Annales
Geophysicae
Open Access
Ann. Geophys., 31, 2163–2178, 2013
www.ann-geophys.net/31/2163/2013/
doi:10.5194/angeo-31-2163-2013
© Author(s) 2013. CC Attribution 3.0 License.
Statistical study of foreshock cavitons
P. Kajdič1 , X. Blanco-Cano2 , N. Omidi3 , K. Meziane4 , C. T. Russell5 , J.-A. Sauvaud1 , I. Dandouras1 , and B. Lavraud1
1 Institut
de Recherche en Astrophysique et Planétologie, University of Toulouse, UMR5277, CNRS, Toulouse, France
de Geofísica, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D. F., México
3 Solana Scientific Inc., Solana Beach, CA, USA
4 Physics Department, University of New Brunswick, Fredericton, Canada
5 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA, USA
2 Instituto
Correspondence to: P. Kajdič (kajdic@gmail.com)
Received: 29 April 2013 – Revised: 30 August 2013 – Accepted: 8 November 2013 – Published: 6 December 2013
Abstract. In this work we perform a statistical analysis of
92 foreshock cavitons observed with the Cluster spacecraft 1
during the period 2001–2006. We analyze time intervals during which the spacecraft was located in the Earth’s foreshock
with durations longer than 10 min. Together these amount to
∼ 50 days. The cavitons are transient structures in the Earth’s
foreshock. Their main signatures in the data include simultaneous depletions of the magnetic field intensity and plasma
density, which are surrounded by a rim of enhanced values
of these two quantities. Cavitons form due to nonlinear interaction of transverse and compressive ultra-low frequency
(ULF) waves and are therefore always surrounded by intense
compressive ULF fluctuations. They are carried by the solar wind towards the bow shock. This work represents the
first systematic study of a large sample of foreshock cavitons. We find that cavitons appear for a wide range of solar wind and interplanetary magnetic field conditions and
are therefore a common feature upstream of Earth’s quasiparallel bow shock with an average occurrence rate of ∼ 2
events per day. We also discuss their observational properties
in the context of other known upstream phenomena and show
that the cavitons are a distinct structure in the foreshock.
Keywords. Magnetospheric
physics
(solar
wind–
magnetosphere interactions) – Space plasma physics
(shock waves; wave–particle interactions)
1
Introduction
The solar wind (SW) is a magnetized plasma that flows away
from the Sun at supersonic speeds. On its way through the
solar system this plasma encounters obstacles such as planets and planetary magnetospheres. When the solar wind hits
a magnetosphere, it is slowed down, heated and deflected to
flow around it. The deceleration and the heating occur mainly
at the planetary bow shocks. The Earth’s bow shock is a high
Mach number shock with typical magnetosonic Mach number (Mms ) ∼ 8. It is also a collisionless shock, meaning that
a free mean path for ion binary collisions (∼ 1 AU at heliospheric distance of 1 AU) is much larger than the size of the
shock and its transition region. Due to its high Mach number,
the Earth’s bow shock is typically supercritical. This means
that a large part of the solar wind’s kinetic energy is dissipated by energizing and reflecting a small portion of its particles back upstream (e.g., Treuman, 2009).
The phenomena that exist upstream of the Earth’s bow
shock depend on the angle between the local-shock normal
and the upstream interplanetary magnetic field (IMF): θBn .
The shock is labeled quasi-parallel or quasi-perpendicular,
depending on whether the θBn is smaller or larger than 45◦ .
The region upstream of the quasi-parallel bow shock is populated by hot ion populations and ultra-low frequency (ULF)
magnetic field fluctuations with periods of ∼ 30 s (Hoppe
and Russell, 1981; Greenstadt et al., 1995). The ULF waves
can appear as sinusoidal, transverse waves propagating almost parallel with respect to the upstream IMF, or they can
be compressive, obliquely propagating fluctuations. The region upstream of the Earth’s bow shock that is magnetically
Published by Copernicus Publications on behalf of the European Geosciences Union.
2164
connected to it, is called the Earth’s foreshock (Le and Russell, 1992a, b; Eastwood et al., 2005; Greenstadt et al., 1995).
In addition to ions and waves, there are also transient
phenomena that populate the Earth’s foreshock. Phenomena such as hot flow anomalies (HFAs) (Thomsen et al.,
1986; Schwartz et al., 1995; Lucek et al., 2004; Zhang et
al., 2010), density holes (Parks et al., 2006, 2008; Wilber et
al., 2008) and foreshock cavities (Sibeck et al., 2001, 2002,
2008; Billingham et al., 2008; Schwartz et al., 2006) have
been studied extensively in the past. Here we study another
transient phenomenon, foreshock cavitons. These structures
have first been described by Lin (2003), Lin and Wang (2005)
and Omidi (2007) based on their hybrid simulation results.
Lin (2003) and Lin and Wang (2005) referred to the cavitons as diamagnetic cavities, while Omidi (2007) still called
them foreshock cavities. The name, cavitons, was used in
later papers (e.g., Blanco-Cano et al., 2009, 2011) in which
hybrid simulation results are compared to Cluster observations and in Kajdič et al. (2011) which is the first multispacecraft study of foreshock cavitons. Examples of simulated foreshock cavitons can be seen in Fig. 1. Panel a shows
density normalized to the solar wind value from a hybrid
simulation. Cavitons are seen as white regions, indicating
low density values. Panels b and c show the magnetic field
strength and plasma density as functions of time as seen by a
virtual spacecraft located in point “X” on panel a. At the time
of a caviton the values of B and n are strongly diminished.
Past numerical simulations predicted B field magnitude
and density drops of ∼ 50 % inside the cavitons, with respect to the ambient values. These drops would be larger for
cavitons closer to the bow shock. A more moderate drop of
∼ 10 % was predicted for solar wind bulk velocity. Simulated
cavitons were also found to be surrounded by a rim of enhanced B and n values. The proposed formation mechanism
for foreshock cavitons includes the nonlinear interaction of
compressive, obliquely propagating and transverse, parallelpropagating ULF waves (Omidi, 2007).
Early hybrid simulations were performed for parallel IMF
geometries and it was Blanco-Cano et al. (2011) who showed
that foreshock cavitons could also be observed for non-radial
IMF configurations. Lin (2003) and Lin and Wang (2005)
also predicted that cavitons would eventually evolve into
structures elongated along the B field lines and that their
pressure pulses may perturb the magnetopause.
The observations in general agreed with the numerical predictions. Blanco-Cano et al. (2011) and Kajdič et al. (2011)
reported B and n depressions between ∼ 40 % and ∼ 50 %
inside the cavitons. Kajdič et al. (2011) showed that cavitons propagate sunward in the plasma frame of reference,
but are carried antisunward by the SW. It was also shown by
these authors that foreshock cavitons are always surrounded
by compressive ULF fluctuations, which is consistent with
their proposed formation mechanism.
Based on recent observations and hybrid simulations, it
is believed that once foreshock cavitons reach and collide
Ann. Geophys., 31, 2163–2178, 2013
P. Kajdič et al.: Foreshock cavitons
Fig. 1. (a) shows the density normalized to the solar wind value
from a hybrid simulation run with Alfvénic Mach number of 11.
The panel is zoomed around the quasi-parallel shock and ion foreshock which shows a number of cavitons identified as white colored
regions. Note the color table is set to maximum of 2 in order to make
the foreshock cavitons visible. The magnetosheath corresponds to
the black region in the figure. (b) and (c) show the magnetic field
strength and number density as a function of time measured by a
simulated spacecraft located at point “X” in (a) and illustrate the
signatures of a foreshock caviton in the time series data.
with the bow shock, they produce another phenomenon, the
so called spontaneous hot flow anomalies (SHFA, see Omidi
et al., 2013a; Zhang et al., 2013). SHFAs seem to be an important part of shock dissipation processes and in turn impact
the magnetosheath.
