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Advances in Space Research 56 (2015) 736–741
www.elsevier.com/locate/asr
Probabilities of magnetic reconnection encounter at different
activity levels in the Earth’s magnetotail
L.Q. Zhang a, A.T.Y. Lui b, W. Baumjohann c, J.Y. Wang d,⇑
a
State Key Laboratory of Space Weather, National Space Science Center Chinese Academy of Sciences, Beijing 100080, China
b
Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA
c
Space Research Institute, Austrian Academy of Sciences, 8042 Graz, Austria
d
Information Engineering College, Central University for Nationalities, Beijing 100081, China
Received 23 January 2015; received in revised form 4 May 2015; accepted 4 May 2015
Available online 12 May 2015
Abstract
With the upcoming Magnetospheric Multiscale mission by NASA to investigate magnetic reconnection (MR) in detail, it is imperative
to identify more precisely the occurrence probabilities of observing MR signatures in different magnetospheric activity levels. An extensive investigation is conducted on the probabilities of observing MR feature at different magnetospheric activity levels with data from
Geotail satellite. A newly developed method is used to categorize the state of magnetosphere in five different activity levels. The result
shows quantitatively the probabilities in encountering MR features for these five different activity levels, providing valuable guidance to
satellite operations to enhance encounter of MR in the Earth’s magnetotail.
Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: BBFs; X-lines; Substorm; SMC
1. Introduction
Research on magnetic reconnection is a major endeavor
in space community since this process is perceived to occur
throughout the plasma universe. The Earth’s magnetosphere provides an ideal natural laboratory in the Earth’s
vicinity for detailed investigation of this process. The
X-line in the magnetotail was reported to be observed in
a wide region at the downtail distance of 15 RE (e.g.
Ohtani, 2004a, Ohtani et al., 2004b; Runov et al.,
2008a,b; Nagai et al., 1998; Nagai and Machida, 1998;
Machida et al., 1999). Observations from Geotail satellite
found the X-line site to depend highly on solar wind conditions, at closer distances to the Earth with stronger solar
wind (Nagai et al., 2005; Nagai, 2006). A later more
⇑ Corresponding author.
E-mail address: [email protected] (J.Y. Wang).
http://dx.doi.org/10.1016/j.asr.2015.05.001
0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
extensive statistical study utilizing TC-1, Cluster, and
Geotail observations to cover the downtail distances from
8 to 30 RE showed that the occurrence frequency of
X-line signatures increases with stronger solar wind condition (Zhang et al., 2010).
The commonly adopted method to infer the presence of
an X-line in the vicinity is through detection of fast plasma
flows accompanied by the appropriate signature of the
north–south magnetic field component Bz, i.e., fast earthward plasma flows with positive Bz or fast tailward plasma
with negative Bz. However, the observation probabilities of
the earthward and tailward fast flows during different
phases of a substorm are evidently poorly matched: the
earthward fast flows could be observed at quiet time and
any phase of a substorm, while the tailward fast flows are
mainly observed simultaneously with the auroral breakup
within a few minutes (Ieda et al., 2008; Miyashita et al.,
2009).
L.Q. Zhang et al. / Advances in Space Research 56 (2015) 736–741
737
Magnetic reconnection developed with the appearance
of an X-line has been considered to play a key role in the
magnetosphere and substorm dynamics. A desirable step
that would facilitate magnetic reconnection research is to
ascertain the probabilities of observing X-line signatures
in the Earth’s magnetotail at different magnetospheric
activity levels. This is also a timely task because of the
impending launch of a NASA mission called
Magnetospheric Multiscale (MMS) tentatively scheduled
for March, 2015. MMS mission is comprised of four satellites with the goal of detailed investigation of the physical
processes in the neighborhood of a magnetic reconnection
region. Knowledge on the occurrence probabilities in the
X-line regions will provide valuable guidance in
fine-tuning the MMS operations to enhance the chance of
X-line encounter and the success of the mission.
In this paper, the occurrence probabilities of the earthward/tailward plasma flows with the correlated positive/negative Bz from 10 RE to 30 RE are examined
statistically based on observations from Geotail satellite.
The probabilities are sorted into five different magnetospheric activity levels (MALs) by processing the AE index
with a newly developed automatic technique. This result
shows quantitatively the dependence of these probabilities
on the MALs.
