above). The reason why the steady state is
mostly achieved during active intervals (except for northward IMF quiet-time
conditions) still needs to be explained. Recently, Walach et
and Milan (2015)
showed that a large fraction of SMCs can be viewed as “driven expansion
phases”, i.e. where the IMF remains southwards for a prolonged time
interval after substorm onset.
Tanskanen et al. (2005) also studied SMC intervals (which they called
continuous magnetospheric dissipation events) discriminating them from other
magnetospheric modes by the steadiness of the total pressure in the tail. In
that study, intervals were considered to be SMC events when the total pressure
did not increase by more than a factor of 2 nor decrease by more than a factor
of 2, distinguishing them from loading intervals, during which the pressure
could increase by more than a factor of 2, and unloading intervals, during
which the total pressure could decrease by more than a factor of 2. This
approach thus relates to energy loading and unloading of the magnetosphere
if we consider the total pressure as an energy density. These authors also
pointed out that BBFs occur more often and at a lower
velocity during SMC intervals than during unloading intervals.
Juusola et al. (2013) studied the relation between SMCs and the ring
current. They found that the ring current is generally enhanced during SMC
intervals and has a stabilizing effect that prevents near-Earth reconnection
to occur. They also found that the solar wind driving before and during the
SMC interval can be similar, the SMC mode appearing when the ring current
reaches a sufficiently large value.
Kissinger et al. (2012a, b) showed that SMC intervals are nearly always
preceded by a substorm expansion, which sets up SMC-specific conditions in
the magnetotail: the total pressure is enhanced and the earthward return
flow is then diverted along the tail flanks, transporting towards the
dayside newly closed magnetic flux produced along a neutral line located
downtail at a distance of between 35 and 45 Earth radii. This suggests a
possible preconditioning of the magnetosphere by preceding geomagnetic
conditions before an SMC can occur.
Since diagnosing stable conditions in magnetospheric convection from
ionospheric data alone has long been challenging, SMC intervals have often
been identified based on a set of criteria. First, stable, continuously
southward IMF should be present for more than 4–6 h. Second, enhanced
convection must occur during the interval,producing increased levels of the auroral upper (AU) and auroral lower (AL) indices (Davis and Sugiura, 1966), with the auroral electrojet (AE) index > 200 nT. Third, no
substorm signatures should be observed on the ground during the SMC
interval. Fourth, no current sheet disruption or plasmoid ejection in the
near-Earth magnetotail should be recorded, i.e. no substorm expansion
signatures in the tail (Sergeev and Lennartson, 1988; Sergeev et al., 1996).
The relation between AE and the steady convection state has been used by De
Jong and Clauer (2005) to identify SMCs. These authors proposed that any
interval with AE > 200 nT, no substorm signatures and a stable
polar cap area (so that the dayside and nightside magnetic reconnection
rates were roughly in balance) can be considered an SMC. De Jong et al. (2007)
analysed a set of SMC intervals whose selection was based on their
stable polar cap area, high activity (AE > 200 nT) and the
absence of substorm signatures. They used remote sensing of the global
aurora to compare the magnetospheric open flux during SMCs, sawtooth events and substorms. They found that the polar cap is fairly stable during SMCs,
in contrast with substorms and sawtooth intervals, during which it varies
significantly. McWilliams et al. (2006) studied SMC intervals selected using
the criterion of O'Brien et al. (2002) and analysed ionospheric convection
data from the Super Dual Aurora Radar Network (SuperDARN). They suggested
that the convection pattern was consistent with the production of open flux
in the tail lobes resulting from dayside magnetic reconnection occurring at
a prenoon, high-latitude Southern Hemisphere merging site. They also showed
the formation of a double auroral oval during an SMC case study (another
feature common to SMCs), which points to two regions of upward field-aligned
current poleward and equatorward of a downward field-aligned current,
consistent with the vorticity of the ionospheric convection recorded using
SuperDARN. McWilliams et al. (2006) also analysed in situ particle data from the Defense Meteorological Satellite Program (DMSP) showing signatures of magnetic reconnection on the
dayside. They suggested, based on the large extent of the dayside merging
site inferred from the DMSP data, that intense reconnection must take place
on the dayside magnetopause, compensated for by flux closure in the tail.
We have developed a method that combines SuperDARN observations of
ionospheric convection with global images of the proton aurora recorded with
the Spectrographic Imaging at 121.8 nm (SI12) instrument (Mende et al.,
2000a, b) onboard the Imager for Magnetopause to Aurora Global Exploration
(IMAGE) satellite, to estimate the open magnetic flux threading the polar
cap and the reconnection rates at the dayside magnetopause and in the
magnetotail (Hubert et al., 2006a). These rates are expressed as electric
voltages from the application of Faraday's law (1 Wb s-1= 1 V). Since
the SI12 images are almost uncontaminated by dayglow, the method has the
advantage of working during any season. The method has been validated
against DMSP observations by Hubert et al. (2006a), who also applied the
method to several substorm intervals, showing the flux opening and closure
associated with the growth and expansion phases of the substorm cycle. They
also showed that magnetic flux is closed by pseudo-breakups and that
poleward boundary intensifications (PBIs) observed during the recovery phase
result from minor reactivations of flux closure in the tail. In addition to
the DMSP validation done by Hubert et al. (2006a), Hubert et al. (2010)
compared the global-scale boundary determination from the IMAGE-FUV (Far Ultraviolet)-SI12 observations with the polar cap boundary location determined locally at a higher space and time resolution using the European Incoherent Scatter Scientific Association (EISCAT) facility. Both methods
showed an acceptable agreement: for most of the analysed intervals, the
polar cap boundary determined by both methods is collocated within the
space resolution of both methods, i.e. ∼ 0.5∘ MLAT
on average (this number was found to depend on substorm phase; we refer the
interested reader to the original study). Hubert et al. (2010) also show an
interval for which the discrepancy can reach ∼ 1.9∘ MLAT on average, which remains relatively good considering that the space
resolution of the SI12 instrument is on the order of 1∘ MLAT.
These authors also undertook a comparison with the location of the magnetic
convection reversal boundary (MCRB) and with the boundary location found
from observation of the OI(1D) emission at 630 nm. Here again a
satisfactory agreement was found: the SI12 and MCRB boundary were generally,
but not always, collocated considering the resolution of both methods except
for notable intervals showing large discrepancies (not larger than
4∘ MLAT), especially close to the Harang discontinuity where the
MCRB does not necessarily follow the vicinity of the polar cap boundary. The
method has also been applied to the study of flux closure induced by solar
wind dynamic pressure pulses (Hubert et al., 2006b, 2009), showing that a
strong compression of the tail by a solar wind pressure discontinuity
extends to the plasma sheet and stimulates the process of flux closure.