Few observations have been reported until now, and no
systematic study of a larger sample of foreshock cavitons has
been performed yet. In this paper, we study a sample of 92
foreshock cavitons that were found in the Cluster 1 data during the period 2001–2006. The full list of events is provided
in Table 1. From our sample of events, we calculate the average values of their sizes, the magnitude of magnetic field
www.ann-geophys.net/31/2163/2013/
P. Kajdič et al.: Foreshock cavitons
and plasma-density depletions inside the cavitons and their
durations in the data. We show that B and n inside the cavitons are much more correlated than in case of surrounding
ULF fluctuations. We also show that cavitons are surrounded
by compressive ULF fluctuations and are associated with diffuse ion populations. Finally, we estimate the occurrence rate
of observable foreshock cavitons to be ∼ 2 events per day.
Cavitons exist in regions also populated by intense ULF
waves. In the data, these fluctuations appear immediately before and after the cavitons and persist for several minutes or
even hours. All this makes the cavitons difficult to identify.
One needs to be cautious in order to really distinguish foreshock cavitons from other phenomena in their surroundings.
Many caviton candidates have been discarded during the selection process.
The phenomenon that observationally most resemble the
foreshock cavitons are the foreshock cavities (Sibeck et
al., 2001, 2002, 2008; Billingham et al., 2008, 2011). Due
to apparent similarities there has been some doubt in the
past whether the two phenomena are really different structures. However there are some important observational differences that enable us to distinguish between them. Cavitons will always be found in regions populated by compressive ULF waves. The suprathermal ion populations and the
total (plasma + magnetic field) pressure inside them will be
the same as in their immediate surroundings. Cavities, on
the other hand, exhibit hot ion populations in their interiors,
while in regions that surround them the distributions correspond either to pristine SW population or to field aligned ion
beams. The total pressure inside the cavities exceeds the one
in their surroundings.
We show here that foreshock cavitons are a common feature in the Earth’s foreshock different from other foreshock
phenomena. They appear for a large range of SW and IMF
conditions. We demonstrate that B field magnitude and SW
density inside the cavitons are highly correlated and we design a new criteria which enables us to distinguish the cavitons from the surrounding ULF fluctuations.
2
Observations
Cluster is a four-spacecraft mission in orbit around the Earth
that provides magnetic field and plasma measurements in the
near-Earth environment. The Cluster satellites carry several
instruments onboard. Here we use the magnetic field data
provided by the Fluxgate Magnetometer (FGM, Balogh et
al., 2001) and the Cluster Ion Spectrometer (CIS, Rème et
al., 2001). The FGM data are available in three time resolutions: 22 s−1 , 5 s−1 and 1 vector per spin (4 s). The CIS-HIA
instrument provides full, 3-D ion distributions and moments
in the energy range between 5 eV and 32 keV with 1 spin time
resolution. The HIA is composed of the “high-G” or “highsensitivity” (HS) and “low-g” or “low-sensitivity” (LS) sections. In the magnetospheric operational modes (MS), the
www.ann-geophys.net/31/2163/2013/
2165
HIA performs a full energy sweep 32 times per spin, thereby
accounting for the angular resolution of 11.25◦ . In the solar
wind modes, the sweep is truncated above the energy of alpha particles whenever the “high-G” section faces the Sun.
When the field of view of the “low-g” section is within 45◦
centered on the solar wind direction, this section performs
eight sweeps with 5.625◦ angular resolution. Hence, the SW
is detected only by the “low-g” side and only this data is used
for the calculation of the SW moments.
Foreshock cavitons are identified as simultaneous depressions of B field magnitude and plasma density surrounded
by a rim of enhanced values of these two quantities. We set
a threshold of the minimum depressions of B and n to be
20 % in order for the event to be taken into account. Also,
these depressions have to be lower than the minimum level
of surrounding ULF fluctuations. The foreshock cavitons in
our sample also tend to be wider (i.e., last longer in time series) than the wavelengths of the surrounding ULF waves and
are easily recognizable by eye as distinct features.
In order not to confuse cavitons with other foreshock phenomena, we require that (1) the plasma temperature inside
the cavitons remains the same as in their surroundings, (2)
there is no flow deviation inside the cavitons, and (3) there
are no IMF discontinuities associated with the events.
It should be mentioned that hybrid simulations by Omidi
et al. (2013a) have shown that close to the bow shock, the
plasma temperature and velocity changes may be associated
with the cavitons. Since these variations are not inherent to
the cavitons and because they are also observed in association with other foreshock phenomena, such as HFAs and
foreshock cavities, we discard caviton candidates that exhibited them. The sample is a consequence of our stringent selection criteria.
Figure 2 shows an example of a foreshock caviton that
was observed on 26 April 2006. During this time, the Cluster spacecraft 1 was operating in a solar wind mode. The
panels show (from top to bottom): magnetic field magnitude
with 4 s time resolution in nanoteslas (nT), magnetic field
components in geocentric solar ecliptic (GSE) coordinate
system (nT), solar wind density (cm−3 ), thermal pressure
(nPa), total solar wind velocity (km s−1 ), solar wind velocity components (km s−1 ), and CIS-HIA spectrogram (HS) for
suprathermal ions and CIS-HIA spectrogram (LS) for solar
wind ions. The two vertical red lines delimit the time interval
during which the caviton was observed (from 09:15:56 UT
to 09:17:12 UT). The duration of the caviton was 76 s. The
two small blue vertical lines mark the times of ion distributions shown in Fig. 3. We can see that the event is surrounded by a region populated with compressive ULF fluctuations of B field and plasma density. The average values of B
and n in the surrounding medium during the presented time
interval are 3.8 nT and 5.1 cm−3 , respectively. During the
event, these two variables reach minimum values of 1.6 nT
and 1.8 cm−3 . This represents a 58 % drop in B field and
65 % drop in n. The interior of the caviton is surrounded
Ann. Geophys., 31, 2163–2178, 2013
2166
P. Kajdič et al.: Foreshock cavitons
Table 1. List of foreshock cavitons in the sample. The columns contain the following information (from left to right): date and time of
cavitons, their durations, their coordinates in the GSE coordinate system, operational mode of the spacecraft at time of observation of
cavitons, magnitudes of depletions of B and n inside the events, SW Alfén number and SW alfvénic Mach number.