We remove its fast fluctuating component with a finite
PN
impulse response (FIR) filter: y k ¼ n¼N hn ¼ hn xkn ,
where xkn is the input signal of the original AE index,
and yk is the output of the filter AE index, and filter coefnp
ficient hðnÞ ¼ 100 cosð2N
Þ. Due to the time symmetry, there
is hn ¼ hn . In this paper, the absolute number for N is chosen to be 20. The processing result for 8 Aug 2001 is shown
in Fig. 1(b). Clearly, after processing, small fluctuations
and spikes in the AE index are eliminated, and the filtered
AE index becomes smoother than its original.
We further obtain the temporal change rate of the filtered AE index (dk). Let ypeak denotes the peak value of
yk, yth denotes the threshold value to separate quiet stage
from the other stages, and dth denotes the threshold value
of dk between the growth stage and the expansion stage,
then, the different MALs could be distinguish as:
2. Determination of the MALs from AE index
In this paper, we choose that yth equals to 100 nT, and
dth equals to 10 nT/min.
The SMC period is characteristic of a high AE index and
slow change rate of AL index (O’Brien et al., 2002;
McWilliams et al., 2008). To find whether the remnant period is consistent with the SMC or not, we show the simultaneous change of AL index in Fig. 1(c). Apparently, the
change of the AL index is much smoother during the remnant period than during the expansion phase.
Consequently, the remnant period is closely related to the
SMC period.
There may be individual cases in which the magnetospheric activity deviates from the assigned MALs,
Typically, the peak of an AE index corresponds to the
maximum intensity of an auroral electrojet (Akasofu,
1964; Baumjohann, 1986). The growth/expansion/recovery
phases correspond to slowly-ascending/rapidly-ascen
ding/descending trends in the AE index, respectively
(Rostoker, 1972). Thus, it is feasible to distinguish the different substorm phases via the temporal trend of the AE
index. An example of the temporal evolution of AE index
on 08 Aug 2001 is shown in Fig. 1(a). To identify clearly
the AE index trend, we process the AE index in the
following manner:
1) quiet time: yk < yth;
2) growth
phase:
yth < yk < ypeak
and
2 nT/min < dk < dth;
3) expansion phase: yth < yk < ypeak and dk > dth;
4) recovery phase: yth < yk < ypeak and dk < 2 nT/min;
5) remnant period (yk > 100 nT and | dk | < 2 nT/min),
which is actually closely related with the steady magnetospheric convection (SMC) period.
Fig. 1. The original and processed data of the AE index on 08 Aug, 2001. (a) the original data of AE index; (b) the processed AE index with the red, blue,
and yellow colors correspond to the growth, recovery, and expansion phases of substorms, respectively. The white and green colors correspond to the quiet
time and the SMC period, respectively; (c) the AL index in the same period.
L.Q. Zhang et al. / Advances in Space Research 56 (2015) 736–741
especially for the small substorm activity. However, it is
likely that these outliners would not alter the results with
a large set of statistical samples.
With the 1-min resolution AE index collected from 2001
to 2005, we analyzed statistically the duration of each AE
index stage in each month. The number of substorms in a
given month is defined as the number of transitions from
the growth phase to the recovery phase in that month.
The monthly sums in substorm intervals and the number
of substorms are shown in Fig. 2(a). We can see that the
number of substorms varies between 150 and 350, implying
that there are 5–10 substorms per day on average. This
result indicates that the occurrence frequency of substorms
is quite variable and is likely related to the solar wind condition (Zhang et al., 2010).
Among the three substorm-related MALs, the monthly
sums of growth phase interval have only a small variability
range around 150 ± 50 h, as shown in Fig. 2(a). This small
range suggests that the time scale for energy storage process in the magnetotail is quite limited. The monthly sums
of intervals for other two substorm-related MALs show
that the recovery phase has the highest value while the
expansion phase has the lowest. Both have a consistent
change tendency with the number of substorms. In comparison with the growth phase, the monthly intervals of
expansion phase and recovery phase have larger variations.
It seems that the number of substorms is proportional to
the temporal scale of energy release process during substorms, i.e., the expansion and recovery phases.
The monthly intervals of quiet time and SMC period are
shown in Fig. 2(b). Both have considerable change above
400 h. On Average, the monthly sum of intervals for
SMC period is much shorter than that for quiet time.
Comparing with Fig. 2(a), the monthly sum of intervals
for SMC period and that for recovery have opposite trends.
Consequently, the higher the number of substorms, the less
is the number of SMCs.
We further calculated the total accumulated time for
each MAL and the results are shown in Fig. 3.
Obviously, the total time for SMC is much shorter than
18000
16000
14000
12000
Hour
738
10000
8000
6000
4000
2000
0
quiet
growth
expansion
recovery
SMC
Fig. 3. The total duration of each AE index stages from 2001 to 2005.
the other MALs. For substorm periods, the expansion
phase has distinctly a shorter time than the other substorm
phases. From 2001 to 2005, the total number of the substorm events is 12832. The total number of days is 1826.
