Investigation of Hot Flow Anomaly Structure Observed Near the Earth's Bow Shock

Abstract

The work is dedicated to investigation of Hot Flow Anomaly (HFA), formed at the front of Earth’s bows hock. Using Interball-Tail data we estimated orientation of the current sheet that was a cause of the anomaly. From the ion energy-time spectrogram we divided the anomaly into several regions. The motional electric fields near the HFA were estimated with 3D model of Earth’s bow shock. In accordance with previous investigations of HFA’s formation conditions these fields were directed towards the current sheet on both sides of it. We also provided the picture of HFA’s motion along the bow shock and calculated its speed. Analyzing ions’ bulk velocities within the HFA we found that the anomaly is expanding. This conclusion was supported by estimation of thermal and magnetic pressure balance. Ion energy-time spectrogram shows that anomaly is a complicated structure consisting of two parts—leading and trailing. Comparison of ion velocity distributions, magnetic field data and ion energy-time spectrogram provides better understanding of the phenomena and indicated the region that is the source of thermal and convective energy inside HFA.

Full text

ISSN 00167932, Geomagnetism and Aeronomy, 2012, Vol. 52, No. 1, pp. 16–27. © Pleiades Publishing, Ltd., 2012.
Original Russian Text © A.Yu. Shestakov, O.L. Vaisberg, 2012, published in Geomagnetizm i Aeronomiya, 2012, Vol. 52, No. 1, pp. 18–30.
16
1
1. INTRODUCTION
The regions of highly thermalized plasma near the
Earth’s bow shock where plasma flow directions had
strong deviation from those of solar wind and within
the magnetosheath were discovered in the middle of
1980th [Burgess, 1989; Schwarz et al., 2000]. Magnetic
field value in these regions was often smaller than in the
solar wind. These hot flow anomalies were found to be
related to interaction of interplanetary current sheet with
the bow shock where ions reflected from the bow shock
were injected within current sheet structure.
After early studies of HFAs and theoretical expla
nation of versatile structures of HFAs the interest to
this phenomenon decreased. However after observa
tion of 1999 event, when anomaly with fast (in about
7 min) displacement of magnetopause to the distance
of about 5
R
e
with strong influence on Earth’s iono
sphere was observed, interest to HFAs grew up again
[Sibeck et al. 1988; Sibeck, 1999].
Formation of HFA depends on several parameters,
especially magnetic field and current sheet orientation
within solar wind. Previously established relationship
between HFAs and the interplanetary current sheets
were investigated due to observations of solar wind
particles reflected from the bow shock. [Burgess,
1989]. When an interplanetary magnetic field orienta
tion is such that motional electric field vector
is directed towards the current sheet,
these particles are injected back along the current
sheet oppositely to the solar wind flow. Burgess also
1
The article was translated by the authors.
[]
1
EVB
c
=− ×
mentioned the key role of motional electric field in
HFA formation, that was confirmed by simulation. In
agreement that
n
cs
⋅
V
sw
< 0 (
n
cs
—normal to the cur
rent sheet,
V
sw
—solar wind velocity), the angle
between
E
and
n
cs
should be less than
90
°
in front of
HFA and more than
90
°
behind it. Later in 1991 sim
ulations confirmed the necessity of this condition, and
showed that the HFA is located on the bow shock and
reproduced all described processes. These simulations
have also confirmed previous assumptions that HFAs
are formed at the tangential discontinuity rather on
rotational one [Thomas et al., 1991].
In summary, it was found that necessary conditions
for formation of HFA are:
•
Presence of an interplanetary current sheet with
electric field directed to the sheet’s plane velocity at least
at one side of it (at the laboratory coordinate system).
•
Current sheet normal makes a large cone angle
(
>60
°
) with solar wind velocity.
•
The current sheet is a tangential discontinuity.
•
Quasiperpendicular bows hock geometry at least
at one side of current sheet.
This paper is devoted to analysis of main characteris
tics of Hot Flow Anomaly (HFA) that was formed at the
bow shock as a result of interaction of interplanetary cur
rent sheet with the bow shock. This phenomenon was
observed by the Tail probe of Interball project on
03.14.1996. Preliminary analysis of this HFA was given in
[Vaisberg et al., 1999].
In this paper we describe one HFA observed with
InterballTail, conditions for formation of HFA, HFA’s
internal structure and various characteristics of its regions.
