Investigation of the Structure of IMF Substorm Triggers Using Multi-Satellite Observations
T.-S. Hsu and R.L. McPherron
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, 90095-1567
Tel: 310-825-1882 / Fax: 310-206-8042
e-mail: thsu@igpp.ucla.edu / rmcpherron@igpp.ucla.edu
ABSTRACT
An outstanding question in magnetospheric physics is
whether substorms are always triggered externally by
changes in the interplanetary magnetic field (IMF) or
solar wind plasma, or whether they sometimes occur
spontaneously as a result of internal processes.
While the association of IMF triggers and substorm
onsets has been demonstrated, it is also found that not
all of substorms are triggered. Previous study has shown
that the ratio of triggered and non-triggered substorm is
about 60% and 40%. A surprising result is that triggered
substorm show a stronger response than non-triggered
substorm. It was suggested that this may be due to
undetected small scale structures in the IMF, which
have weak driving fields of short duration and hence
transfer less energy to the magnetosphere.
We use a large database of 1978 ~1979 ISEE 2 and
IMP8 IMF observation to examine whether the IMF
small scale structure occur frequently to account for the
40% non-triggered substorms. It was found that the
probability of observing IMF small scale structures is
less than 13%. The low probability (13%) does not
match the occurrence frequency of 40% of the nontriggered substorm onset. It is thus unlikely all of the
non-triggered substorm can be attributed to a missing
small scale IMF triggers.
INTRODUCTION
To understand the magnetospheric substorm, it is
necessary to determine whether substorm onset is
always externally triggered by the interplanatery
magnetic field (IMF) or whether substorm onset
sometimes occurs spontaneously as a result of internal
processes. Lyons [1995; 1996] argued that substorms
must be triggered by external changes in the IMF and/or
the solar wind. Specifically, Lyons [1996] argued that
events without apparent triggers were likely to be a nonsubstorm disturbance such as a convection bay [Pytte et
al., 1978]. The hypothesis that most or perhaps all
substorms are triggered has initiated considerable
interest in substorm triggering studies. Over the past
decade, several studies have demonstrated that a
majority of substorms (~60%) appear to be triggered by
the IMF. However, 40% of all substorms appear to
begin without obvious IMF perturbations.
A statistical study performed by Hsu and McPherron
[2002] has demonstrated that the association between
IMF triggers and substorm onsets is a real physical
phenomenon. A statistical analysis determining the
average characteristics of triggered and non-triggered
substorm in the magnetotail and geosynchronous orbit
was performed by Hsu and McPherron [2004]. It was
found that the average response in the tail field and
plasma suggests no qualitative difference between the
two classes of events. However, the magnitude of the
response is different. Triggered substorm exhibit a
larger response than non-triggered ones. This surprising
result has been suggested to be a manifestation of
undetected small scale structures in the IMF. Small
structures are suggested to have weak driving fields of
short duration and hence transfer less energy to the
magnetosphere.
To investigate this hypothesis, multi-satellite
observations are required to eliminate the possibility of
missing IMF trigger structures. In this study the authors
will use multi-satellite observations to examine how
frequently different IMF structure are observed at
different locations in the solar wind. Specifically, data
from 1977 to 1984 when two spacecrafts, ISEE2, and
IMP8 were in the solar wind is used to examine the size
and scale of the structures IMF triggers that may trigger
substorm onsets.
DATA PRESENTATION AND ANALYSIS
During the fall season of 1978 ~1985 ISEE 2 provide
solar wind observation near the subsolar region, while
IMP 8 was circling the earth. ISEE2 orbit was near the
subsolar region during fall season of this time span. A
schematic orbit diagram is shown in Figure1. An
automatic procedure [Lyons et al., 1997] was used to
identify possible IMF triggers of substorm onset for
ISEE 2 and IMP 8 solar wind observation. Both ISEE 2
and IMP 8 IMF triggers were visually inspected to
reject false identified events. Finally, two set of IMF
triggers were time propagated to the subsolar region to
determine whether they are associated. We have
Figure 1: Schematic diagram for the ISEE-2 and IMP8
data for IMF triggers structure analysis.