Thus, there are on average 7 substorms per day. The average durations of growth phase, expansion phase, and
recovery phase are, respectively, 42 min, 21 min and
70 min. This is consistent with the result of Rostoker
(1972).
Table 1 shows the occurrence rates of each MAL: 27.5%
for quiet time, 8.1% for SMC period, 20.3% for growth
phase, 10.1% for expansion phase, and 34% for recovery
phase. The sum of all substorm intervals occupies about
64.4% of the observation time. Apparently, the magnetosphere is mostly in geomagnetic active periods.
3. Plasma flow selection
The 12-s resolution data from Geotail magnetometer
(Kokubun et al., 1994) and the low-energy particle (LEP)
experiment (Mukai et al., 1994) were collected from 2001
to 2005. The LEP data on Geotail are over the energy
range of several eV to 43 keV. The selection criterion of
the earthward bursty flow (EBF) is that the duration of
V\ > 200 km/s exceeds 50 s, and the angle between the
velocity and magnetic field exceeds 45°. Here, V\ is the
velocity component perpendicular to the magnetic field.
The criteria of the tailward bursty flow (TBF) are that
the duration of V\ < 200 km/s exceeds 50 s and Bz < 0.
There are a total of 3256 EBF events and 167 TBF events
inside
the
region
of
30 RE < X < 10 RE,
10 RE < Y < 10 RE and 4 RE < Z < 4 RE.
4. Statistical analyses
Fig. 2. The monthly duration of each AE index stage. The dots in the
curve represent the total duration of corresponding AE index stage in a
month. The top (bottom) panel refers to the high (low) level of
geomagnetic activities. “Peak” is the numbers of the monthly substorms.
4.1. Occurrence probabilities of TBF
The occurrence of the TBF in each MAL, normalized by
the occurrence probability for each MAL, is shown in
L.Q. Zhang et al. / Advances in Space Research 56 (2015) 736–741
739
Table 1
Occurrences of different stages of the AE index (%).
Quiet time
Growth phase
Expansion phase
Recovery phase
SMC
27.5
20.3
10.1
34.0
8.1
Table 2. Clearly, the occurrences of the TBF during quite
time as well as SMC period are quite low, only 8%.
About 84% of X-lines occur during substorm intervals,
consisting of 26% for the growth phase, 42% of the
X-lines during expansion phase, and 17% for the recovery
phase. The occurrence of the TBF during the expansion
phases is distinctly higher than the other MALs.
Consequently, the near-Earth X-lines are closely related
with substorm onset.
4.2. Occurrence probabilities of EBF
The observed probability of EBF in each MAL, normalized by the total number of EBF events, is shown in
Table 3. The result indicates that the probability of EBF
is highly dependent on the MAL. Few EBF can be
observed during SMC period. However, the probability
of the EBF during the quiet time is quite high. During substorm interval, the EBF can be observed during any phase,
but more often observed during the recovery phase.
The occurrence of EBF in each MAL, normalized by the
occurrence probability for each MAL, is also shown in
Table 3. It appears that the EBF occurs at any MAL.
The occurrences of EBF during different MALs are most
equal, except that the occurrence of EBF is evidently higher
during the recovery phase.
Comparison between the observation and normalized
occurrences in Table 2 and Table 3 shows that although
the probabilities of observing EBF during the expansion
phase and SMC period are low, their occurrences of EBF
are quite high. This is due to the low occurrences of the
expansion phase and SMC period as given in Table 1.
Similarly, the high occurrence of EBF during recovery
phase is due to the high probability of recovery phase.
As also shown in Table 3, the occurrences of the
EBF/TBF during SMC period and quiet time are quite
close. In comparison with other MALs, the occurrences
of TBF during the quiet time and SMC period are evidently lower. The occurrences of EBF are almost normal
during these two MALs periods. Consequently, the
X-lines mainly locate outside 30 RE during the quiet time.
It appears that there is the possibility of X-lines existing
in the magnetotail even during quiet time. Moreover, the
locations of X-lines are different during different MALs.
To make clear if the EBF/TBF during the quiet time is
at the time of the small substorms, we showed the distributions of EBF/TBF as a function of AE/Kp index in Fig. 4.
Clearly, EBF/TBF can occur during both quiet time and
geomagnetic activity period. During quiet time
(AE < 100 nT), the EBF has higher probability than the
TBF. On the contrary, during geomagnetic activity period
(AE > 100 nT), the TBF has higher probability than the
EBF.