Investigation of Hot Flow Anomaly Structure Observed Near
the Earth’s Bow Shock
1
A. Yu. Shestakov and O. L. Vaisberg
Space Research Institute RAS, Moscow
email: sartiom1@yandex.ru
Received June 29, 2010; revised May 18, 2011
Abstract
—The work is dedicated to investigation of Hot Flow Anomaly (HFA), formed at the front of Earth’s
bows hock. Using InterballTail data we estimated orientation of the current sheet that was a cause of the
anomaly. From the ion energytime spectrogram we divided the anomaly into several regions. The motional
electric fields near the HFA were estimated with 3D model of Earth’s bow shock. In accordance with previous
investigations of HFA’s formation conditions these fields were directed towards the current sheet on both
sides of it. We also provided the picture of HFA’s motion along the bow shock and calculated its speed. Ana
lyzing ions' bulk velocities within the HFA we found that the anomaly is expanding. This conclusion was sup
ported by estimation of thermal and magnetic pressure balance. Ion energytime spectrogram shows that
anomaly is a complicated structure consisting of two parts—leading and trailing. Comparison of ion velocity
distributions, magnetic field data and ion energytime spectrogram provides better understanding of the phe
nomena and indicated the region that is the source of thermal and convective energy inside HFA.
DOI:
10.1134/S0016793212010136

GEOMAGNETISM AND AERONOMY
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2012
INVESTIGATION OF HOT FLOW ANOMALY STRUCTURE OBSERVED NEAR 17
2. OBSERVATIONS
Observations were performed with Interball Tail
probe on March 13, 1996. Measurements were made
with complex plasma spectrometer SCA1 [Vaisberg
et al., 1995], electron spectrometer ELECTRON
[Sauvaud et al., 1995], and magnetometer MIFM
[Klimov et al., 1995]. SCA1 provided measurements
of flux density in the energy range
E
/
q
from 50 eV/q to
5 keV/q in 64 directions (altogether 960 points in
velocity space) every 10 seconds. MIFM provided
measurements of 3 components of magnetic field with
sampling rate of 1 Hz.
Magnetic field and plasma data visualization were
provided by lkstdv and lk3ds applications developed by
L.A. Avanov with use of IDL language.
Figure 1 shows the time interval, where an HFA
was detected. The panels (from top to bottom) are: two
energytime (dynamic spectra) spectrograms of ions,
obtained by solar direction sensor and antisolar
direction sensor, ion flow parameters n, T, three veloc
ity components, Mach number and three magnetic
field components.
This time interval can be divided into 7 parts:
•
First part: from the beginning to about 1256:00 UT –
solar wind flux.
•
Second part: 1256:00–1256:27—magnetosheath
between quasiperpendicular bow shock formed in
front of HFA and HFA itself.
•
Third part: from 1256:27 to 1257:13 UT—the
leading part of HFA.
•
Fourth part: 1257:13–1257:18 UT—transition
region between leading and trailing parts of HFA.
•
Fifth part: 1257:18–1259:08 UT—trailing part of
the anomaly.
•
Sixth part: 1259:08–1259:34 UT—ambient flow
in front of anomaly.
•
Seventh part: solar wind region.
These regions will be discussed in detail later.
Weakly fluctuating values of solar wind plasma flux and
interplanetary magnetic field within 1255:56 UT corre
spond to presence of the spacecraft in solar wind in front of
quasiperpendicular bow shock. Strongly fluctuating
parameters after 1259:34 UT correspond to presence of
spacecraft in front of quasiparallel bow shock. Transition
from almost stationary plasma and magnetic field param
eters before the HFA to strongly fluctuating values suggests
that interplanetary current sheet passed the satellite within
this interval. Thereby the event, registered within
1255:59–1259:34 UT was, most likely a HFA.
We need to point out that number density and tem
perature values in solar wind, calculated from SCA1
data, may not be reliable. It is due to saturation of
MCP of sunward sensor by solar with flux in a small
cone angle since it was mostly designed for magneto
spheric plasma measurements. However we can rea
sonably trust the values of speeds in solar wind.