1
assumed the magnetic structures are aligned along the
average spiral direction. Since ISEE-2 was near the
subsolar region, we have used the ISEE-2 IMF triggers
as the base of comparison. The statistics of point
process is used to create the association list and to
determine the optimal time association window [Hsu
and McPherron, 2002]. An optimal time association
window is found to be ± 10 minutes, which is consistent
with a study conducted by Hsu and McPherron [2002].
After all of the above data processing, we found there
are 2531 ISEE2 IMF triggers and 1873 IMP8 IMF
triggers without regard to the existence of simultaneous
IMF observation in both satellites. If we restrict
ourselves to the time interval which both ISEE2 and
IMP8 have simultaneous IMF observations, we have
1455 ISEE2 IMF triggers and 871 IMP8 IMF triggers. It
is obvious that ISEE2 has higher identification rate of
IMF triggers than IMP8. This is very possibly due to the
better quality (few data gaps) of ISEE2 magnetic data.
These event lists are used to study the dependence of
IMF triggering and small scale structure of IMF
perturbation.
spatial distribution and the blue line shows the IMP8
spatial distribution. Since this rho distribution is
calculated for all IMP8 and ISEE2 solar wind
observations, the percentage in each rho bin can
represent the time IMP8 and ISEE2 spent in that
particular rho bin. It is obvious that IMP 8 has a very
little observation from -15 to 15 Re to the Earth-Sun
line, a factor attributed to the IMP8 high inclination
angle respect to the ecliptic plane. In the ISEE2 IMF
triggers distribution, most of the observations occur
inside 15 Re to the Earth-Sun line. The (b) and (c)
shows the identified IMF triggers distribution in IMP8
and ISEE2, which is very similar to the spatial
distribution in Figure 2 (a). The IMF triggers spatial
distribution must be weighted by the number observed
in each bin by the reciprocal of the fraction of time is
spent in a given bin. This “normalized ratio” for both
satellites observations is defined as follow:
n
f 
(1)
N tot
f T 
R T 
t
(2)
Ttot
f
fT

n
N tot

Ttot
t
(3)
where  is the distance from IMP-8/ISEE2 to earth-Sun
line, n is the number of identified IMF triggers for each
 bin, Ntot is the total number of identified IMF triggers
in this analysis, t is the time IMP-8/ISEE2 spent in
each  bin, and Ttot is the total time of solar wind
observation in this analysis, f  is the occurrence
probability for IMF triggers in each  bin,
f T is the
fraction of time IMP8/ISEE2 spent in each  bin. R T
Figure 2: SEE-2 and IMP8 IMF triggers spatial
distribution.
DEPENDENCE OF TRIGGEING ON LOCATOIN OF
SOLAR WIND MONITOR
Hsu and McPherron [2003] examined the spatial
distribution of IMF triggers and found that there is no
significant spatial dependence of IMF trigger
identification, i.e., the detection of IMF triggers is not a
strong function of the distance from solar wind monitor
to the earth-sun line. In this study, we reinvestigated
this problem with almost 10 years data.
The spatial distribution of both satellites is presented in
Figure 2. (a) The Rho is the distance from satellite to the
Earth-Sun line defined as Rho=sqrt(Y^2+Z^2). The +/sign, which is correspondent to GSM coordinate was
added to the spatial distribution to examine the
foreshock effect. The green line represents the ISEE2
is the time normalized ratio for each  bin for triggered
or non-triggered events. It should be noticed that the
time-normalized ratio is not a probability function.
The most obvious features in Figure 2 (d) is that, except
for fluctuations probably due to noise, the ratio for both
IMF trigger distribution is near 1.0. From the definition
of this ratio in equation (3) it can be seen that this
implies the number of events observed in a bin is
proportional to the time the spacecraft spend in the bin.
Furthermore, the constant of proportionality does not
change with rho, contrary to the Lyons hypothesis
[Lyons, 1996; Lyons et al., 1997] that states that the
detection of IMF trigger is a strong function of rho.
It is noted that, however, a slightly higher rate of
identification at the dawn side of the magnetosphere.
This slightly higher ratio of IMF triggers identification
may be due to waves in the foreshock region and these
waves have caused some “additional” IMF triggers.
Nevertheless, the overall ratio is almost the same
without regard to dawn or dusk region.