Date
DD/MM/YYYY
Time [UT]
HH:MM:SS
Duration [s]
MM:SS
xGSE
RE
yGSE
RE
zGSE
RE
15/02/2001
15/02/2001
15/02/2001
15/02/2001
15/02/2001
15/02/2001
21/02/2001
08/04/2001
08/04/2001
12/02/2002
12/02/2002
16/02/2002
16/02/2002
21/02/2002
21/02/2002
21/02/2002
21/02/2002
21/02/2002
09/03/2002
09/03/2002
16/03/2002
16/03/2002
22/05/2002
03/02/2003
04/02/2003
04/02/2003
04/02/2003
04/02/2003
05/02/2003
08/02/2003
09/02/2003
15/02/2003
16/02/2003
16/02/2003
25/02/2003
27/02/2003
06/03/2003
08/03/2003
15/03/2003
22/03/2003
23/03/2003
23/03/2003
03/04/2003
03/04/2003
08/04/2003
08/04/2003
22/04/2003
22/04/2003
27/04/2003
07/05/2003
11/05/2003
11/05/2003
24/01/2004
08:09:03
08:41:56
08:50:08
09:24:22
09:30:40
11:10:46
21:49:20
03:18:52
03:38:27
11:59:41
12:09:30
08:33:37
09:33:28
06:47:31
07:16:27
07:58:11
08:01:43
17:30:12
13:03:30
13:25:00
13:03:15
13:38:08
11:27:20
10:58:04
09:02:24
09:06:48
10:30:54
10:34:48
22:35:20
12:49:16
02:35:41
14:25:20
01:29:46
04:11:03
07:03:27
21:49:27
23:15:32
14:02:02
16:21:57
18:04:25
01:22:43
03:17:54
17:23:11
23:34:10
15:07:58
15:13:07
21:35:56
22:41:22
16:37:02
05:53
20:51:54
23:40:12
02:32:22
01:01
02:25
02:28
00:44
00:42
00:38
01:19
01:36
00:54
00:52
01:00
00:54
01:04
01:04
00:57
00:37
00:38
00:27
00:58
01:13
01:12
01:16
00:41
01:00
01:40
01:08
00:38
00:28
02:31
00:55
01:06
00:55
00:50
00:44
01:44
01:01
00:58
01:19
00:57
00:52
00:45
01:02
00:47
00:29
00:56
00:35
00:55
01:30
00:52
00:31
00:48
00:47
00:52
18.86
18.87
18.87
18.87
18.87
18.77
14.27
13.64
13.8
14.67
14.57
16.25
16.73
18.3
18.44
18.6
18.6
18.29
14.1
14.4
11.21
11.78
4.7
14.23
13.32
13.22
11.88
12.23
15.75
17.41
13.92
17.93
16.54
15.15
18.63
17.17
17.58
14.48
13.81
12.38
16.66
17.18
13.09
15.55
14.22
14.24
11.83
12
10.97
8.25
7.62
7.62
14.17
5.21
5.08
4.95
4.82
4.75
4.36
7.93
7.44
7.44
1.87
1.78
5.91
5.8
3.83
3.76
3.61
3.61
1.3
7
6.8
7.91
7.75
4.13
9.4
3.01
3.01
2.26
2.13
8.67
7.06
2.11
5.22
1.9
0.94
1.03
−1.29
−3.03
1.19
−0.25
−1.25
−4.44
−5.14
−4.9
−8.07
−8.06
−8.11
−11.22
−11.84
−12.61
−10.75
−13.42
−15.18
11.96
1.7
1.31
1.18
0.85
0.72
−0.12
4.94
−6.81
−6.96
−6.8
−6.98
4.68
4.15
2.44
2.17
1.82
1.82
−3.69
0.94
0.88
0.34
0.18
−16.45
3.19
−8.58
−8.71
−9.09
−9.09
1.71
−1.41
−8.5
−0.44
−6.68
−7.88
−3
−6.3
−5.26
5.34
5.77
6.43
2.64
1.49
5.55
2.14
3.65
3.6
3.66
3.04
3.15
5.72
4.4
2.82
−0.62
Ann. Geophys., 31, 2163–2178, 2013
Operational
mode
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
MS
MS
MS
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
MS
MS
SW
SW
MS
SW
SW
SW
SW
SW
SW
MS
MS
SW
SW
1B/B
1n/n
VA
km s−1
MA
0.55
0.67
0.37
0.53
0.47
0.47
0.59
0.51
0.29
0.49
0.61
0.26
0.30
0.44
0.35
0.35
0.27
0.37
0.51
0.68
0.62
0.57
0.41
0.34
0.52
0.36
0.23
0.26
0.48
0.35
0.73
0.28
0.40
0.36
0.39
0.33
0.39
0.71
0.74
0.84
0.36
0.64
0.39
0.29
0.24
0.20
0.49
0.50
0.79
0.54
0.73
0.67
0.63
0.70
0.70
0.46
0.50
0.50
0.54
0.63
0.60
0.38
0.50
0.60
0.31
0.46
0.33
0.48
0.38
0.35
0.29
0.63
0.71
0.38
0.59
0.47
0.41
0.49
0.48
0.24
0.34
0.43
0.39
0.75
0.30
0.50
0.50
0.52
0.32
0.42
0.64
0.68
0.85
0.52
0.68
0.46
0.32
0.28
0.27
0.67
0.57
0.80
0.61
0.74
0.73
0.55
87
85
90
87
98
90
53
90
91
88
88
81
72
97
94
99
99
81
57
59
56
57
45
69
100
99
124
119
105
82
78
82
97
86
41
82
63
52
100
91
62
79
89
59
63
62
91
79
74
120
119
93
36
5.9
6.2
5.9
6.0
5.3
5.8
6.4
5.0
5.1
5.1
5.1
4.0
4.4
4.7
4.7
4.5
4.5
5.0
6.7
6.8
5.4
5.3
9.0
6.9
5.5
5.5
4.4
4.6
5.0
5.5
5.6
7.1
5.7
6.4
10.0
5.9
7.4
7.7
6.1
6.0
8.9
7.2
5.0
7.3
6.6
6.7
5.5
6.4
6.3
5.6
5.4
6.8
14.4
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P. Kajdič et al.: Foreshock cavitons
2167
Table 1. Continued.
Date
DD/MM/YYYY
Time [UT]
HH:MM:SS
Duration [s]
MM:SS
xGSE
RE
yGSE
RE
zGSE
RE
24/01/2004
04/02/2004
16/03/2004
16/03/2004
23/03/2004
28/03/2004
28/03/2004
28/03/2004
02/04/2004
11/04/2004
14/04/2004
15/04/2004
19/04/2004
19/04/2004
21/04/2004
25/04/2004
05/05/2004
05/05/2004
05/02/2005
19/03/2005
19/03/2005
26/03/2005
17/04/2005
27/04/2005
23/01/2006
24/01/2006
24/01/2006
26/01/2006
26/01/2006
01/03/2006
02/03/2006
03/03/2006
29/03/2006
29/03/2006
26/04/2006
26/04/2006
26/04/2006
28/04/2006
29/04/2006
02:36:36
19:42:42
09:36:06
11:05:07
07:32:10
11:18:49
21:40:38
21:44:02
15:51:08
08:18:18
00:53:33
22:05:23
11:03:19
11:06:23
16:03:46
20:18:14
08:12:09
08:17:34
09:45:14
11:24:19
14:50:55
23:44:16
01:26:20
03:54:39
03:32:44
05:43:43
09:39:27
08:36:02
09:00:39
04:48:23
19:41:25
12:05:01
10:51:05
11:58:52
09:17:08
18:53:11
19:49:43
23:02:12
04:51:46
02:22
00:30
00:42
00:54
01:18
00:55
00:35
00:46
01:05
01:13
01:09
01:03
00:57
02:13
00:31
01:41
00:46
01:04
01:00
01:03
01:12
00:58
00:53
02:53
00:57
01:31
01:00
00:42
01:33
01:10
01:37
01:07
02:06
00:56
01:14
01:44
00:59
01:03
00:40
14.19
14.57
17.97
18.2
15.65
16.87
13.75
13.73
12.72
13.55
13.93
10.97
7.27
7.25
8.82
11.26
8.13
8.11
13.92
17.9
18.03
16
13.59
6.82
6.79
13.21
11.67
14.68
14.65
10.04
18.46
11.5
12.68
11.95
12.3
9.59
9.17
10.75
8.61
11.96
8.95
−3.92
−4.35
−4.16
−8.76
−9.77
−9.76
−10.84
−9.12
−12.73
−7.27
−12.84
−12.82
−14.86
−14.74
−16.48
−16.5
3.16
−4.53
−5.5
−8.74
12.84
−14.38
11.1
7.12
4.65
9.71
9.54
−3.83
0.9
−4.07
−9.02
−9.01
−3.12
−8.1
−8.5
−5.72
−8.48
−0.65
1.8
−0.63
−1.5
2.42
−3.22
−8.27
−8.28
−8.42
2.24
−2.21
4.55
−9.75
−9.76
−8.34
−1.13
−2.69
−2.74
−9.82
−1.57
−3.59
−6.66
−2.4
−9.39
3.58
−9.98
−10.8
−7.6
−7.79
−11
−5.01
−11
−9.97
−10.2
−13.5
−14.82
−14.75
−15
−15.12
by rims of enhanced B and n. The maximum values of B
in the upstream and downstream rims are 4.8 nT and 5.7 nT
(26 % and 50 % increase with respect to the average ambient
value). The corresponding maximum values of plasma density are 6.3 cm−3 and 7.6 cm−3 (23 % and 49 % increase).