3. INTERPLANETARY CURRENT SHEET
As we mentioned before, one of main conditions to
form HFA is presence of an interplanetary current
sheet. We determined values of components of mag
netic field for the intervals before we cross supposed
current sheet and after it. We selected intervals without
significant variations. After averaging values for inter
val 1250:00–1255:00 UT before crossing HFA and for
interval 1301:00–1306:00 UT after it, we finally
received:
—magnetic field vector before crossing HFA:
n
B
= (0.782; –0.417; 0.462),
—one after crossing HFA:
In assumption that the current sheet is a tangential
discontinuity we can calculate a normal to it by multi
plication [
B
×
B
'
]:
n
int
= (–0.22; 0.50; 0.83).
To identify this interplanetary current sheet we
analyzed data, obtained by WIND spacecraft, that is
located at the libration point at about 1.5 millions kilo
meters in front of Earth. It could register this current
sheet. We need to estimate time it takes for solar wind
with frozenin current sheet to cover the distance
between WIND and Interball. After making a correc
tion we can calculate the approximate time when this
current sheet passed the WIND.
GSE
coordinates of WIND at at this time were
Х
=
7.53
×
10
5
km,
Y
= 2.66
×
10
5
km,
Z
= 9320 km. Allow
ing for Interball’s position at the time of the anomaly
detection we can estimate the distance between these
spacecraft along
Х
axis. It makes about 700000 km.
Solar wind speed within this interval was about 515–
520 km/s. Hence the time of flight of current sheet
from one SC to another was about 23 min. Here are
solar wind magnetic field data from WIND for that
time interval. For better clearness we compare them
with Interball data (Fig. 2).
After examining magnetic field profiles we can
notice some correspondence of specific field jumps in
both cases. For example
В
x
and
В
y
components are
positive at both spacecraft and
В
z
changes sign from
negative to positive.
We will calculate the normal to current sheet in
WIND data. Average values of magnetic fields and
directions of their unit vectors fot intervals 1220:00–
1223:00 UT and 1230:00–1235:00 UT.
Before current sheet detection:
n
= (0.777; –0.562; 0.281)
After it:
n
'
= (0.978; 0.058; 0.199).
In assumption of tangential discontinuity we will
find current sheet normal as a result of multiplication
(
)
'
0.915;0.401;0.044 .
B
n
=

18
GEOMAGNETISM AND AERONOMY
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No. 1
2012
SHESTAKOV, VAISBERG
–10
1256
0
1257 1258 1259 1300
7.20
11.76
12.31
7.19
11.74
12.31
7.19
11.73
12.30
7.18
11.71
12.30
7.17
11.70
12.30
X
GSE
Y
GSE
Z
GSE
UT
10
–5
5
15
–15
–10
0
10
–5
5
–15
B
z
, nT
B
y
, nT
0
5
5
15
20
B
x
, nT
M
2
4
6
8
V
z
, km/s
–50
0
50
100
150
0
50
100
150
200
250
V
y
, km/s
–400
–200
0
200
400
V
x
, km/s
T
, eV
100
10
1000
1
2
3
4
5
0
n
, см
–3
1.0
E
, keV
1.0
E
, keV
1996/03/14
3
2
1
0
log(CR)
Θ
= 17
°Θ
= 163
°
V
, km/s
B
, nT
Fig. 1.
SCA1 and magnetic field data obtained on Interball on March 14, 1996. Graphs of
x
component of magnetic field (black)
and magnetic field absolute value (grey) are shown on
B
x
panel.
GSE
coordinates, geomagnetic time and latitude of satellite are
given at the bottom.

GEOMAGNETISM AND AERONOMY
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INVESTIGATION OF HOT FLOW ANOMALY STRUCTURE OBSERVED NEAR 19
of normalized vectors:
n
wind
= (–0.21; 0.10; 0.96). As
we can see this vector’s direction is not significantly
different from the one we calculated from Interball
data.
n
int
= (–0.22; 0.50; 0.83).
Thereby the HFA detected by Interball could be
potentially formed by a current sheet of similar config
uration. Unfortunately we can’t say with certainty that
current sheet detected by WIND was the one to form
the HFA because it had moved to the Interball loca
tion 10 min before Interball detected the anomaly.
Moreover, its duration (thickness) doesn’t correspond
assumption of a tangential discontinuity.