Hubert et al. (2007) analysed the magnetic reconnection associated with
auroral streamers, i.e. the ionospheric counterpart of BBFs, and proposed
that these events are initially produced by flux closure, possibly followed
by subsequent acceleration by other processes. Using the same method, Hubert
et al. (2008) showed, as already outlined above, that sawtooth events take
place when the magnetosphere is overloaded by open magnetic flux produced by
magnetic reconnection with the IMF at very high rates on the dayside, faster
than it can be closed by the usual substorm cycle, such that the
magnetosphere accumulates a large amount of open magnetic flux, which is
eventually closed at a high rate in the tail.
The FUV experiment onboard the IMAGE satellite not only
provides images of the proton aurora. The Wideband Imaging Camera (WIC)
observes the aurora between 120 and 200 nm, while the Spectrographic Imaging
at 135.6 nm instrument (SI13) is sensitive between ∼ 130 and
∼ 140 nm (Mende et al., 2000a, b). Both instruments provide
images of auroral emissions mainly excited by secondary electrons produced
by both the electron and proton precipitation, the most important of which
are the OI 130.4 and 135.6 nm, NI 149.2 nm, and N2 LBHLyman-Birge-Hopfield (LBH) emissions. The three
FUV imagers, namely WIC, SI13 and SI12, can be used simultaneously to
monitor the evolution of the aurora and to identify the commencement of an
expansion phase, for example. It must be noted that dayglow luminescence is
excited by photoelectrons, which are produced in the same kinetic energy
range as the auroral secondary electrons, so that both the WIC and SI13
instruments are sensitive to dayglow. By contrast, the SI12 imager detects
Doppler-shifted Lyman-α photons emitted by precipitating protons
that have captured an electron, so that it is nearly insensitive to dayglow
emissions, the instrument being designed to efficiently reject the nearby
geocoronal HI-Lyman-α 121.6 nm and NI -120 nm emissions. The
choice by Hubert et al. (2006a) to avoid using the data from the WIC and
SI13 instruments in the estimation of the polar cap boundary location was
not justified by the sensitivities of the WIC and SI13 instruments, which
are very good too. It rather relied on the need to use dayside auroral
images to estimate the open magnetic flux and reconnection voltages in all
seasons, including when the dayside aurora is largely immersed in the
dayglow, where the Poisson noise of the images can easily dominate the
auroral signal. In principle, the WIC and SI13 images could thus also be
used to study the polar cap boundary on the nightside. However, we focus on
the SI12 observation of the proton aurora because we are interested in both
the dayside and nightside parts of the oval.
In this study, we analyse several SMC intervals previously identified by
McWilliams et al. (2006) and De Jong et al. (2007), for which good quality
(i.e. with convenient viewing geometry and auroral intensity) SI12 images of
the proton aurora are available simultaneously with SuperDARN measurement of
the ionospheric convection. We combine the SI12 images and the SuperDARN
data to estimate the dayside and nightside magnetic reconnection rates and
the open magnetic flux using the method described and validated by Hubert et
al. (2006a). Our scientific objective is not only to characterize the
magnetic reconnection process during SMC intervals but also to compare our
results with other magnetospheric situations, namely quiet time, substorm
cycle and sawtooth events, and to determine the ranges of open magnetic flux
and reconnection rates relevant to those well-identified magnetospheric
modes. We thus finally discuss our results in the context of our previous
studies, presenting quiet times, the auroral substorm cycle, SMC intervals and sawtooth events as four magnetospheric modes which occur depending on
the input provided by the solar wind and the accumulated open magnetic flux.
Case studies
We have analysed a set of 11 intervals during which SMC conditions occur.
These intervals encompass a total of ∼ 1700 IMAGE-FUV images
representative of SMC conditions. In Sect., 2.1, 2.2 and 2.3, we will
first present three SMC cases in detail. Eight other SMC intervals will be
briefly described in Sect. 2.4, concentrating on the modest differences
existing in these eight cases compared with those of Sect. 2.1, 2.2 and 2.3.
SMC interval on 3 January 2001
An SMC interval was identified by McWilliams et al. (2006) on the 3 January 2001 between 02:57 and 06:46 UT, at the end of a substorm expansion phase with
onset at 02:35 UT. The interval was identified based on the AE > 200 nT criterion and imposing that the decrease rate of AL was less than
25 nT min-1 to ensure no substorm onset. The magnitude of both the AL and
AU indices increases after 02:30 UT indicating a progressive increase in the
convection, together producing an AE index larger than 400 nT (Fig. 1). The
three indices indicate significant activity, but this differs from that of
the substorm cycle. We also verified from the detailed magnetograms from the
Fennoscandian International Monitor of Auroral Geomagnetic Effecs (IMAGE, not to be confused with the IMAGE satellite) magnetometer chain and from the Canadian Array for Realtime Investigations of Magnetic Activity (CARISMA) network (Mann et al., 2008) that no clear substorm signatures are
present (not shown). Indeed, the AE, AU and AL indices are composite
quantities that summarize the data from a large number of magnetometers
distributed in longitude, and one should not expect to find a signature from
a sharp substorm expansion in magnetograms when these indices reveal none.
The IMAGE-FUV instruments provide auroral images between 00:00 and 05:41 UT,
showing that the auroral activity was high after the onset at 02:35 UT and
during the following SMC interval. The solar wind properties remained fairly
stable during a long interval that day, as shown in Fig. 2. The solar wind
velocity varied very slowly from ∼ 330 to ∼ 350 km s-1 over ∼ 5.5 h, i.e. an average rate of variation of
only ∼ 0.001 km s-2. The solar wind dynamic pressure
Pdyn was more variable, due to the variations in the solar
wind density. The IMF remained southward for ∼ 5 h,
allowing the magnetospheric and interplanetary magnetic fields to merge and
produce open magnetic flux at the dayside magnetopause. It is thus not
surprising that the observed aurora remained active for a long interval.
(a) AE, (b) AL and(c) AU indices recorded on 3 January 2001.
Solar wind properties recorded by the ACE (Advanced Composition Explorer) satellite on 2 and 3 January 2001.
The timescale has been shifted by 79 min to approximately
account for the propagation time from the spacecraft to the Earth. The solar
wind dynamic pressure in (c) is computed from the number density
and the velocity shown in (a) and (b). The IMF remained
southward for ∼ 5 h, as shown in (d) (GSM
coordinates).