The solar wind thermal pressure (panel d) shows a similar
depression as B and n. This is due to the fact that the SW
temperature shows no variation during the presented time interval. Total velocity (e) diminishes from ∼ 340 km s−1 to
∼ 300 km s−1 (by 13 %) at the upstream edge of the caviton,
and shows a peak of 365 km s−1 (7 % increase) inside the
caviton. There are velocity fluctuations in the surrounding
www.ann-geophys.net/31/2163/2013/
Operational
mode
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
MS
MS
MS
SW
SW
SW
SW
SW
SW
SW
SW
SW
SW
MS
SW
SW
SW
SW
MS
SW
SW
SW
SW
SW
SW
SW
SW
SW
1B/B
1n/n
VA
km s−1
MA
0.51
0.34
0.47
0.37
0.74
0.45
0.60
0.46
0.58
0.60
0.60
0.57
0.28
0.33
0.67
0.57
0.48
0.38
0.35
0.26
0.37
0.48
0.50
0.66
0.46
0.58
0.35
0.28
0.24
0.47
0.42
0.54
0.41
0.53
0.58
0.57
0.62
0.35
0.29
0.67
0.47
0.54
0.30
0.84
0.60
0.75
0.67
0.60
0.57
0.62
0.67
0.40
0.46
0.81
0.74
0.55
0.40
0.62
0.34
0.44
0.60
0.47
0.71
0.41
0.67
0.38
0.35
0.29
0.44
0.40
0.48
0.53
0.49
0.66
0.48
0.56
0.50
0.50
36
105
80
98
44
155
126
126
68
54
83
74
53
53
61
74
65
64
48
78
60
77
50
41
103
48
72
77
84
85
44
45
45
43
36
32
32
67
55
14.4
4.9
5.2
4.2
8.3
4.5
4.9
4.9
5.4
7.5
4.8
9.4
6.6
6.6
6.4
5.2
6.7
6.8
7.5
4.9
6.0
7.9
8.2
9.1
3.6
11.6
7.3
6.1
5.8
4.3
8.2
8.7
7.2
7.6
7.8
10.3
9.9
5.2
6.7
medium (at 09:11:52 UT and 09:13:58 UT) that reach similar
or even lower values than the one described here. Hence it is
not clear if the velocity fluctuation observed at the time of the
caviton was really caused by it. The energy HS spectrogram
(g) shows an intense suprathermal ion population inside as
well as outside of the caviton, while the LS energy spectrogram (h) shows a continuous solar wind beam centered at
∼ 600 eV. The HS spectrogram and the highly disturbed B
and n panels show that the caviton is located well inside the
foreshock.
In Fig. 3, we show cuts of the ion distribution functions from the “high-G” section inside the caviton at
Ann. Geophys., 31, 2163–2178, 2013
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P. Kajdič et al.: Foreshock cavitons
Fig. 3. Ion distributions just outside (top) and inside (bottom) the
caviton. The times of the distributions are marked in Fig. 2 with
two short vertical blue lines. Logarithm of ion distribution function
is shown. The distributions are obtained from the “high-G” section
of the CIS-HIA instrument, so the solar wind distribution does not
appear on these panels. vpar and vperp refer to velocities parallel and
perpendicular to the IMF.
inside the caviton and in its surroundings are of the same
type. We also revised the ion distributions throughout the
event and found that they remain very similar.
2.1
Fig. 2. Foreshock caviton observed on 26 April 2006. The two red
vertical lines delimit the time of the caviton. The two small blue
vertical lines mark the times of ion distributions shown in Fig. 3.
09:16:28.759 UT (top panels) and those in the surrounding
region at 09:15:01.839 UT (bottom panels). The times of the
distribution are marked in Fig. 2 with two short vertical blue
lines. The panels show the logarithm of phase space density
in the spacecraft frame of reference. Since the spacecraft was
operating in a solar wind mode and the data is provided by
the HS section, the SW beam does not appear in these panels.
vpar and vperp stand for velocities parallel and perpendicular
to the magnetic field. We can see that for both times, a hot,
diffuse ion distribution is present. Hence, ion distributions
Ann. Geophys., 31, 2163–2178, 2013
Surrounding ULF waves
In this section, we show how the observational properties of
foreshock cavitons differ from those of the surrounding ULF
waves.
Panels a through d in Fig. 4 present Cluster 1 observations
between 08:59:57 UT and 09:21:04 UT on 26 April 2006.
B field magnitude is exhibited on panel a, Bx component
in panel b, By (thick, black line) and Bz (thin, blue line)
components in panel c and the plasma density in panel d.
During this time, the IMF and SW density show no large
variations other than those caused by the ULF waves and the
caviton, so meaningful averages of both quantities (3.76 nT
and 5.14 cm−3 ) could be calculated.
We first perform fast Fourier and minimum variance analyses (MVA) of the ULF waves during the exhibited time interval. The power spectrum (Fig. 4f) shows that these waves
are predominantly transverse although a strong compressive
component is also present. The spectrum of transverse component peaks for periods ∼ 50 s. The MVA analysis (Fig. 4g)
reveals that the ratio of intermediate to minimum variance
is only 2.3, which introduces a large uncertainty in their
direction of propagation with respect to the local B field
www.ann-geophys.net/31/2163/2013/
P. Kajdič et al.: Foreshock cavitons
2169
April 26, 2006
c)
d)
e)
B [nT]
Bx [nT]
By,z [nT]
b)
7
-3
χ [nT⋅ cm-3] N [cm ]
a)
4
1
-1
1
-1
-4
-7
4
1
-1
-4
10
6
3
0
8
4
1
-2
08:59:57
09:04:10
09:08:24
09:12:37
09:16:50
09:21:04
Time [UT]
103
f)
Smoothed Power Spectrum
g)
Compressive
2
10
2
0
-2
-4
6
101
Min Var
Power [nT2/Hz]
4
Max Var
Transverse
100
-2
4
2
0 2 4
Min Var
6
ΘBk= 13 ° ± 85 °
Int/Min= 2.3
0
-2
10-1
10-4
-4 -2 0 2
Int Var
10-3
10-2
10-1
Frequency [Hz]
4
100
Fig. 4. (a) magnetic field magnitude, (b) xGSE component and (c) yGSE and zGSE components of B field, (d) plasma density and (e) the χ
function between 08:59:57 UT and 09:21:04 UT on 26 April 2006. (f) power spectrum of ULF waves. (g) minimum variance analysis results.
direction (θBk = 13◦ ±85◦ ). This error was estimated according to Hoppe et al. (1981).
During the presented time interval, we identified 27 wavefronts in the x component of the magnetic field and 27 in density (see Fig. 4a and d) of different amplitudes and durations.
However, the B field magnitude does not seem to correlate so
well with the density. There are 41 peaks, which have smaller
amplitudes. In the following paragraphs we compare perturbations in B and n caused by the ULF waves and the foreshock cavitons.
Figure 5 shows distributions of (panel a) relative amplitudes (1B/B) of ULF fluctuations in B field, (panel b) relative density amplitudes (1n/n) of ULF waves, and (panel c)
wave durations in B and (panel d) in n. In Fig. 5a and b the
red columns represent the amplitudes of wave minima while
the blue bars represent the amplitudes of the wave maxima.
Relative frequencies are shown in each panel. The black column represents the foreshock caviton. The average, the median values and the standard deviations of the distributions
are also given. In the case of 1B/B and 1n/n, these values were calculated from the sample that includes the wave
maxima and the absolute values of their minima. We can see
www.ann-geophys.net/31/2163/2013/
that the average (median) B field depletions of surrounding
ULF waves were 0.19(0.20) ± 0.15 and average (median)
depletions in density were 0.21(0.20) ± 0.18. This is about
three times less than the corresponding depletions produced
by the caviton. Also, the average (median) periods of waves
in B field and n were 29 (25) s ± 21 s and 50 (37) s ± 33 s, respectively. Again, with the duration of 76 s, the caviton lasts
longer than this.