4. NORMAL TO THE BOW SHOCK
We used a 3D model of Earth’s bow shock [Form
isano, 1979]. According to this model Earth’s bow
shock can be approximated by a surface described by
following equation:
B
z
, nT
UT
–10
–15
1240 1250 1300 1310 1320
B
, nT
–5
0
5
10
15
–10
–15
–5
0
5
10
B
y
, nT
0
5
10
15
20
B
x
, nT
B
z
, nT
UT
1220:00 1230:00 1240:00 1250:00 1300:00
1.0
0.5
1.5
2.0
2.5
1210:00
0
–4
B
y
, nT
–2
0
2
4
3
4
5
6
7
B
x
, nT
Fig. 2.
Combined graphs of interplanetary magnetic field according to the WIND (top) and Interball (bottom) measurements.
Graphs of
x
component of magnetic field (black) and magnetic field absolute value (grey) are shown on
B
x
panel. Data are com
bined in accordance with calculations of flight time from one SC to another.

20
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2012
SHESTAKOV, VAISBERG
z
2
+
k
1
y
2
+
k
2
xy
+
k
3
x
2
+
k
4
y
+
k
5
x
+
k
6
= 0,
where the coefficients are equal to:
k
1
= 1,
k
2
= 0.12,
k
3
= 0.06,
k
4
= –4.92,
k
5
= 43.9,
k
6
= –634.
Using this model we can calculate from geometrical
considerations the normal to the bow shock at the
location of the HFA:
n
bs
= (0.83; 0.35; 0.44).
Now, when we have possibility to analyze a three
dimensional system it makes sense to calculate the
equation that describes current sheet plane. Average
values of magnetic field before and after bow shock
crossing are:
—before:
B
= (4.50; –2.39; 2.66)
—after:
B
'
= (3.46; 1.86; 0.61).
We can calculate current sheet normal as a cross
product of
B
and
B
'
(in assumption of tangential dis
continuity)
Thus the equation of current sheet plane that
crosses location of the HFA at (7.19; 11.74; 12.3) GSE
can be written as follows:
–0.337
x
+ 0.34
y
+ 0.877
z
– 12.355 = 0.
5. GEOMETRY OF CURRENT
SHEET—BOW SHOCK SECTION LINE
First of all we need to calculate velocity of shock
current sheet section line (at the location of the satel
lite). Geometry of this process is schematically shown
on Fig. 3. Now we will use an equation derivated pre
viously [Schwartz et al., 2000]
(1)
Here is a projection of solar wind velocity vec
tor
V
sw
on the notmal to current sheet,
Θ
cs:bs
—the
angle between current sheet normal
n
cs
and bow shock
normal
n
bs
.
Averaged solar wind velocity vector before crossing
bow shock
V
sw
~ (–490; 26; –11) km/s in
GSE
coordi
nate system.
Current sheet normals calculated from two space
crafts data are:
n
wind
= (–0.21; 0.19; 0.96),
n
int
= (–0.22; 0.50; 0.83),
Angles between normal vectors and solar wind
velocity vectors are, respectively:
α
wind
≈
79.3
°
and
α
wind
≈
77.5
°
.
Now we will estimate the angle between
n
bs
and
n
cs
Now we can estimate speed of displacement of cur
rent sheet along bow shock surface from Eq. (1):
V
tr
≈
(–70; 45; 86) km/s,
|
V
tr
|
~ 120 km/s.
Since all vectors were normalized, the result we
obtained is nothing else but the component of current
[
]
()
×
==−
×
cs
'
'
0.337;0.340;0.877 .
BB
nBB
()
cs
tr cs cs:bs bs
cs:bs
2
cos .
sin
n
V
Vnn=−Θ
Θ
cs
n
V
[
]
cs sw cs Schwartz et al 2
n
VVn
=⋅
., 000 .
cs
cs bs bs cs
sw cs
arccos 67 2
also 11
:
().,
0.
n
nn
VVn
Θ= ⋅ = °
≡⋅∼
n
cs
θ
cs:bs
n
bs
V
tr
V
ncs
n
cs
Shock bow
Current sheet
Fig. 3.
Scheme of interaction between bow shock and cur
rent sheet. Their normals (
n
bs
,
n
cs
respectively), solar wind
velocity (
V
sw
) and velocity of current sheet displacement
along the bow shock are shown (
V
tr
) [Schwartz et al., 2000].