SuperDARN observations of the ionospheric convection were also available
simultaneously with the IMAGE-FUV observations and were used to reconstruct
the ionospheric electric field in the polar cap, which is needed to allow us
to estimate the opening (Vop) and closure (Vcl)
electric potentials that represent the rates of magnetic reconnection
(Hubert et al., 2006a). The open magnetic flux (Φ) threading
the polar cap, delineated using the SI12 observations of the proton aurora,
was also estimated (Fig. 3a). The open magnetic flux increases after 01:00 UT
due to reconnection with the IMF. The reconnection at the magnetopause is so
efficient that the flux closure associated with the expansion phase observed
after 02:35 UT does not prevent the open magnetic flux from increasing.
Figure 3b shows several SI12 images in polar view, obtained during that
interval, with the estimated location of the polar cap boundary overlaid.
This boundary is represented using a Fourier series, allowing interpolation
in unconstrained MLT sectors (i.e. MLT sectors where the aurora is too dim
to be detected with the SI12 instrument so that the location of the boundary
cannot be determined from observation). This choice also has another
advantage: when the magnetic field can be assumed to be dipolar (which is
certainly the case at ionospheric altitudes for the purpose of computing the
magnetic flux), the magnetic flux threading the polar cap (i.e. the open
magnetic flux) delineated by such a Fourier series can be easily computed
analytically (Appendix A). The auroral brightness obviously increases as the
activity rises, first slowly between 00:01 and ∼ 02:30 and more
sharply thereafter to become very bright after 03:00. The polar cap area
nevertheless remains roughly constant between 03:00 and 04:00 UT. The auroral
brightness is even larger after 04:00, when flux closure reduces the
magnetospheric open flux. Apparent fluctuations of the boundary appear
versus UT and are also present versus MLT (although it does not appear in
the figure). These fluctuations are efficiently filtered out using an
appropriate time smoothing over a timescale of ∼ 6 min full width at half maximum (FWHM).
The smoothing is realized by applying successive boxcar averaging with
decreasing width. This procedure fairly mimics convolution by a Gaussian
function but with a smaller computational cost. In this study, we use
widths varying from 3 to 6 (with steps of 1), and when the width is an even
number, the next larger odd number is used instead. Tests already conducted
by Hubert et al. (2006a) showed that this procedure efficiently smooths time
variations of the estimated open magnetic flux occurring at a too large rate
to be physically meaningful. On the other hand, the time-smoothed Fourier
series representing the polar cap boundary is less able to correctly account
for short-lived real variations of the polar cap boundary taking place on a
small MLT scale. The increase (decrease) of the polar cap area associated
with net flux opening (flux closure) is conspicuous over the interval,
comparing the polar cap boundary prior to and after 03:00 UT (04:00 UT,
respectively).
(a) Open magnetic flux estimated using IMAGE SI12 observations of
the proton aurora on 3 January 2001. (b) Polar view of the proton aurora
observed with the SI12 instrument, shown in geomagnetic coordinates. The
colour scale is expressed in counts. Concentric circles are 10∘ MLAT
apart and noon is at the top of each snapshot (12 h MLT). The ionospheric
convection velocity vector field deduced from SuperDARN measurements is also
plotted, averaged on a 5∘ MLAT × 2 h MLT grid. A 1 km s-1 reference
arrow is shown in the lower right corner of each picture. The average of the
SuperDARN measurements of the ionospheric velocity over the polar caps
shown is, in chronological order, 248, 247, 442, 594, 536, 502, 467, 496 and 462 m s-1. The location of the polar cap boundary deduced from the SI12
images and represented with a Fourier series is overlaid. Uncertainties in
the polar cap boundary location produce artificial noisy variations of the
estimated open magnetic flux (a), which can be eliminated by applying
appropriate smoothing as shown.
The ionospheric convection velocity vectors deduced from the SuperDARN data
are also overlaid in each image, after averaging on a 5∘ MLAT × 2 h MLT
grid for the sake of readability of the figure. Despite local variations of
the velocity field, the broad brush properties of the convection pattern
remain rather stable during the SMC interval, especially between 03:00 and
04:00 UT, with an important west–east component in the midnight sector and a
fairly stable return flow observed in the dawn sector. It must, however, be
stressed that it is not easy to follow the convection pattern using the
SuperDARN radar network during an extended interval because the MLAT–MLT
region covered by the observations changes as the planet rotates, no radar
being available across the Siberian region. Figure 4a shows our estimated
net reconnection voltage, which gives the time derivative of the open
magnetic flux. As expected, the net voltage is significantly positive when
the open magnetic flux grows at a sustained rate between 01:00 and 03:00 UT.
After 03:00 UT, the net voltage is close to zero, and the open magnetic flux
remains fairly constant for ∼ 1 h. This stability of the
open magnetic flux can be considered a symptomatic feature of SMCs, as it
was proposed earlier by Yahnin et al. (1994), Sergeev et al. (1996), De Jong
and Clauer (2005), and De Jong et al. (2007). Sergeev et al. (1996) also
pointed out that a considerable amount of open magnetic flux had to be
closed in the magnetotail during SMCs. Figure 4b and c show that the
reconnection rate between the IMF and the geomagnetic field is large at the
time the open flux grows, peaking above 120 kV, whereas it returns to
smaller though still large values around ∼ 50 kV between 03:00
and 04:00 UT, when the open flux is steady. The flux closure voltage reaches
∼ 80 kV during the expansion phase starting at 02:35 UT, which
is lower than that often found during a substorm expansion, when a flux
closure rate peaking above 100 kV is not uncommon. The relatively low value
of the closure voltage during this expansion phase is consistent with the
open flux still increasing at that time, the net reconnection rate remaining
positive until 03:05 UT. Between 03:00 and 04:00 UT, when the open magnetic flux
remains fairly steady, the flux closure voltage stabilizes around 60–70 kV, a value comparable with the dayside reconnection voltage, allowing a
near balance of the magnetic opening and closure rates. The value that we
find is significantly larger than the quiet-time reconnection rate of some
∼ 30 kV found by Hubert et al. (2006a), but it remains lower
than that found during substorm expansion phases (∼ 100–140 kV), while sawtooth intervals can have reconnection rates significantly
above that of substorms, with the open magnetic flux reaching ∼ 1.2 GWb (Hubert et al., 2008).
(a) Net reconnection voltage, (b) magnetic flux opening rate and (c) magnetic flux closure rate deduced from SI12 and SuperDARN observations
on 3 January 2001. The net voltage in panel (a) is the sum of those in
panels (b) and (c).