In order to further examine the uncertainty of the
2
Figure 3:Examination of triggering spatial
dependence by Bootstrap statistics. Both ISEE-2 and
IMP8 IMF triggers has been combined.
identification of IMF triggers, we have used bootstrap
method to estimate the fluctuation in each rho bin [e.g.
Efron and Tibshirani, 1993]. The bootstrap is a
procedure that involves choosing random samples with
replacement from a data set and analyzing each sample
the same way. Sampling with replacement means that
every sample is returned to the data set after sampling.
The range of sample estimates you obtain enables you
to establish the uncertainty of the quantity you are
estimating. In this study, the resample iteration is
10000. The combined bootstrapped estimation of ratio
is shown in Figure 3 for both IMP8 and ISEE2 IMF
trigger distribution. The shaded region represents the
uncertainty (± 1 standard deviation). It is clear that the
detection of IMF trigger is unlikely to be a strong
function of distance to the earth-sun line.
TIME ASSOCIATION BETWEEN TWO SET OF IMF
TRIGGERS
A more critical examination is to use the time period
which both satellites have IMF observations. In order to
associate both IMF observations, we use a technique
called point process to estimate the association of IMF
triggers [Hsu and McPherron, 2002]. The point process
analysis shows that the optimal choice to select IMF
triggers association is ± 10 minutes.
To further quantify the comparison, we have used cross
correlation analysis to study the structure of the IMF at
ISEE2 and IMP8, and to correct errors in time
propagation. An additional criterion of 75% data
presence for two set of IMF triggers is used.
Furthermore, because ISEE2 was near the subsolar
region, ISEE2 is used as base for comparison. After
time propagated both IMP8 and ISEE2 IMF triggers to
the subsolar region, we found that some triggers have
simultaneous triggers observed at both satellites but
some were seen only on or the other. With the
simultaneous data and data presence criterion, we found
725 ISEE2 IMF triggers and 433 (60%) of these ISEE2
triggers have simultaneous IMP8 triggers with +/- 10
minute window.
In figure 4, the upper left panel is an example of
simultaneous observation of IMF triggers by ISEE2 and
IMP8. It is obvious that both satellites observe the same
IMF structure in this example. The bottom half shows
the scatter plot of maximum cross correlation
coefficient vs. separation between ISEE2 and IMP8).
Two dotted line of 0.8 and 0.4 has been added for
reference of examination, which was used in Crooker et
al [1982]. Majority of the events with simultaneous IMF
trigger observations has a high correlation coefficient.
However, it is noted that a small fraction of events has
poor correlation coefficient while IMF triggers were
observed at both satellite. After further examination, we
found that these events are caused by the data gap in the
observation and the visual inspection suggests that these
are almost the same IMF structure. The upper right
panel of figure 4 shows an example of this class of
events, simultaneous IMF trigger observation but poor
correlation coefficient. Overall, we found that 60% of
the events have simultaneous IMF trigger observation
and 40% of the events have no IMF trigger associated
within ± 10 minutes. We have a further examination of
these 40% of non-associated events. Figure 5 bottom
panel shows the scatter plot of correlation coefficient vs.
satellite separation. We found that most of them have a
very high correlation coefficient (bottom panel of figure
4), which suggest very similar IMF observations. Yet,
the identified IMF triggers was outside the association
selection criterion ± 10 minutes. Two examples of this
class are shown in Figure 5 upper panels. In order to
clarify whether these non-associated events is due to
different IMF structure or time propagation error, an
Figure 4 The upper panel shows examples of
ISEE2 IMF trigger with simultaneous IMP8
triggers. The bottom panel shows the scatter plot
of maximum cross correlation between ISEE2
and IMP8 IMF observation vs. satellite
separation.
3
additional time delay is applied. We have added the
time delay of the maximum cross correlation to the time
shift, i.e., the final time propagation = solar wind time
propagation + time delay of maximum cross correlation
It was found 70% (27% of over all) of these nonassociated IMF triggers have trigger associated if cross
correlation time shift is added and these events have a
very high correlation coefficient. If rule out of these
events, we only found 13% of the over all events have
no IMF trigger association. Out of these 13% overall
non-associated events, we found that 8% have high
correlation coefficient. These 8% events may be caused
by some irregular point in the data. Figure 6 shows an
example at upper left panel. Finally, only 5 % of the
overall events have a different IMF structure (Figure 6
upper right panel).