Z
Y
X
E
1
E
2
N
cs
N
bs
E
1 = –1/c[
V
1
×
B
1]
before current sheet crossing
Current sheet
Bow shock (BS)
E
2 = –1/c[
V
2
×
B
2]
after current sheet crossing
Fig. 4.
Scheme of mutual orientation of Earth’s bow
shock, current sheet, normal to bow shock (
N
bs
), normal
to current sheet (
N
cs
) and directions of motional electric
field before and after current sheet crossing (
E
1,
E
2). Axis:
from figure’s plane—
X
(
GSE
), to the right—
Y
(
GSE
), to
the top—
Z
(
GSE
).

GEOMAGNETISM AND AERONOMY
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INVESTIGATION OF HOT FLOW ANOMALY STRUCTURE OBSERVED NEAR 21
sheet velocity along the tangent to the bow shock at the
location of the HFA. Now we will estimate anomaly’s
size along its trajectory through location of Interball
spacecraft. Noting that duration of HFA observation is
about 160 seconds, and observed plasma velocity—
about 119 km/s we can estimate crosssection dimen
sion of HFA as
1.9
×
10
4
km (~3 Earth’s radii).
6. REVERSE ION INJECTION
One more significant point of HFA formation is the
phenomenon of solar wind ion reverse injection after
mirror reflection at bow shock. The definitive factor in
this phenomenon is motional electric field
that is a result of solar wind motion.
Let us discuss our situation. We know magnetic field
vectors before and after current sheet passage, thus we
can estimate motional electric fields on both sides of
current sheet:
—motional electric field before crossing HFA:
= = (–1.4; –41.6; –35.1)
⋅
10
–8
CGS
units, and
|
E
1
| = 54.4
×
10
–8
CGS units, that is directed
along (–0.03; –0.77; –0.65); it means that it is
directed towards the current sheet (negative
Y
compo
nent, Fig. 4).
—motional electric field after crossing HFA:
= = (–1.1; –8.5; 32.1)
⋅
10
–8
CGS
units, and
|
E
2
| = 33.1
⋅
10
–8
CGS units, that is directed
towards the current sheet (–0.03; –0.26; 0.97), so it is
also directed towards the current sheet (negative value—
alond the
Y
axis, but the main positive value—along the
Z
axis) (Fig. 4).
Thereby motional electric field in the bow shock
reference coordinate system has a component directed
towards the current sheet on both sides of it (Fig. 4).
This means that ions reflected from the bow shock will
be moving towards the current sheet and will form near
it a 2 or 3 component ion velocity distribution. It is
known that twobeam ion velocity distribution leads to
an instability. Free plasma energy that refers to that
type of distribution initiates strong
EM waves that
lead to plasma heating.
7. CHARACTER OF PLASMA MOTION
WITHIN HFA
Now we will take a closer look at plasma flows
within HFA. Let’s look at the data. After averaging
each velocity component within HFA we will obtain
following values in GSE system:
V
x
~ –240 km/s,
V
y
~ 200 km/s,
V
z
~ 6 km/s.
[]
1
,
EVB
c
=− ×
1
E
[]
1
1
VB
c
−×
2
E
[]
2
1
VB
c
−×
It is easy to see from table that we are dealing with
plasma moving away from the current sheet both in the
leading and the trailing parts of HFA.
As we can see in Fig. 5, plasma flow velocity vectors
are directed from center to edges of the HFA in both
leading and trailing parts.
Let’s take a closer look at plasma motion within the
anomaly. Vector projections of these velocities on
YZ
(
GSE
)
plane are shown in Fig. 6.
Deviation of velocity from the mean value within the
anomaly
Tim e
dV
x
dV
y
dV
z
1256:30 –39.1 23.0 2.9
1256:41 –50.5 48.9 37.8
1256:48 –30.6 30.3 31.0
1256:59 –38.8 17.0 24.6
1257:10 –28.8 –6.0 51.4
1257:18 –34.9 6.0 44.4
1257:29 –6.6 –18.3 47.3
1257:39 25.7 43.6 31.6
1257:48 10.00 48.2 4.5
1257:59 27.3 14.0 3.6
1258:07 29.4 –4.1 –44.0
1258:17 9.0 3.5 –21.2
1258:28 19.6 –18.6 –11.4
1258:36 13.8 –30.2 –59.9
1258:47 29.0 –62.5 –54.4
80
60
40
40 60
Z
, km/s
20
8020
Y
, km/s
–20
–40
–60
–80
–10–40–60–80
Fig. 5.