SMC interval on 21 August 2000
An SMC interval was reported to occur on 21 August 2000 by De Jong et al. (2007). The AE index remained above 200 nT between 20 August 22:07 UT and
22 August 00:45 UT (with a short-lived excursion below 200 nT on 21 August
around 01:22 UT), the AU and AL indices both reaching a high magnitude
indicating enhanced magnetospheric activity, as shown in Fig. 5. As for the
first interval presented above, the detailed magnetograms from the Canadian
CARISMA and Scandinavian IMAGE networks are compatible with the AE, AU and
AL indices, as expected. Simultaneous IMAGE FUV and SuperDARN observations
were again available on that day, except before 04:32 UT and between 14:10
and 18:30 UT. During more than 1 hour after 04:32 and 18:30 UT, the IMAGE
spacecraft was however leaving its perigee and remained too close to the
planet for the viewing geometry to allow a global treatment of the images of
the proton aurora. No substorm expansion signatures appeared in the global
FUV imaging of the aurora with the IMAGE-FUV instruments between 04:32 and
09:01 UT. Between 09:01 and 09:30 UT, an auroral bulge appears, indicating that
some magnetic flux is being closed in the tail, suggesting that the
magnetosphere was not in a state of steady magnetic convection at that time.
This holds between 10:50 and 11:50 UT as well, an expansion being observed
with a marked poleward retraction of the nightside polar cap developing
after 11:04 UT, followed by what seems to be a long recovery phase showing
PBIs, i.e. still allowing a small amount of magnetic flux closure. An
intensification that we identify as a pseudo-breakup is seen in the FUV
auroral images at 21:42 UT, followed by a substorm expansion phase with onset
at 21:50 UT, which could signal the end of the steady convection state of the
magnetosphere.
(a) AE, (b) AU and (c) AL indices recorded on
21 August 2000.
Solar wind properties measured by the Wind satellite on 21 August 2001 are
shown in Fig. 6. The solar wind velocity and IMF Bz component
were fairly stable after 02:00 UT. The solar wind density varied a bit more,
causing the solar wind dynamic pressure to vary between ∼ 1 and 2.4 nPa after 02:00 UT. The dynamic pressure remains low despite the
rather large density (∼ 8 cm-3), due to the low velocity.
The southward orientation of the IMF did allow magnetic reconnection to
efficiently open magnetic flux at the Earth's magnetopause during most of
the interval, so that active conditions can develop in the magnetosphere, as
obviously appears in the AE index shown in Fig. 5a.
Solar wind properties measured by the Wind satellite on 21 August 2000 in the same format as Fig. 2. The timescale has been shifted by 11 min
to approximately account for the propagation time between the spacecraft and
the Earth.
Open magnetic flux estimates using the SI12 images of the proton
aurora obtained on 21 August 2000 between (a) 05:55 and 13:30 UT and (b) 19:25
and 23:59 UT, in the same format as Fig. 3a. SI12 images of the proton aurora
in geomagnetic polar view (c and d) with the ionospheric convection velocity
deduced from SuperDARN observations and with the estimated location of the
polar cap boundary, in the same format as Fig. 3b, obtained during the time
intervals corresponding to panel (a) and (b), respectively. The average of the
SuperDARN measurements of the ionospheric velocity over the polar caps
shown is, in chronological order, 392, 467, 212, 332, 364, 428, 493, 502, 508, 453,
508 and 319 m s-1.
The open magnetic flux estimate based on the SI12 observations of the
proton aurora on 21 August 2000 is shown in Fig. 7. This remains fairly
stable, ranging between ∼ 0.8 and 0.9 GWb from 05:55 to
∼ 09:00 UT, as shown by the first two SI12 images in Fig. 7c.
The increased activity seen in the FUV images of the aurora after 09:00 UT is
obviously related to the reduction in the magnetic flux starting after 09:00 UT, whereas the activation of the auroral oval observed after 10:50 UT
relates to the conspicuous flux closure shown at that time in Fig. 7a. In
view of these results, it seems that the magnetosphere slightly departs from
a state of SMC between 09:00 and 13:30 UT: the AE index remains compatible
with the SMC conditions although it shows transient large variations around
09:30 and 13:00 UT, but significant open flux variations nevertheless take
place. There is no variation of the solar wind conditions that could
obviously be considered a trigger for the flux closure. The variations of
the open magnetic flux deduced from the SI12 proton aurora observations
therefore rather appear as transient variations around the more stable
conditions of the SMC flow, although our dataset cannot clearly reveal
exactly what happened in the magnetosphere at that time. One possibility is
the occurrence of several BBFs during a relatively short time interval,
since Tanskanen et al. (2005) pointed out that BBFs often occur during SMC
intervals, while Hubert et al. (2007) showed that these are related to flux
closure. By contrast, the open magnetic flux estimated between 05:55 and 09:00 UT is fully compatible with an SMC state. The open magnetic flux shown in
Fig. 7b between 19:45 and ∼ 21:45 UT is stable as well, around
∼ 1.02 GWb, which is compatible with a state of SMC. Figure 7c
shows the SI12 and SuperDARN observations at a few selected UT times between
05:55 and 13:30 UT, with the estimated location of the polar cap boundary
overlaid. The high-resolution fluctuations of the boundary that appear in
Fig. 7c (and in Fig. 7d, to be discussed later in this paragraph), as in Fig. 3b, are efficiently removed by an appropriate time smoothing. The polar cap
area decreases as flux closure is going on, and the brightening of the
aurora corresponding to the beginning of the flux closure is obvious around
11:00 UT. The convection pattern is mainly observed on the dayside at this
time, such that its stability is hard to assess in sectors where the field
lines can reasonably be assumed to map to the nightside lobes of the
magnetotail. Figure 7d shows the fair stability of the polar cap area prior
to 22:00 UT and its decrease when flux closure goes on after 21:42 UT, as shown
in Fig. 7b. The ionospheric convection pattern deduced from the SuperDARN
observation (averaged on a 5∘ MLAT × 2 h MLT grid for the sake of figure
readability) shows a fair stability in the 12:00–24:00 MLT sector before 21:48 UT.
The convection pattern appears to change during and after the contraction of
the polar cap, becoming oriented eastward in the pre-midnight sector. The
flux closure that takes place after 21:42 UT (Fig. 7b) that corresponds to a
sharp contraction of the polar cap (Fig. 7d) is a clear signature of a
substorm expansion, starting with a pseudo-breakup at 21:42 UT and an
expansion onset at 21:50 UT (not shown).
Reconnection voltages estimated using SI12 observations of the
proton aurora and SuperDARN measurements of the ionospheric convection on 21 August 2000. The net reconnection voltage (a) and (b) results from the
imbalance between the rate of magnetic flux opening (c) and (d) and
closure (e) and (f).