Although the caviton produced the largest negative depletions in B and n during the studied time interval, there were
still a few ULF fluctuations that were almost as deep. Hence,
the described statistics are not enough to distinguish cavitons from the surrounding ULF waves. However, cavitons
produce B and n depletions simultaneously. Their shapes in
B and n data are very similar. In order to show this, we define
the following function:
χ (t) = (n(t)− < n >) · (B(t)− < B >),
(1)
where < n > and < B > are the average values calculated on
the exhibited time interval. We plot this function in Fig. 4e.
We see that the caviton produces by far the largest positive
peak with the value of 7.2. The average value of χ during the
Ann. Geophys., 31, 2163–2178, 2013
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P. Kajdič et al.: Foreshock cavitons
0.4
<Δ B/B> = 0.19
µ = 0.20
σ = 0.15
a)
0.4
0.3
0.1
0.1
N/Ntot
0.3
<Δ n/n> = 0.21
µ = 0.20
σ = 0.18
b)
0.0
0.0
-1.0
0.4
-0.6
-0.2 0.2
Δ B/B
0.6
1.0
-1.0
0.4
c)
<PB> = 29
µ = 25
σ = 21
0.3
0.1
0.1
d)
-0.2 0.2
Δ n/n
0.6
1.0
80
100
<Pn> = 50
µ = 37
σ = 33
N/Ntot
0.3
-0.6
0.0
0
0.0
20
40
60
tB [s]
80
100
0
20
40
60
tn [s]
Fig. 5. Distributions of (a) relative amplitudes (1B/B) of ULF fluctuations, (b) relative density amplitudes (1n/n) of ULF waves, (c)
wave durations in B field and (d) wave durations in n. The red
columns in (a) and (b) represent the amplitudes of wave minima
while the blue bars represent the amplitudes of the wave maxima.
The black column represents the foreshock caviton.
presented time interval (the covariance between B and n, the
thick red line in Fig. 4e) is < χ >= 0.19 and the standard
deviation of χ (the dashed red lines in Fig. 4e) is σχ = 0.77.
This means that the peak produced by the caviton is 9 σχ
larger than < χ >. The largest value of χ produced by the
ULF fluctuations is 4, which is slightly less than 5 σχ larger
than < χ >.
Hence we add an additional requirement for an event to
be recognized as a foreshock caviton: the value of χ during
the event must reach values at least 5 standard deviations σχ
larger than the average value of < χ > during the studied
time interval.
Finally, we calculate the Pearson correlation coefficients
for B field and density for subintervals with and without
the caviton. Their respective values are 0.77 and 0.38, which
again shows the high correlation of B and n inside the cavitons.
2.2
Statistical analysis
We surveyed the Cluster 1 data between the years 2001–
2006. We found 92 foreshock cavitons, of which 79 were observed when the CIS was in the SW operational mode and 13
were observed when it was in the MS operational mode. We
Ann. Geophys., 31, 2163–2178, 2013
should stress out that the relatively small number of events
in our sample is a consequence of our stringent selection criteria and the fact that the Cluster 1 spacecraft spent in total only ∼ 50 days in the foreshock region during the mentioned time period. It is likely that their formation processes
are very common in the regions populated by compressive
ULF waves and that the cavitons are much more recurrent.
Hence, the statistics presented in this section apply only for
those foreshock cavitons that evolved sufficiently in order to
be distinguished from the surrounding ULF fluctuations.
Figure 6 shows the positions of these events in the GSE
coordinate system. The crosses mark the locations of the
cavitons observed when spacecraft was operating in the SW
modes and the diamonds mark those events that were observed in the MS modes. The diamonds tend to appear closer
to the bow shock than the crosses. This is because the MS
modes are used during time intervals between 2 h before the
inbound crossing of a nominal bow shock, until 2 h after its
outbound crossing, so when the spacecraft is closer to the
shock. In the GSE coordinate system, the Earth is in the center, the x axis points towards the Sun, the y axis is in the
ecliptic plane pointing towards dusk (opposite the Earth’s
motion) and the z axis is parallel to the ecliptic pole. Panels a,
b and c show xGSE yGSE , xGSE zGSE and zGSE yGSE planes, respectively. The dashed curves on top panels in Fig. 6 represent the nominal bow shock as modeled by Narita et al.
(2004). We can see that the caviton locations in Fig. 6 extend
more dawnward (yGSE & −18 RE ) than they do duskward
(yGSE . 15 RE ). RE stands for Earth radius. Also, the range
of negative zGSE values (& −18 RE ) is larger than the range
of positive zGSE values (. 8 RE ). There seems to be a region (−10 RE ≤ z ≤ 0 RE and 10 RE ≤ x ≤ 17 RE ) where no
cavitons were observed.
The locations at which the foreshock cavitons were detected are influenced by the caviton’s actual distribution in
the Earth’s foreshock and by the way the spacecraft traveled
through the foreshock. At the beginning of the Cluster mission, including the period between 2001 and 2006, the Cluster spacecraft were in a highly elliptical orbit that was almost perpendicular to the ecliptic. Whenever the spacecraft
crossed the ecliptic, their xGSE coordinates were large, while
at small xGSE the zGSE was large. Events with small xGSE
and small zGSE coordinates could still be observed when the
angle between the IMF and the radial direction was large. As
we can see in Fig. 6 there is one such event at xGSE ∼ 7 RE
and zGSE ∼ −2 RE .
From Fig. 6 we also see that the cavitons were predominantly observed upstream of the dawn-side bow shock. This
can be explained in terms of the orientation of the nominal
Parker spiral. Reflected particles, responsible for foreshock
formation, stream along the IMF lines, and it is due to this
that the orientation of the foreshock is preferentially in the
negative yGSE direction.
www.ann-geophys.net/31/2163/2013/
20
20
10
10
ZGSE (RE)
YGSE (RE)
P. Kajdič et al.: Foreshock cavitons
0
-10
-20
0
2171
0
-10
5
10
XGSE (RE)
15
20
-10
0
ZGSE (RE)
10
20
-20
0
5
10
XGSE (RE)
15
20
20
YGSE (RE)
10
0
-10
-20
-20
Fig. 6. Coordinates of the observed foreshock cavitons in the GSE
coordinate system. The crosses represent the events observed in the
SW modes, while the diamonds represent those cavitons observed
in the MS modes. The dashed curve on the two top panels represents
the nominal bow shock. A nominal bow shock model of Narita et
al. (2004) was used.
(200 km s−1 < V < 700 km s−1 ) and Alfvénic Mach number
(2 < MA < 15). The average density, velocity and MA are
4.8 cm−3 , 456 km s−1 and 6.5, respectively. Their respective
median values are very similar: 4.5 cm−3 , 445 km s−1 and
6.0.
We can see that the average and median properties of
the SW and IMF, shown in the middle row, differ from
those in the top row. During the period 2001–2006, the
average (median) IMF strength was 6.0 nT (5.8 nT). The
average (median) SW density, velocity, Alfvén velocity
and Alfvénic Mach number were 7.8 cm−3 (6.5 cm−3 ),
424 km s−1 (399 km s−1 ), 75 km s−1 (78 km s−1 ) and 6.5
(6.0), respectively.
From Fig. 7 we can see that proportionally more cavitons
were found for higher-than-average IMF strengths, while
most of the cavitons were observed during times of lowerthan-average solar wind densities. Very few foreshock cavitons were found for Alfvén Mach numbers larger than 10.
The bottom row in Fig. 7 shows these tendencies. If the
cavitons were observed with equal probability for all IMF
and SW conditions, the histograms in this row would be flat.
However, this is not the case. It can clearly be seen that cavitons favor higher B fields, lower densities, larger velocities
and Alfvén speeds, when compared to the average SW properties.
2.2.2
2.2.1
Ambient solar wind and IMF conditions
In this section we analyze properties of SW and IMF at times
when the cavitons were observed and compare them to the
overall SW and IMF properties during the period 2001–2006.