Figure 5: The upper panel shows examples of
ISEE2 IMF triggers with simultaneous IMP8
triggers. However, these IMF triggers was not
registered because the time difference between IMF
triggers are larger than 10 minutes. The bottom
panel shows the scatter plot of maximum cross
correlation between ISEE2 and IMP8 IMF
observations vs. satellite separations.
DISCUSSION AND CONCLUSION
A preliminary examination to associate two set of IMF
triggers (ISEE2 and IMP8) shows that 60% of ISEE2
triggers have simultaneous IMP8 triggers. The 40% of
non-associated events are not actually observing a
different solar wind structure. As a matter of fact, a
further examination shows that only 13% of the nonassociated events can be attributed to different solar
wind observations. Majority of the non-associated
events are due to the selection association time windows
± 10 minutes. This immediately suggests that time
propagation algorithm is not accurate for the IMF
triggering study, a factor has been suggested by Hsu
and McPherron [2002]. A more accurate solar wind
time propagation method should be used such as the
algorithm developed by Weimer et al. [2002].
Nevertheless, even with a crude solar wind time
propagation method, we did not find supporting
evidence for a small scale solar wind structure occur
frequently. Overall, there is only 13% of different solar
wind observation can be seen in this study. The low
probability (13%) does not match the occurrence
frequency of 40% of the non-triggered substorm onset.
It is thus unlikely all of the non-triggered substorm can
be attributed to a missing small scale IMF triggers.
Figure 6 The upper panel shows examples of ISEE2
IMF triggers without simultaneous IMP8 triggers. The
bottom panel shows the scatter plot of maximum cross
correlation between ISEE2 and IMP8 IMF
observations vs. satellite separations.
Support for this project was provided by the National
Aeronautic and Space Administration with grant
NASA-XXX-XX-XXXX.
REFERENCES
Crooker, N.U., G.L. Siscoe, C.T. Russell, and E.J.
Smith, Factors controlling degree of correlation
between ISEE 1 and ISEE 3 interplanetary
magnetic field measurements, Journal of
Geophysical Research, 87 (A4), 2224-30,
1982.
Efron, B., and R.J. Tibshirani, An Introduction to the
Bootstrap, Chapman and Hall,, New York,
1993.
Hsu, T.-S., and R.L. McPherron, An Evaluation of the
Statistical Significance of the Association
between Northward Turnings of the IMF and
Substorm Expansion Onsets, Journal of
4
Geophysical Research, 107 (A11), 1398,
doi:10.1029/2000JA000125, 2002.
Hsu, T.-S., and R.L. McPherron, Occurrence
Frequencies of IMF Triggered and NonTriggered Substorms, Journal of Geophysical
Research, Space Physics, 108 (A7),
doi:10.1029/2002JA009442, 2003.
Hsu, T.-S., and R.L. McPherron, Average
characteristics of triggered and non-triggered
substorms, Journal of Geophysical Research,
Space Physics, 109 (A07208),
doi:10.1029/2003JA009933, 2004.
Lyons, L.R., A new theory for magnetospheric
substorms, Journal of Geophysical Research,
100 (A10), 19069-19081, 1995.
Lyons, L.R., Substorms: fundamental observation
features, distinction from other disturbances
and external triggering, Journal of Geophysical
Research, 101 (A6), 13011-26, 1996.
Lyons, L.R., G.T. Blanchard, J.C. Samson, R.P.
Lepping, T. Yamamoto, and T. Moretto,
Coordinated observations demonstrating
external substorm triggering, Journal of
Geophysical Research, 102 (A12), 27039-51,
1997.
Pytte, T., R.L. McPherron, E.W. Hones, Jr., and H.I.
West, Jr., Multiple-satellite studies of
magnetospheric substorms, III. Distinction
between polar substorms and convectiondriven negative bays, Journal of Geophysical
Research, 83 (A2), 663-679, 1978.
Weimer, D.R., D.M. Ober, N.C. Maynard, W.J. Burke,
M.R. Collier, D.J. McComas, N.F. Ness, and
C.W. Smith, Variable time delays in the
propagation of the interplanetary magnetic
field, Journal of Geophysical Research, 107
(A8), SMP29-1-15, 2002.
5