The estimated reconnection rates based on the IMAGE SI12 remote sensing of
the proton aurora and the SuperDARN observation of the ionospheric
convection are shown in Fig. 8. The net reconnection voltage presented in
Fig. 8a and b show, as expected, that the net voltage remains close to
zero during intervals of quasi-steady open magnetic flux, when the flux
opening and closure rates nearly compensate for each other. This balance seems to be
achieved when the dayside reconnection rate, which can be viewed as imposed
by the solar wind properties, amounts to ∼ 50 kV, prior to
09:00 UT. The expansion phases observed after 09:00 and 10:50 UT obviously
result from an intensification of the magnetic flux closure voltage shown in
Fig. 8e, the expansion phase observed at 10:50 UT being preceded by an
intensification of the magnetic flux opening voltage to ∼ 100 kV (Fig. 8c). This can be seen in the increase in the polar cap area between
10:27 and 11:00 UT (Fig. 7c) followed by its retraction as shown at 11:24 and
12:03 UT. The intensification of the reconnection rate in the magnetotail
during the expansion phase observed after 21:42 UT is manifest in Fig. 8f.
Prior to that time, the polar cap area delineated at 20:55, 21:01 and 21:22
(Fig. 7d) remains fairly constant, after which it progressively shrinks as
shown at 21:48, 22:00 and 22:33 UT. The peak magnitude of the three expansions
reported above ranges between 120 and 140 kV. Between 19:45 and 21:45 UT,
however, the open magnetic flux is quasi-steady, and the net reconnection
voltage is close to zero (Fig. 8b). The balance between opening and closure
is achieved when those voltages equilibrate around ∼ 50–60 kV. The ionospheric convection measured by SuperDARN is also compatible with
sustained dayside merging.
SMC interval on 26 January 2001
An SMC interval was reported by De Jong et al. (2007) on 26 January 2001
between 04:00 and 07:50 UT. The AE, AU and AL indices shown in Fig. 9 reveal
that the magnetosphere was active at that time, with AE larger than 200 nT
after 04:00 UT, i.e. compatible with SMC conditions. As for the first
interval presented above, detailed magnetograms from the Canadian CARISMA
and Scandinavian IMAGE networks are compatible with the AE, AU and AL
indices, as expected. The solar wind properties measured by the ACE (Advanced Composition Explorer) satellite (Fig. 10) show a stable slow solar wind velocity. The solar wind
density varies between ∼ 2 and ∼ 8 cm-3.
The solar wind dynamic pressure remains small throughout the interval. It is
rather stable, despite the rapid variation around 06:30 UT, which has a small
absolute amplitude. The IMF Bz remains steadily southward
after 03:00 UT, allowing magnetic reconnection at the magnetopause to open
magnetic flux during a prolonged period of time, which can stimulate
magnetospheric activity, as expected when AE > 200 such as during
this SMC interval.
AE (a), AU (b) and AL (c) indices recorded on 26 January 2001.
After 04:00 UT, the AE index has a value larger than 200 nT, compatible with
SMC conditions.
Solar wind properties measured by the ACE satellite on 26 January 2001 (same format as Fig. 2). The timescale has been shifted by 78 min to
approximately account for the propagation time between the spacecraft and
the planet.
The open magnetic flux estimates based on the SI12 remote sensing of the
proton aurora are shown in Fig. 11a. After 02:00 UT, the open magnetic flux
increases at a slow rate. This growth terminates around 07:30 UT. Indeed, the
IMAGE-FUV images of the Earth's aurora show an active oval throughout the
interval, with possible brightening such as is observed at 05:00 UT and an
expansion onset occurring at 07:30 UT followed by a conspicuous poleward
motion of the oval. Consequently, the estimated open magnetic flux decreases
rapidly after 07:30 UT. The variation of the polar cap area during this
interval can be seen in Fig. 11b that shows the SI12 observation of the
proton aurora at several UT times, with the estimated location of the polar
cap boundary: the polar cap area progressively increases between 02:00 and
07:30 UT, after which a dramatic flux closure takes place which reduces the
polar cap area (07:32–08:01 UT) as the auroral brightness becomes very
large in the pre-midnight sector. Figure 11b also shows the ionospheric
convection velocity field deduced from the SuperDARN observation, averaged
on a 5∘ MLAT × 2 h MLT grid for the sake of figure clarity. The gross
properties of the convection pattern appear fairly stable versus time, as
far as this stability can be analysed from SuperDARN observations during
such a long interval. The general convection pattern even seems to persist
when flux closure takes place, between 07:32 and 08:00 UT. The expansion is
also evident in the net voltage (Fig. 12a) and in the flux closure rate
(Fig. 12c) that reached ∼ 165 kV. Between 02:00 and 06:00 UT,
the closure voltage (Fig. 12b) ranges between ∼ 50 and
∼ 70 kV. The flux closure rate does not exactly compensate for the
dayside merging rate, allowing the open magnetic flux to increase slowly as
shown in Fig. 11a, b. Nevertheless, we find again the same range for the
reconnection voltage, i.e. around ∼ 60 kV. This event has,
however, the special property of presenting a slowly increasing open
magnetic flux, suggesting that we should have some tolerance on the
steadiness of the system when considering SMC intervals, i.e. the
magnetosphere seems to be capable of developing stable convection, even when
a slight regular imbalance persists between flux opening and flux closure,
not only producing fluctuations of the open magnetic flux but also allowing
a slow but sustained variation of that flux in the long run. This will be
considered again on more quantitative grounds in the discussion section. It
is interesting to note that, for all three SMC cases that we have detailed,
the solar wind velocity was rather low, between ∼ 330 and
∼ 360 km s-1.
Open magnetic flux estimated using the SI12 images of the Earth's
proton aurora on 26 January 2001, in the same format as Figs. 3 and 7. The
average of the SuperDARN measurements of the ionospheric velocity over the
polar caps shown is, in chronological order, 332, 424, 412,477, 498, 416,
354, 468 and 444 m s-1.
(a) Net reconnection voltage, (b) magnetic flux opening rate
and (c) magnetic flux closure rate deduced from SI12 and SuperDARN observations
on 26 January 2001. The values in panel (a) are the sum of those of
panels (b) and (c).
Other SMC intervals
We have also analysed several other SMC intervals that occurred on 12 and
30 September, 26 October, 20 November, 22 December 2000, 21 January, 12 May, and 16 November 2001 (De Jong et al., 2007). The
general trends of these events are similar to those described above, with
some variability. For these events, the solar wind velocity is generally
low, below 400 km s-1, with one exception on 12 May 2001, for which the
solar wind velocity reaches 650 km s-1 during a part of the interval but for which the velocity stays around 400 km s-1 for most of the
interval. The open magnetic flux recorded during these events ranges between
∼ 0.45 and 0.95 GWb, with a general trend around
∼ 0.7 GWb. The SMC interval of 9 December 2000 is an
exception: the open magnetic flux was between 1 and 1.1 GWb on that day. The
opening and closure voltages also have some variability and range between
∼ 40 and ∼ 80 kV. These voltages generally
balance around ∼ 50–70 kV. The event of 12 May 2001 departs
from this picture because a very active interval is found between 09:30 and
12:00 UT, with the closure voltage peaking at 150 and 180 kV, although the
FUV observation of the aurora does not show a well-defined substorm
expansion with an onset but rather a strongly disturbed oval. The opening
voltage also reached large values during that part of the interval, with
peaks at 150 and 120 kV. It must be noted that this disturbed interval is
found after the arrival of a moderate dynamic pressure discontinuity in the
solar wind and while the solar wind velocity was increasing to values well
above 500 km s-1. Discontinuities in the solar wind dynamic pressure
are known to be capable of stimulating magnetic flux closure in the tail
(Boudouridis et al., 2004; Hubert et al., 2006b, 2009). This part
of the interval has several properties that strongly depart from those of
the other SMC intervals, and it is not clear that it can be considered to be representative of SMC conditions.