The top row in Fig. 7 shows the statistics of properties
of the ambient SW and IMF during times when the cavitons were observed. The presented quantities are averages
calculated on intervals of several minutes around the observed cavitons. On vertical axes we show relative frequency
(N/Ntot ). The columns show from left to right: magnetic
field magnitude in units of nanoteslas (nT), SW plasma density (cm−3 ), velocity (km s−1 ), Alfvén velocity (km s−1 ) and
Alfvénic Mach number (MA ). The middle row shows the
same statistics but calculated for 750 1 h time intervals during the years 2001–2006, when Cluster 1 was in pristine solar
wind. With this we learn about the SW and IMF properties
during the mentioned time period and can then compare them
to the properties at times when the cavitons were observed
(shown in the top row). We obtained the distributions in the
bottom row by dividing the distributions from the top row by
the distributions form the middle row, bin by bin.
From Fig. 7 we can see that the cavitons appear for a
wide range of IMF magnitudes (3 nT < B < 12 nT). The average and the median B magnitude in the sample are 6.9 nT
and 6.6 nT, respectively. The cavitons also appear for almost
any SW density (between .2 cm−3 and 20 cm−3 ), velocity
www.ann-geophys.net/31/2163/2013/
Caviton properties
Figure 8 shows the statistics of foreshock caviton properties.
The panels show the distributions according to panel a the
relative depth of the depression of the magnetic field magnitude, 1B/B, panel b the relative depth of the depression
of plasma density, 1n/n, panel c the caviton duration in the
data and panel d the calculated extents (in RE ). The latter
were calculated by multiplying the caviton durations with the
average surrounding SW speed.
Three distributions are shown on Fig. 8: the dark-blue
color represents the statistics for the cavitons that were observed in MS operational mode, the light-blue shows the distributions of the cavitons observed in solar wind mode and
the white columns with red borders show the statistics for
the entire sample.
We see that the 1B/B values range between 0.2 and 0.9
with the average and the median values being 0.47. The distribution decreases strongly beyond the values of 0.7.
The picture is similar for 1n/n values. These values also
range between 0.2 and 0.9. The distribution looks more symmetric around the average and median values of 0.5 and 0.52,
respectively. The distribution is quite flat between 0.3 and
0.7.
The caviton durations in the data range between 20 s and
180 s. The average and the median durations are 65.4 s and
58 s and the distribution shows a large spread of 29.3 s. The
most common durations are between 50 s and 70 s (41 cavitons, 44.6 % of the sample).
Ann. Geophys., 31, 2163–2178, 2013
2172
P. Kajdič et al.: Foreshock cavitons
#cav / #SW freq.
N/Ntot SW intervals
N/Ntot cavitons
0.5
0.4
<B> = 6.9
µ = 6.6
σ = 2.0
<n> = 4.8
µ = 4.5
σ = 3.0
<B> = 6.0
µ = 5.8
σ = 2.2
<n> = 7.8
µ = 6.5
σ = 21.1
<V> = 456
µ = 445
σ = 95
<Va> = 75
µ = 78
σ = 24
<Ma> = 6.5
µ = 6.0
σ = 1.9
0.3
0.2
0.1
0.0
0.5
0.4
<V> = 424
µ = 399
σ = 98
<Va> = 51
µ = 47
σ = 21
<Ma> = 9.2
µ = 8.7
σ = 3.2
0.3
0.2
0.1
0.0
0.30
0.24
0.18
0.12
0.06
0.00
0
3
6
9
B [nT]
12
15
0
5
10
15
n [cm-3]
250
20 350 450 550 650 750
0
V [km/s]
40
80 120 160 200
0
Va [km/s]
3
6
10 13
Ma
16
20
Fig. 7. Top row: properties of the solar wind and IMF at times when the cavitons were observed. Middle row: solar wind and IMF properties
for the period between 2001–2006. Bottom row: normalized statistics of the SW and IMF properties at times of caviton observations. The
columns show, from left to right: magnetic field magnitude (nT), plasma density (cm−3 ), SW velocity (km s−1 ), Alfvén velocity in the SW
(km s−1 ) and Alfvénic Mach number (MA ).
The extents range between 1 and 13 RE with the average
and median values being 4.6 RE and 4.1 RE , respectively. The
most common extents are between 3 RE and 5 RE (56 cavitons, 61 %).
We have looked at possible correlations between different caviton properties. The only meaningful correlation was
found between 1B/B and 1n/n (Fig. 9). Figure 9 shows
that the two quantities are very well correlated with the linear Pearson correlation coefficient being 0.85. In the figure,
the asterisks represent the cavitons observed in the SW operational mode and the diamonds illustrate those observed
on the MS mode. There does not seem to be any difference
between the two subgroups, as expected. The thick line is
a linear fit to the distribution. The strong 1B/B vs. 1n/n
correlation points towards the fast magnetosonic nature of
foreshock cavitons.
2.2.3
Cavitons in the solar foreshock coordinate system
Solar foreshock coordinate system relates upstream coordinates to a normalized bow shock. It enables us to compare
the locations of upstream phenomena by eliminating the effects of variable solar wind properties and IMF orientation.
Solar foreshock coordinates (SFC) were first introduced
by Greenstadt and Baum (1986) who studied the location
of the ULF compressional waves in the Earth’s foreshock.
Meziane and D’Uston (1998) used these coordinates in order to describe the observed locations of the intermediate ion
boundary and then compared their observations to those by
Greenstadt and Baum (1986).
Foreshock cavitons are always located upstream of the
quasi-parallel bow shock. They are surrounded by intense
compressive ULF waves and hot suprathermal populations.
Ann. Geophys., 31, 2163–2178, 2013
Fig. 8. Caviton properties. The following quantities are shown:
(a) the relative depth of the magnetic field magnitude depression,
1B/B; (b) the relative depth of the plasma-density depression,
1n/n; (c) duration in the data and (d) extent of the cavitons in units
of RE . The dark-blue columns show distributions for cavitons observed in MS modes, the light-blue for those observed in solar wind
modes while white columns show distributions for the entire sample.
They should therefore always appear downstream of the ULF
compressional boundary and of the intermediate ion boundary. We show this by comparing the SFC of foreshock cavitons with those of the two boundaries.
In order to calculate these coordinates one has to first calculate the cross section of a model bow shock with the B − x
plane, which is defined by the observation point, the x axis
and the IMF direction. The locations of all points on this
plane are described by rectangular (x, η) coordinates (see
Fig. 10). The locations of the foreshock phenomena are described by another set of coordinates, XF and DBT . XF is
parallel to the x axis and measures the distance between the
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P. Kajdič et al.: Foreshock cavitons
1.00
2173
Solar foreshock coordinates
K = 0.85
Foreshock boundary
Bow
sho
ck
0.80
|dN|/N
0.60
XF
0.40
Event
η
0.20
0.40
0.60
|dB|/B
0.80
1.00
Fig. 9. Correlation between the magnetic field magnitude and
plasma-density depletions inside the foreshock cavitons. Asterisks
mark cavitons observed in solar wind operational modes while diamonds mark those events that were observed in MS modes.
observation point to the field line which is tangent to the
shock. DBT measures the distance along the tangent field line
from the shock to the point on the plane that has the same
value of η as the observed event.
We follow the procedure described by Greenstadt and
Baum (1986). These authors describe the shape of the bow
shock by a hyperboloid. Its intersection with the B − x plane
is then given by the equation:
2
,
(2)
η2 = A (X − BD0 )2 + CD 2 − DBX
where A, B and C are constants and their values are 0.04,
39.22 and 1461, respectively. D0 = 13.5 RE is the geocentric
distance of the subsolar point and DBX is the distance between the Sun–Earth axis and the (x, η) plane. In order to
obtain the direction of the magnetic field at the time of the
cavitons, we average the surrounding B field during time intervals with typical durations of several minutes.