Values of convective velocities within HFA in coor
dinates
YZ
(
GSE
). Black circles are values of the leading
part, white circles are values in trailing part, dashed line
shows direction of current sheet normal.

22
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2012
SHESTAKOV, VAISBERG
From this figure we can see that the plasma is mov
ing away from the current sheet along its normal
through all line of anomaly’s section by spacecraft.
This indicates that plasma is expanding, at least along
the line of measurements.
It also makes sense to analyze expansion velocities
in more convenient coordinate system.
1. Origin is set at the spacecraft location
M
(7.19;
11.74; 12.3).
2. Axis
y
'
is drawn along the current sheet normal
n
cs
. Its direction the same and is defined in
GSE
system
as (–0.34; 0.34; 0.88).
3. A plane is defined by two vectors
n
cs
and
n
bs
and
point
M
. Equation of the plane is written as follows:
⎯
0.16
x
+ 0.87
y
– 0.40
z
– 4.24 = 0.
4. Normal to this plane (–0.16; 0.87; 0.40) is
selected as negative direction of
z
'
.
5. Since axes
y
'
and
z
'
are perpendicular by defini
tion we can obtain
x
'
as their crossproduct; these axes
define right orthogonal base
x
' = [
y
'
×
z
']
= (0.90; 0.27;
0.24).
Now we need to move to
x
’
y
'
plane of coordinate
system we obtained. We will project plasma velocities
vectors onto it. The results are presented on Fig. 7.
As on Fig. 6 we have obtained typical picture for an
expanding region. On Fig. 7 plasma expanding from
the current sheet is more obvious. We need to mention
that in the middle of this HFA it is possible to note
small interval which can be identified as solar wind
type flow, since it has a significant component in anti
solar direction.
8. PRESSURE BALANCE WITHIN HFA
Next we are going to compare total and internal
pressure within HFA with external pressure. Internal
pressure is defined as a sum of kinetic (thermal) pres
sure of plasma
P
гк
= n
i
kT
i
+ n
e
kT
e
and magnetic pres
sure
P
m
=
B
2
/8
π
. External pressure on HFA’s side is
defined by thermal pressure of ambient solar wind
P
ksw
=
P
esw.
+
P
msw.
and magnetic pressure
P_m
. Figure 8 pre
sents diagram of thermal and magnetic pressures
within the anomaly. Solar wind dynamic pressure on
the sunward side of anomaly is
We will estimate thermal pressure on the anomaly
by solar wind. After averaging solar wind data for time
interval 1250:03–1254:53 UT, we will obtain ion ther
mal pressure:
P
msw.
~ 3.17
⋅
10
–10
erg/cm
3
.
To estimate thermal pressure of electrons we need
to look at the data obtained by ELECTRON. It is
known that when one makes measurements of parti
cles with homogeneous isotropic Maxwellian distribu
tion by an electrostatic analyzer maximal count rate is
reached at the energies of 2 T. Thus we can estimate
temperature of electrons from data, presented on Fig. 9.
According to this picture maximal count rate within
the HFA body (~1258:00 UT) at the energy of 100 eV.
In solar wind this energy is 35 eV. Therefore tempera
2
.
dp
PmV
=ρ⋅ ⋅
–80
–120
–160
–200 2001501000–100–200 –50–150 50
V
y
, km/s
–40
0
40
80
120
160
200
V
z
, km/s
Tra il in g
part
Leading part
Fig. 6.
Directions of convective velocities along the trajec
tory of satellite through HFA. Long line shows approxi
mate current sheet orientation, arrow shows direction of
its displacement. Vectors from the leading part are to right
are, vectors from trailing part are to left. Graph is in
YZ
(GSE) plane.
–100
–150
–200
2001501000–100–200 –50–150 50
V
y
'
, km/s
–50
0
50
100
150
200
V
z'
, km/s
Tra il in g p ar t
Leading part
Fig. 7.
Convective velocities in the anomaly in coordinate
system relative to bow shock and current sheet normals.
Long grey line indicates current sheet orientation, arrow
shows direction of its displacement. Velocities in leading
part of HFA are at the top, velocities in the trailing part are
at bottom.