Discussion
Properties of SMCs
We have analysed several intervals of steady magnetospheric convection.
Combining the global observations of proton aurora and ionospheric
convection for these SMC events, we estimate that the open magnetic flux
remains fairly stable between ∼ 0.6 and 0.9 GWb, with some
variability from case to case, compatible with the range of open magnetic
flux estimated by De Jong et al. (2007) using observations from the WIC
instrument. The rates of opening and closure of magnetic flux are typically
between ∼ 35 and 75 kV, which roughly corresponds to the
previously reported cross-polar cap potential of ∼ 60–90 kV
(Sergeev et al., 1996, and references therein), given that the cross-polar cap potential does not necessarily correspond to the reconnection rate
in the tail or near the magnetopause. The statistical properties of our
estimated open magnetic flux and reconnection rates are summarized in Table 1. The tabulated standard deviations reflect the variability that exists
between different SMC intervals but also within a given interval. The net
magnetic reconnection voltage reflects the total rate of change in the open
magnetic flux. On average, we find it to be close to zero during SMCs (Table 1). However,
this quantity is zero on average on long timescales whatever
the magnetospheric state, since over sufficiently long intervals the
magnetosphere cannot indefinitely accumulate open flux. By contrast, the
absolute value of the net reconnection voltage |V|
can largely differ from zero on any short timescale, like during the
substorm cycle for example. The average of |V|
slightly differs from zero during the SMCs studied here and amounts to
roughly one third of the estimated individual voltages because the balance
between magnetic flux opening and closure can never be perfectly reached (as
obviously expected). The slightly positive average value of V could
partly result from the slow sustained growth of the open magnetic flux that
we record on 26 January 2001. This event suggests the possibility for the
magnetosphere to show properties typical of steady magnetospheric convection
even though the long-term steadiness is not perfectly fulfilled.
Nevertheless, the near-stability of the open magnetic flux that we obtain
for most of the intervals treated here stands along the same lines as the
results found by De Jong and Clauer (2005) and De Jong et al. (2007). We
also find indications that the ionospheric convection pattern also remains
fairly stable during SMC intervals and that the solar wind velocity was
rather low for most of the SMC intervals of our dataset, generally below
∼ 400 km s-1. The low solar wind velocity of SMCs was
also found in several previous studies (O'Brien et al., 2002; DeJong et al.,
2009; Huang et al., 2009; Partamies et al., 2009a, b). It is thought to be
related to the lower reconnection electric field of the slower solar wind
and with specific internal properties of the magnetosphere possibly
regarding magnetotail convection, but a full understanding of the mechanism
is still needed.
Statistical characteristics of the estimated open magnetic flux
(Φ), absolute value of the magnetic flux closure voltage
(Vcl), magnetic flux opening voltage (Vop), net
reconnection voltage (Vnet) and its absolute value
(|Vnet|), residence timescale of the
open magnetic flux (τ), cross-tail plasma velocity estimated
assuming a 20 RE tail radius (vz20), tail radius
estimated from the ACE solar wind data using the model of Petrinec and
Russel (1993, 1996) (RT), and cross-tail plasma velocity estimated assuming
the tail radius is that estimated using the model of Petrinec and Russel (1993, 1996) (vz). The estimated averages and standard
deviations are given with the number of SI12 images used in the statistics.
m
σ
n
Φ (GWb)
0.745 ± 0.004
0.16
1723
Vcl (kV)
54.6 ± 0.5
21
1723
Vop (kV)
57.7 ± 0.5
21
1723
Vnet (kV)
3.0 ± 0.6
27
1723
|Vnet| (kV)
20.1 ± 0.4
17.6
1723
τ (h)
4.068 ± 0.035
1.42
1672
vz20 (km s-1)
9.91 ± 0.10
4.1
1672
RT (RE)
32.41 ± 0.13
4.36
1159
vz (km s-1)
15.35 ± 0.16
5.4
1159
In an oversimplified model, the magnetosphere could be viewed as composed of
two “reservoirs” of magnetic flux: the open and closed magnetic flux
reservoirs that exchange magnetic flux through magnetic reconnection taking
place at the magnetopause on the dayside and in the plasma sheet on the
nightside. This approach allows us to define the residence timescale of the
open magnetic flux reservoir as the ratio between its content and its loss
rate: τ = Φ/Vcl.
Clearly this expression is exact in the case of a steady state but is
employed here more generally as an instantaneous indicator of the timescale
on which the open flux reservoir would be emptied in the absence of further
open flux production. We computed this ratio for each of the 1723 SMC images
of our dataset. We analysed the statistical characteristics of
τ excluding ∼ 3 % of the data with extreme
values that we consider as outliers which are able to bias our results
(Table 1). We find that τ ranges across a broad interval of
values. It amounts to 4.07 h on average, with a standard deviation of
1.42 h. The SMC timescale thus appears a bit longer than that of the
substorm cycle (∼ 3 h). Our estimate of τ is
also compatible with the generally accepted timescale of SMCs of 4–6 h.
The concept of residence timescale can also be used to understand that an
SMC can develop despite the apparent unsteadiness of the open magnetic flux
on 26 January 2001 (Fig. 11). The timescale T of the growth of the
open magnetic flux can be estimated across the SMC interval by comparing the
amount of open magnetic flux Φ with its overall rate of
variation as T = Φ/(ΔΦ/Δt) with Φ∼ (0.62+0.85)/2=0.735 GWb, ΔΦ∼0.85-0.62=0.23 GWb and Δt∼ 7 h (ΔQ being the
variation of quantity Q), so that T ∼ 19 h,
much longer than τ. The concept of steadiness could then be
moderated as follows: a significant, sustained, variation of the open
magnetic flux (a 30 % increase in this case), which takes place on
timescales much longer than the SMC residence timescale of the open magnetic
flux, does not necessarily prevent the magnetosphere from satisfying the SMC
criteria.