Figure 11 shows positions of the 92 foreshock cavitons
from the sample in the SFC. Here we remind the reader that
the SFC are calculated from the position of the nominal bow
shock model, which is a long-term average. The actual position of the bow shock is time depended and this is why
there are some negative XF values in the figure. The cavitons
are represented by different symbols that stand for different
cone angles (the angle between the solar wind velocity and
the upstream IMF) θBV . The asterisks, diamonds, triangles,
squares and crosses mark cavitons observed for cone angles
between 10◦ and 20◦ , 20◦ and 30◦ , 30◦ and 40◦ , 40◦ and 50◦
and 50◦ and 60◦ , respectively. The black line is a linear fit
to the entire sample. For comparison we also plot the fits for
www.ann-geophys.net/31/2163/2013/
T
B
0.00
0.00
B
D
0.20
X
Fig. 10. Solar foreshock coordinate system. The plot was made following Greenstadt and Baum (1986). The definitions of all variables
are provided in the text.
the intermediate ion boundary (Meziane and D’Uston, 1998)
and the ULF wave boundary (Greenstadt and Baum, 1986)
which are represented by a red dash-dotted and a blue dashed
lines. The two lines are fits for cone angles between 40◦ and
50◦ . The space in this figure is divided into the foreshock region (left of the two boundaries) and the pristine solar wind
(right of the boundaries). The horizontal black dash-dotted
line shows the location of the nominal tangent line. The fits
for the ULF wave boundary and the intermediate ion boundary match quite well and probably represent the same boundary. The line representing the fit to the cavitons lies further
downstream and diverges from the other two boundaries.
We see that foreshock cavitons show larger dispersion
around the thick black line for smaller cone angles. This
probably has to do with the orbits of the Cluster spacecraft.
We can see from the figure that smaller cone angles mean
smaller distances from the shock (DBT ). It seems that at
larger DBT (larger cone angles) the spacecraft could only
barely enter the region populated by the cavitons and could
therefore survey only a small range of XF . When the cone angle was small, the range of coordinates XF that the spacecraft
could survey was larger, hence the larger dispersion.
In Fig. 12, we plot the caviton SFCs for cone angles between 10◦ and 20◦ (panel a), 20◦ and 30◦ (panel b), 30◦
and 40◦ (panel c), and 40◦ and 50◦ (panel d). In these panels the thick black line is the same as in Fig. 11, while the
black dashed line is a fit to the cavitons shown on each
panel. The ULF wave and the intermediate ion boundaries
Ann. Geophys., 31, 2163–2178, 2013
2174
P. Kajdič et al.: Foreshock cavitons
70
Table 2. Coefficients of straight-line fits for foreshock cavitons for
different cone angle ranges.
10° < θBV < 20°
20° < θBV < 30°
30° < θBV < 40°
40° < θBV < 50°
50° < θBV < 60°
XF [RE]
50
Quasi-parallel
Foreshock
30
θBV
k
n (RE )
All angles
10–20◦
20–30◦
30–40◦
40–50◦
50–60◦
0.67
0.41
0.53
0.67
0.69
0.61
−7.7
−5.1
−6.6
−7.9
−8.1
−2.5
Solar wind
10
Tangent line
-10
0
20
40
60
DBT [RE]
80
100
120
Fig. 11. Positions of foreshock cavitons in solar foreshock coordinates. The XF and DBT are given in units of Earth radii. Different symbols represent foreshock cavitons at different cone angles
(θBV ). The thick black line is a linear fit to the entire sample. The
red dash-dotted line and the blue dashed line are fits for the intermediate ion boundary (Meziane and D’Uston, 1998) and the ULF
wave boundary (Greenstadt and Baum, 1986) for cone angles between 40◦ and 50◦ .
for corresponding cone angles are also shown, if they are
provided in Greenstadt and Baum (1986) and Meziane and
D’Uston (1998). We see from the plots that the fit for a subset of cavitons and the fit to an entire sample match at larger
cone angles. In general, when comparing these fits with the
calculated intermediate ion and ULF boundaries, it is clear
that cavitons always appear further inside the foreshock. The
coefficients for all linear fits are provided in Table 2.
3
Discussion
In this work we perform a statistical study of 92 foreshock
cavitons observed by Cluster 1 during the years 2001–2006.
In the spacecraft data the foreshock cavitons appear as regions of diminished values of B and n surrounded by a rim
where these two quantities are enhanced compared to the ambient values.
In order for an event to be identified as a caviton, several
criteria had to be satisfied: depletions of B and n inside the
cavitons had to be deeper than those caused by the surrounding ULF waves; magnetic field and density during the caviton observations must be highly correlated. We show in a
case study that the Pearson correlation coefficient for the two
quantities during the caviton can be twice as large as during the periods of ULF waves. Cavitons thereby stand out as
Ann. Geophys., 31, 2163–2178, 2013
distinct structures, different from the ULF background. Also,
all cavitons were observed at least five minutes after or before the nearest foreshock compressional boundary (FCB),
so that they would not be misidentified with the boundaries.
Many foreshock caviton candidates were rejected in the process and this resulted in a relatively small number of events
in our sample.
The amplitudes of the depletions in B field and plasma
density inside the cavitons are highly correlated (Fig. 9). The
average 1B/B and 1n/n in our sample are 0.47 and 0.52,
respectively. The average duration of the cavitons in the data
was 65 s and their average calculated extents 4.6 RE . The majority of the cavitons (76/92, 83 %) lasted less than 80 s and
77/92 (84 %) had extents less than 6 RE .
The longest lasting caviton was observed during ∼ 3 min,
and the largest extent was 13 RE . The extents were calculated by multiplying the caviton durations by the solar wind
speed. A more accurate method would involve calculating
the actual caviton velocities by using observations from multiple spacecraft. It was shown by Kajdič et al. (2011) that
cavitons propagate sunwards in the SW frame of reference
with velocities that are somewhat smaller than the solar wind
speed. This would reduce the calculated extents. The measured extents do not represent the actual caviton sizes, since
they depend on how a spacecraft actually crosses a caviton.
Cavitons may have irregular shapes and the spacecraft may
cross them closer to their edges or can penetrate deeper into
their interiors.
The hybrid simulations, for example in Blanco-Cano et al.
(2011), show that the caviton sizes can vary. In simulations
it seems that they become larger as they approach the bow
shock. We compared the extents of cavitons in our sample
with their distances from the bow shock (not shown). There
was no correlation between the two variables.
We show that cavitons appear for a wide range of IMF and
SW conditions in the quasi-parallel foreshock, as also suggested by hybrid simulations. However they do not appear
for all IMF and SW conditions with the same probability
(Fig. 7).
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P. Kajdič et al.: Foreshock cavitons
Fig. 12. Positions of foreshock cavitons in solar foreshock coordinates for different cone angles. The black thick line is the same
as in Fig. 11 and the black dashed line is a fit to the shown group
of cavitons. The red dash-dotted and the blue dashed lines represent intermediate ion and ULF wave boundaries for corresponding cone angles. Note that neither boundary was calculated by
Meziane and D’Uston (1998) and Greenstadt and Baum (1986) for
10◦ ≤ θBV ≤ 20◦ and that the ULF wave boundary was also not
provided for 30◦ ≤ θBV ≤ 40◦ .
Cavitons were observed with higher probability for higher
B fields, SW velocities, Alfvén speeds and for smaller
plasma densities and Alfvénic Mach numbers, when compared to overall SW properties. We have also performed a
standard χ 2 test with which we calculated the possibility
that the differences between the two data sets are due to pure
chance. The tests were calculated for distributions of all five
quantities. In all cases the χ 2 values were very high, giving
practically a zero probability that corresponding histograms
in the top and middle rows in Fig. 7 show the same distributions and that their apparent differences are purely coincidental.
When we compare caviton locations in the foreshock with
intermediate ion and ULF wave boundaries (Figs. 11 and
12), we see that cavitons clearly appear further inside the
foreshock. These are the regions populated by compressive
ULF fluctuations. In the future it will be interesting to add
to these figures the locations of observed foreshock compressional boundaries (FCBs) (Omidi et al., 2009, 2013b;
Rojas-Castillo et al., 2013). FCBs separate highly perturbed
foreshock plasma from either pristine SW or from the fieldaligned ion beams (FAB) region. Since strong compressive
ULF fluctuations are required for the FCB formation, it is
www.ann-geophys.net/31/2163/2013/
2175
likely that the average FCB locations in solar foreshock coordinates will appear just upstream of the average locations
of foreshock cavitons.