GEOMAGNETISM AND AERONOMY
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2012
INVESTIGATION OF HOT FLOW ANOMALY STRUCTURE OBSERVED NEAR 23
ture of electrons in solar wind is about 17 eV and is
within HFA ~50 eV.
Electron number density in plasma is equal to ion
concentration with high accuracy. From Interball data
ion number density within HFA is about 3.5 cm
–3
.
From the WIND data in solar wind concentration is
about 2.5 cm
–3
.
Now we can estimate thermal pressure in solar
wind:
P
esw.
~ 9.52
⋅
10
–11
erg/cm
3
P
ksw
=
P
esw.
+
P
msw.
= 4.122
⋅
10
–10
erg/cm
3
.
Magnetic pressure in the solar wind can be esti
mated as:
P
m
=
B
2
/8
π
~ 1.33
⋅
10
–10
erg/cm
3
.
Now we can estimate solar wind dynamic pressure.
From WIND data for the respective time interval we
can estimate average proton density as 2.5 cm
–3
and
solar wind velocity as 500 km/s. At the same time HFA
itself moves in antisolar direction with average speed of
240 km/s; hence we should use relative speed in calcu
lations. Then this dynamic pressure on HFA can be
estimated as:
After analysis of data for the time interval 1256:00–
1259:24 UT we made following conclusions on mag
netic and thermal pressures within the HFA.
Total solar wind pressure on flank of HFA is esti
mated as
4.45
×
10
–10
erg/cm
3
. Total pressure within
HFA is estimated as
2.02
×
10
–9
erg/cm
3
that exceeds
solar wind pressure by factor of about 3. Thus supports
our conclusion about expanding plasma in the body of
anomaly.
93
7.33 1 erg cm
2
~0 .
dp
PmV −
=ρ⋅ ⋅ ×
9. ION VELOCITY DISTRIBUTIONS
WITHIN HFA
Graphical presentation of ion velocity distributions
are very demonstrative for description of transitional
processes within anomaly. Figure 10 shows typical ion
velocity distributions in solar wind at local magnetic
frame. We use measured ion flux density at 15 energy
intervals from 50 to 5000 eV/q in 64 directions to cal
culate particle density in velocity space. The density n
(in assumption that all ions are protons), temperature
Т
and velocity vector
V
are calculated from these mea
surement. Then magnetic field measurements are
averaged for cycle of plasma measurements (~10 s).
Relevant coordinate system is a cylindrical system in
velocity space with main axis along calculated direc
tion of magnetic field and has an origin at point
V
⊥
B
.
Horizontal axis of Fig. 10 is parallel to magnetic field
vector, vertical axis is perpendicular to it. The density
in velocity space is coded according to grey scale
(darker means higher density).
Let’s take a closer look at several regions within the
anomaly and at its surrounding:
1. First region–solar wind, detected by spacecraft
before 1256:00 UT and after 1259:34 UT (Fig. 10).
This is indicated by relatively narrow energy spectrum
of ions (Fig. 10a), by almost stationary magnetic field,
and by weakly fluctuating velocity. Number density
jumps, sharp peaks of magnetic field and slight
decrease of speed are seen at borders of this regions.
2. Second region (1256:00–1256:27 UT)—the one
including all magnetic field jump, significant growth
of temperature, and
Y
and
Z
components of velocity.
Front of this region is bow shock, and the region itself,
as we will see later, is the flow passing the obstacle.
Shock could be identified by a typical jump of mag
netic field about 4 times (magnitude corresponding a
strong quasiperpendicular bow shock), by heating of
declarated plasma and its deflection in
OY
and
OZ
(Fig. 10b).
2.50E–09
0.00E+00
1256:00
erg/cm
3
2.00E–09
1.50E–09
1.00E–09
5.00E–10
1256:22
1256:59
1256:41
1257:18
1257:39
1257:59
1258:17
1258:36
1258:55
1259:16
Fig. 8.
Variations of magnetic and thermal pressures within HFA, Dashed line is magnetic pressure, bold line is thermal pressure.

24
GEOMAGNETISM AND AERONOMY
Vol . 52
No. 1
2012
SHESTAKOV, VAISBERG
3. Third region—leading part of the anomaly, the
region detected from 1256:27 to 1257:13 UT. It is
characterized by highly thermalized plasma, by signif
icant particle flux at antisolar direction (Fig. 10c), by
high number density, and by strong fluctuations of
magnetic field.