The order of magnitude of the residence time of open flux tubes can also be
roughly checked using the convection velocity patterns shown in Figs. 3, 7
and 11. These figures show ionospheric velocity vectors with a magnitude
ranging approximately between 0.25 and 0.75 km s-1 in the polar cap
during several SMC intervals. The detailed trajectory of the ionospheric
plasma is hard to determine, but we can estimate that the length of the path
across which the plasma threaded by open flux tubes has to travel from the
noon sector (roughly mapping to the opening neutral line along the magnetic
field lines) to the midnight sector (roughly mapping to the closure neutral
line along the magnetic field lines) is on the order of ∼ 4500 km, i.e. the length of a circular arc subtended by an angle of 40∘ on a
sphere with a radius of 6471 km. We then estimate that the order of
magnitude of the residence time ranges between ∼ 1.67 and
∼ 5 h, compatible with our previous estimate.
For the sake of obtaining orders of magnitude, the transit time can be used
to approximately determine the GSM z component of the velocity of the plasma
convection in the tail if we consider that τ roughly represents the
time needed for plasma threaded by a particular open flux tube to move from
the magnetopause to the reconnection site of the central plasma sheet.
Assuming that the plasma has to travel along the distance of the tail radius
(in the z direction) arbitrarily set to 20 RE (a reasonable value,
after Kivelson and Russel, 1997), the convection velocity
(vz20) can be estimated for our set of SMC images. These
values are statistically summarized in Table 1. The average of
vz20 is 9.91 ± 0.10 km s-1 (the standard
deviation of the sample being ∼ 4 km s-1), significantly
larger than the average velocity reported by Haaland et al. (2009) based on
Cluster data collected between February 2001 and October 2007 (despite an
overlap due to the scatter of our dataset); these authors found that the z component
of the convection velocity is ∼ 7.7 km s-1 on average in
the tail lobe, based on Cluster observations gathered between
XGSM ∼ -5 and XGSM ∼ -21 RE. This suggests that the enhanced activity of SMC intervals has a
convection velocity enhanced by ∼ 30 % as counterpart in the
tail, SMC conditions representing only a subset of all the conditions
possibly included in the study of Haaland et al. (2009). The value of the
tail radius RT can also be estimated based on solar wind data
from the ACE satellite, using the model of Petrinec and Russel (1993, 1996),
which relates the tail radius to the solar wind dynamic pressure and IMF
Bz. This value was computed at the time of each SMC image of
our SMC dataset when suitable (time-shifted) ACE data were available. We
find that the tail radius was RT ∼ 32 RE
on average at far downtail distance (Table 1). We estimated that the tail
radius RT reaches 90 % of its asymptotic value at a distance
of ∼ 36 RE downtail from the Earth on average. Computing
again the order of magnitude of the z component of the convection velocity
in the tail using the estimated RT (for every SMC image), we
find vz ∼ 15.35 ± 0.16 km s-1 on
average (Table 1). This value is essentially twice as large as that reported
by Haaland et al. (2009). Our estimate can however be viewed as an upper
bound to vz because the asymptotic, far tail radius is the
upper bound to the distance plasma has to travel along the z direction
before reaching the reconnection site in the central plasma sheet. It
nevertheless remains that we infer an SMC convection velocity (in the tail)
apparently larger than the global average value. The larger convection
velocity that we infer here does not stem from an exceptionally large rate
of reconnection in the tail. Simply, the solar wind velocity is particularly
low during most of the SMC intervals, giving a very low solar wind dynamic
pressure used in the Petrinec and Russel (1993, 1996) model, which then
produces a rather large estimate for the tail radius and a proportionally
large value for vz. Given that τ∼ 4.1 h, one would retrieve vz ∼ 7.7 km s-1
if the plasma had to travel across a distance of ∼ 18 RE, only a little more than the half of the average asymptotic tail
radius that we have estimated. It must be noted that, in the frozen-in
approximation, an enhanced vz leads to an enhanced cross-tail
electric field Ey, compatible with a sustained magnetic flux
closure rate, which is one of the defining features of SMC intervals.
Typical values of the open magnetic flux and magnetic reconnection
rates estimated during four magnetospheric modes (pk stands for peak
values).
Quiet time
SMC
Substorm
Sawtooth
Φ (GWb)
< ∼ 0.4–0.5
∼ 0.6–0.9
∼ 0.65–0.9
∼ 1.0–1.4
0.7–0.96 pk
Vop, Vcl (kV)
< ∼ 40
∼ 35–75
∼ 70–140 pk
∼ 60–160
Intercomparison of magnetospheric convection modes
The statistical properties that we infer for SMC intervals should be placed
in the context of the previous studies of Hubert et al. (2006a, 2008)
concerning quiet-time conditions, the substorm cycle and sawtooth events.
We propose that the magnetosphere can exhibit four different modes differing
from each other through the amount of open magnetic flux in the
magnetosphere and the magnetic reconnection rates. Table 2 lists the typical
values found for these four modes, namely (in ascending reconnection rate)
quiet-time conditions, SMC, the substorm cycle and sawtooth modes. For the
substorm mode, we analysed an extended set of 629 substorms found between
May 2000 and November 2001. We used the substorm list of Frey et al. (2004)
and examined every interval individually to verify that the estimated
magnetic fluxes and reconnection voltages were suitable: we excluded
intervals which could apparently not really be considered a substorm, such
as shock-induced auroral activity or parts of sawtooth event intervals for
example. More importantly, we excluded intervals with insufficient data
coverage, or for which our automatic software did not properly treat the
data. We were left with 629 intervals for which the average value of the
peak value of the open magnetic flux is ∼ 0.83 GWb with a
standard deviation of 0.13 GWb and peak reconnection voltages of 103 kV
(closure) and 104 kV (opening) on average, both with a standard deviation of
∼ 36 kV so that, on average over the studied set of substorms,
the average of the peak values of the opening and closure voltages can be
considered statistically equal. The substorm growth and expansion phases can
be expected to have different properties considering that the magnetosphere
accumulates open magnetic flux during the growth phase, which is mostly
closed somewhat later during the expansion phase. Focusing on the expansion
phase, the mean value of the flux and closure reconnection voltage are
computed over each individual interval, then the average and standard
deviation of this set of mean values is computed. We find the averages and
standard deviations (not to be confused with the uncertainty over the
estimated averages) < Φ > = 0.7743 GWb, σΦ = 0.1214 GWb and
< Vcl > = -66.70 kV σVcl = 22.05 kV, while the opening reconnection voltage is more relevantly
appreciated during the growth phase:
< Vop > = 64.36 kV σVop = 28.93 kV. Table 2 instead lists
the average peak values for the substorm mode because we think that the
explosive nature of the substorm expansion phase is better described by
extrema than by averages, although averages remain valuable indicators.