Several transient phenomena exist in the region upstream
of the Earth’s quasi-parallel shock. Some of them may exhibit similar signatures in the spacecraft data, so one needs
to pay special attention in order to distinguish different structures. In the following paragraphs, we will briefly discuss
how cavitons differ from or relate to other phenomena commonly observed in the foreshock region.
It is well known that deep inside the quasi-parallel foreshock, two structures arise from ULF fluctuations: the
shocklets and the short-large amplitude magnetic structures
(SLAMS) (Hoppe and Russell, 1981; Greenstadt et al., 1995;
Scholer et al., 2003; Schwartz and Burgess, 1991; Schwartz,
1991; Schwartz et al., 1992; Giacalone et al., 1993). In the
magnetic field data, the shocklets exhibit a compressive character with one steepened, shock-like edge, often accompanied by a whistler wave precursor. Their amplitudes (1B/B)
are typically 50 % and their periods range between ∼ 25 s
and ∼ 100 s. SLAMS are the latest stage of evolution of ULF
waves. They appear as isolated structures or as embedded
inside the long pulsations (LP). SLAMS are regions of enhanced B field, typically between two and five times higher
than the average value in the surrounding medium. It has
been proposed that shocklets and SLAMS are formed due
to the steepening of ULF waves as they pass through the regions of strong suprathermal ion pressure gradients. Eventually they are convected by the SW towards the quasi-parallel
bow shock, where they play an important role in its reformation. When compared with the foreshock cavitons, shocklets
and SLAMS do not produce depletions in B field and plasma
density and SLAMS are observed only very close to the
quasi-parallel bow shock. The main difference between the
formation mechanisms of SLAMS and shocklets on one side
and cavitons on the other is that shocklets and SLAMS arise
from steepened ULF waves whereas cavitons form due to interaction of two types of ULF waves – transverse, parallelpropagating and compressive, obliquely propagating fluctuations (Omidi, 2007).
Another phenomenon often observed at the Earth’s bow
shock are the hot flow anomalies (HFA) (Thomsen et al.,
1986; Schwartz et al., 1995; Lucek et al., 2004; Zhang et
al., 2010). HFAs occur when a tangential IMF discontinuity interacts with the bow shock. If the conditions are such
that the motional electric field on at least one side of the discontinuity points towards it, this field channels the shock reflected suprathermal ions towards the discontinuity and confines them to its immediate vicinity. Such heated plasma then
expands and creates depletions of B and n which are surrounded by a rim of enhanced values of the two quantities.
There are however several HFA properties that make them
easily distinguishable from foreshock cavitons: the plasma
inside the HFAs is strongly heated and deviated from its original direction of propagation. Also, inside the HFAs there are
Ann. Geophys., 31, 2163–2178, 2013
2176
always IMF discontinuities (current sheets), which is not the
case for foreshock cavitons.
Perhaps the phenomena that most resemble the cavitons in
the spacecraft data are the foreshock cavities (Sibeck et al.,
2001, 2002, 2008; Billingham et al., 2008, 2011; Schwartz et
al., 2006). They also exhibit depletions of IMF magnitude
and plasma density and are surrounded by enhancements
of B and n. However these structures are found in part of
the foreshock populated by transverse ULF waves and field
aligned ion beams or even in the pristine solar wind. The
ion populations inside the cavities are hot and thus differ
from those in their surrounding regions. The total pressure
(solar wind ions + suprathermal ions + electrons + magnetic
field) inside them exceeds the surrounding pressure. The two
mechanisms that have been proposed for cavities include
varying IMF orientations. In the first scenario the surplus total pressure in their interiors causes cavities to expand (total
pressure inside the cavitons is the same as in their surrounding thereby, excluding thermal expansion as their formation
mechanism, see Kajdič et al., 2011). In another scenario the
cavities are just signatures in the spacecraft data due to back
and forth motions of the FCBs across the spacecraft. In this
case the increased pressure and hot ion populations are observed because the spacecraft briefly enters the highly perturbed section of the foreshock. The global hybrid simulations of the Earth’s bow shock also show the foreshock cavitons for any IMF and SW conditions (Omidi, 2007; BlancoCano et al., 2009, 2011), while foreshock cavities appear
only in presence of IMF rotations (Omidi et al., 2013b).
4
Conclusions
We study the foreshock cavitons observed by the Cluster 1 spacecraft during the years 2001–2006. In order not
to misidentify other foreshock phenomena for cavitons, we
use stringent criteria in the selection process. Thus only 92
events were included in our sample. The main condition for
the formation of the cavitons is the interaction of transverse
and compressive ULF waves. These fluctuations are commonly observed upstream of the quasi-parallel section of the
Earth’s bow shock. We calculate their occurrence rate to be
∼ 2 events per day. We cannot exclude the possibility that
many more cavitons were present in the data but that they
were not recognized as such due to their shallow B and n
profiles that made them difficult to distinguish from the surrounding ULF background. The statistical results in this paper only apply to those cavitons that evolved sufficiently in
order to be included in our sample.
We show that cavitons appear for a wide range of IMF and
SW parameters upstream of the quasi-parallel section of the
Earth’s foreshock. However, cavitons were found preferentially for higher B field, SW velocities, Alfvén speeds and
for smaller plasma densities when compared to average SW
properties.
Ann. Geophys., 31, 2163–2178, 2013
P. Kajdič et al.: Foreshock cavitons
Inside the cavitons, the B and n diminished by between
20 % and ∼ 85 % when compared to the ambient values (the
lower limit was chosen as one of the selection criteria). The
average depletions were 47 % and 52 % for B and n, respectively. The magnitudes of B and n depletions were well correlated with the correlation coefficient K = 85 %. Their average duration in the data was 65 s and their average extent
was 4.6 RE . 83 % of the cavitons lasted for less than 80 s and
84 % had extents less than 6 RE . The longest lasting cavitons
was observed for ∼ 3 min and its calculated extension was
13 RE . The comparison of the cavitons sizes and their distance from the bow shock revealed no correlation between
the two quantities.
Additionally we show that foreshock cavitons are not associated with any discontinuities in the IMF and that B and
n inside the cavitons are highly correlated, much more than
it is the case for the surrounding ULF waves.
We also compare the cavitons with other foreshock phenomena, such as shocklets, SLAMS, HFAs and foreshock
cavities and discuss their possible relations. Among the most
convincing arguments that show that we correctly identified
the foreshock phenomena as foreshock cavitons are the facts
that cavitons are not associated with any solar wind plasma
heating, flow deflections or IMF discontinuities. The cavitons
appear in parts of the foreshock region that are populated by
compressive ULF fluctuations. In the future it will be interesting to compare the locations of the cavitons in the solar
foreshock coordinates with those of the foreshock compressional boundaries (FCB). We expect that cavitons will appear
located just downstream of some average FCB location. This
will provide further insight about the complex phenomena in
the foreshock region.
Acknowledgements. The authors acknowledge the CL/CLWeb
team (http://clweb.cesr.fr), the Automated Multi Dataset Analysis
(AMDA) team (http://cdpp-amda.cesr.fr/DDHTML), the Cluster
CIS instrument team, the Cluster FGM team (PI Elizabeth Lucek)
and the Cluster RAPID team (PI Patrick W. Daly). The work at
IRAP was supported by CNRS and CNES. X. Blanco-Cano’s
work was supported by UNAM-DGAPA-PAPIIT grant IN110511.
N. Omidi’s work was supported by NSF grant AGS-1007449. Work
at UCLA was supported by the NSF under grant ATM04-02213.
Topical Editor C. Owen thanks two anonymous referees for
their help in evaluating this paper.
The publication of this article is
financed by CNRS-INSU.
www.ann-geophys.net/31/2163/2013/
P. Kajdič et al.: Foreshock cavitons
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