5. Properties of EBFs
To make clear the difference of the geomantic activity
during quiet time and SMC period, we further statistically
analyzed the properties of EBFs.
The distributions of EBF as a function of temperature
of the thermal ions (T) are shown in Fig. 5. Apparently,
the probability of EBF peaks around 6 keV for SMC and
around 4 keV for quiet time. The probability of EBF with
T less than 5 keV is much lower during SMC than during
quiet time. Clearly, EBFs tend to have higher temperature
during SMC than during quiet time.
The distribution of the magnitude of the magnetic field
B of EBF is shown in Fig. 6. The occurrence of EBF above
8 nT is distinctly higher during SMC than during quiet
time. EBFs tend to have higher magnitude of B during
SMC than during quiet time.
According to the analysis above, the properties of ions
and the magnetic field associated with the EBF during
quiet time and SMC period are different.
Table 2
Occurrences of TBF during different AE stages (%).
Geotail (10–30 RE)
Quiet time
Growth phase
Expansion phase
Recovery phase
SMC
8.3
25.9
41.7
15.6
8.5
Table 3
Occurrences of EBF during different AE stages (%).
Observations
Normalized
Quiet time
Growth phase
Expansion phase
Recovery phase
SMC
24.4
19.5
18.0
19.4
8.5
18.3
43.6
28.1
5.5
14.7
740
L.Q. Zhang et al. / Advances in Space Research 56 (2015) 736–741
−3
Occurrrence Frequency
3.5
x 10
TBF
EBF
3
2.5
2
1.5
1
0.5
0
0
200
400
600
AE(nT)
800
1000
Fig. 4. Distributions of EBF/TBF as a function of AE/Kp index.
−4
x 10
SMC
1.5
Occurrence Frequency
1
0.5
0
0
5
10
15
−4
x 10
2
Quiet
1
0
0
5
10
15
T(keV)
Fig. 5. Distributions of EBF with T.
SMC
Occurrence Frequency
0.1
0.05
0
0
4
8
12
16
20
Quiet
0.1
Acknowledgements
0.05
0
Till now, all substorm models explaining the relationship between substorm onset and MR is based on the
assumption of a single X-line in the magnetotail. Our analysis shows the probability of X-lines existing in the magnetotail at different MALs periods. However, the near-Earth
X-lines predominantly occur during the geomagnetic activity periods. Basically, the number of X-lines inside 30 RE
begins to increase during the growth phase, reaches to
the peak during the expansion phase, and then sharply
decreases during the recovery phase. Taking into account
the temporal scale of a substorm, the X-lines during the different phases of a substorm should not be the same one.
X-lines during the different substorm phases may result
from different physical mechanisms (Baumjohann, 1999;
Kan, 2007).
The SMC period has been found to be a special magnetospheric state. Previous observations showed that few
EBF can be observed during SMC period (Sergeev, 1996;
Huang et al., 2009). Our analysis shows that the occurrences of the EBF during SMC period and quiet time are
quite close. This is basically consistent with previous results
(e.g., Pulkkinen et al., 2013). Further analysis showed that
the properties of EBF during these two MALs periods are
different. Consequently, the properties of EBF significantly
affect the magnetospheric state in the low level geomagnetic
activities period.
The main conclusions are that: (1) the possibility of
X-lines exists in the magnetotail at all MALs period. In
general, the X-lines are mostly located outside 30 RE during the periods of the low level of the geomagnetic activities, and located inside 30 RE during the periods of the
high level of the geomagnetic activities; (2) for the high
level geomagnetic activities period, the occurrence of
X-line is 26% for growth phase, 42% for expansion
phase, and 16% for recovery phase; (3) for the low level
geomagnetic activities period, the occurrence of X-lines is
8% for quiet time as well as SMC period. However,
the properties of EBF during quiet time and SMC are
different.
0
4
8
12
16
20
B(nT)
Fig. 6. Distributions of EBF with B.
6. Discussion and conclusions
The relationship between MR and substorm onset has
been a key issue in magnetospheric dynamic. As shown
in Table 2, about 84% of X-lines occur during the period
of a substorm. Apparently, the X-line inside 30 RE corresponds to the high level geomagnetic activities comprising
three different phases of a substorm. The X-line outside
30 RE corresponds to the low level geomantic activities
comprising quiet time and SMC period.
We thank the DARTS system in ISAS for supplying the
data from Geotail, and the Japanese world geomagnetic
data center for providing the material. Project supported
by the specialized research fund for state key laboratories.
This study is supported by the National Natural Science
Foundation of China (41174145), (40974102), and
(41231067).
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