The sawtooth numbers listed in Table 2 are based on the seven intervals
treated by Hubert et al. (2008), rejecting the case on 4 October 2000,
which had a somewhat higher noise level due to a poorer determination of the
open/closed boundary location. For the open magnetic flux, Table 2 gives the
average plus/minus the standard deviation of the main local maxima reached
during the set of sawtooth events (< Φmax > = 1.21 GWb, σΦmax= 0.21 GWb).
Indeed, several intervals of flux accumulation and flux closure follow
each other during a sawtooth event. The average flux closure voltage and its
standard deviation are obtained by isolating the most active subintervals of
each sawtooth interval of Hubert et al. (2008). We selected the 66 % data
points with the largest reconnection rates of each interval (separately for
opening and closure), grouped those subsets together and computed the value
of the average and the standard deviation of that subset (|<Vcl>|= 110 kV, σVcl= 49 kV, < Vop > = 109 kV,
σVop= 45 kV) from which we obtain the range listed in
Table 2. (If thresholding is ignored, we find < Vop > = 85 kV, σVop= 52 kV
and |<Vcl>|= 86 kV,
σVcl= 50 kV.) The thresholding procedure that we use
is somewhat arbitrary. We simply inspected the flux closure time series and
saw that this 66 % thresholding excludes most of the less active
subintervals, during which the flux closure rate is reduced while flux
opening already announces the following subinterval of intense flux closure.
We also noticed that the same threshold efficiently rejects intervals with a somewhat reduced flux opening rate when applied to the flux opening
reconnection voltage. Figure 13 shows the application of the thresholding to
the sawtooth event that occurred on 24 October 2002 detailed by Hubert et al. (2008). The sawtooth numbers listed in Table 2 must thus be considered
indicative of the main properties of sawtooth events rather than rigidly
established values. It is also surprising that on average, Vcl
and Vop are roughly equal, no matter whether thresholding is
included or not. One would expect that, in the long run, the amount of
magnetic flux that is opened on the dayside is eventually closed in the
tail, so that the time-integrated voltages should become equal. Having the
same voltage values also suggests in addition that, on average, flux opening
and flux closure take place during time intervals of roughly the same
duration. This property still needs an explanation, which is probably to be
found in the details of the solar-wind-driven magnetohydrodynamics (MHD) plasma flow inside of the
magnetosphere. We speculate that this property is a general characteristic
of the magnetosphere rather than of the sawtooth mode because the
correspondence between average opening and closure voltages is also found
within a few kilovolts for the substorm mode. Indeed, this correspondence is even
found for the peak reconnection voltages, with averages listed in Table 2.
Dayside (a) and nightside (b) reconnection voltages determined by
Hubert et al. (2008) during the sawtooth event that occurred on 24 October 2002. The horizontal dashed lines show how the 66 % thresholding separates
large from smaller reconnection rates.
Despite what Table 2 may suggest, there exists some overlap between the four
listed modes, as is represented in Fig. 14, which sorts them by increasing
open flux and reconnection rate. The behaviour of such a complex coupled
system comprising the solar wind, the magnetosphere and the ionosphere can
obviously not be reduced to just a few numbers, even though the amount of
open magnetic flux and the reconnection rates are among the most important
ones. This mode classification should not hide the key role of the solar
wind properties in the dynamics of the magnetosphere, as has been
statistically studied by DeJong et al. (2009), who highlighted the importance
of the IMF Bz component and of the solar wind velocity,
temperature and Mach number (which control the dayside reconnection rate in
large measure). For example, the importance of having a low solar wind
velocity for the development of the SMC mode does not appear in the present
analysis. One could speculate that the SMC mode has to be tuned such that
the rate of transport of magnetic flux from the magnetopause to the plasma
sheet inside of the magnetosphere matches the rate at which new open flux
tubes are transported in the nearby interplanetary medium as the solar wind
flows by the Earth, keeping the magnetic topology sufficiently stable to
avoid the breakup of an expansion phase. If the rate of transport inside of
the tail is limited by the internal properties of the magnetosphere, then it
would seem natural that the solar wind velocity has to stay within some
acceptable bounds (to be determined) and thus stays relatively small.
Further detailed analysis would however be needed to assess the validity of
that idea.
Different magnetospheric modes organized versus the open magnetic
flux Φ (left) and versus the opening and closure voltages
Vop and Vcl (right).
The magnetospheric modes considered in this study are driven by the solar
wind input: the quiet-time mode is the consequence of a reduced merging rate
at the dayside magnetopause when the IMF is oriented (approximately)
northward, the substorm cycle develops based on the imbalance on a short
timescale (less than ∼ 3 h) between magnetic flux closure
and opening, and the SMC condition can develop when the dayside reconnection
rate ranges around 55 ± 20 kV (Table 1) (at low solar wind velocity),
while the sawtooth event stems from the overfeeding of the magnetosphere
with open magnetic flux by very intense magnetic reconnection on the dayside
(Hubert et al., 2006a, 2008). The four magnetospheric modes presented here
thus reflect the existence of (at least) four different particular modes of
interaction between the magnetosphere and the interplanetary medium, at the
heart of which the process of magnetic reconnection plays a key role.
The value of the dayside reconnection rate is not the only important
parameter. The timing is a factor as well, as illustrated by Partamies et al. (2009a): the substorm develops after a growth phase with an intense
reconnection, whereas the sawtooth and SMC events have an intense dayside
merging rate throughout the time interval. In our mode classification, the
average open flux is only slightly larger during substorms than during SMC
intervals, but the peak values met during substorms are found to be nearly
0.1 GWb larger than the SMC value, which is in line with the
results found by Huang et al. (2009). The mode classification versus
reconnection voltage reflects how the intensity of the coupling between the
solar wind and the magnetospheric environment drives the response of the
coupled magnetosphere–ionosphere system. Our results are in line with the
lines of those found by Partamies et al. (2009b), who expressed this
interaction in terms of the ε coupling function and the solar
wind electric field. It also appears that the reconnection voltage better
discriminates between the different modes than the open magnetic flux, which
presents a more pronounced overlap between modes. This indicates that the
key that separates the various magnetospheric modes presented in this study
is to be found in the response of the magnetosphere to the coupling with the
solar wind, and future studies should be conducted to better identify the
solar wind parameters that drive the magnetospheric response. Three
questions that we think need to be answered are as follows.
Does the dayside
reconnection rate history fully determine the magnetospheric mode?
Does
magnetospheric preconditioning influence the development of the different
magnetospheric modes (along the lines of the results of Juusola et al., 2013, and Kissinger et al., 2012a, b)?
Do the properties of the
magnetospheric modes depend on season?