15.4
1255:40 UT
19.8
9.4
B
z
, nT
B
y
, nT
B
x
, nT
20
1.0
E
, keV
1996/03/14
3
2
1
0
log(CR)
Θ
= 17
°Θ
= 163
°
1255:20 1257:00 1257:40 1258:20 1259:00 1259:40
12.0
eV
25.3
32.4
41.5
53.2
68.2
87.3
111.9
143.3
183.6
235.2
301.3
385.9
494.4
633.3
811.3
1039.2
1331.3
1256
15
10
5
0
10
5
0
–5
–10
–15
10
15
5
0
–5
–10
–15
1257 1258 1259 1300
B
, nT
Fig. 9.
At top: dynamic spectrum of ions and magnetic field parameters. Graphs of
x
component of magnetic field (black) and
magnetic field absolute value (grey) are shown on
B
x
panel. At the bottom: dynamic spectrum of electrons. Vertical lines divide
regions of the anomaly identified by dynamic spectra of electrons, ions and magnetic field parameters.

GEOMAGNETISM AND AERONOMY
Vol . 52
No. 1
2012
INVESTIGATION OF HOT FLOW ANOMALY STRUCTURE OBSERVED NEAR 25
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1259:16 – 1259:24
(f)
V
par
, km/s
V
perp
, km/s
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1259:24 – 1259:35
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1258:36 – 1258:47
(e)
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1258:47 – 1258:55
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1257:10 – 1257:18
(d)
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1257:18 – 1257:29
1000
800
100
200
010000–1000 500
600
–500
(c)
1000
800
100
200
010000–1000 500
600
–500
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1256:22 – 1256:30
(b)
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1256:30 – 1256:40
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1255:33 – 1255:41
(a)
1000
800
100
200
010000–1000 500
600
–500
1996/03/14 1255:41 – 1255:52
Fig. 10.
Ion velocity distributions in the anomaly. Graphs refer to time interval 1255:33–1259:35 UT (from left to right, from top
to bottom). Ion density in velocity space is shown in local magnetic coordinate system (
V
perp
–
V
par
). Density increases from grey
to black.
1996/03/14 1256:30 – 1256:40 1996/03/14 1256:41 – 1256:48

26
GEOMAGNETISM AND AERONOMY
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No. 1
2012
SHESTAKOV, VAISBERG
4. Fourth region—1257:13–1257:18 UT—is tran
sition region between leading and trailing parts of
HFA. It is characterized by higher energies of parti
cles. It is clearly seen at electron dynamic spectrogram
(Figs. 10d, 11).
5. Fifth region—1257:18–1259:08 UT—trailing
part of the anomaly. It differs from the leading part of
HFA by large ion flux form antisolar direction.
6. Sixth part—1259:08–1259:34 UT—corre
sponds to the flow behind the bow shock, passing
around the obstacle. It can be identified by abrupt
decrease of number density and magnetic field.
As the spacecraft flies through the anomaly we can
observe a high thermalization of solar wind particles
that is a typical behaviour for a flow interacting with
Earth’s shock bow as an obstacle.
10. CONCLUSIONS
In this work we investigated the HFA detected on
March 14, 1996 near Earth’s shock bow by Interball
Tail probe. From the data of plasma and magnetic field
measurements we analyzed geometry of interaction of
interplanetary current sheet with Earth’s bow shock,
its plasma parameters and flow structure within the
anomaly.
Estimation of magnitude and direction of motional
electric field in solar wind at both sides of current
sheet, interacting with Earth’s bow shock, shows that
ions reflected from the bow shock should be injected
towards the current sheet; that is usually considered as
primary condition of HFA formation.
HFA is an region of highly thermalized plasma with
average temperature about a few hundreds of eV (in
our case ~260eV). We investigated structure of HFA
that turned out to consist of three regions with differ
ent parameters. These parts are anomaly’s leading and
trailing parts where plasma is moving away from the
third part—transitional region between leading and
trailing parts. The transition region differs from nearby
regions by plasma flow direction. This and motion of
plasma away from this region indicate that this region
is the main source of plasma energy. Plasma pressure
within solar wind exceeds the flank pressure of solar
1996/03/14
V
perp
, km/s
B
z
, nT
B
, nT
B
y
, nT
B
x
, nT
UT
1256 1257 1258 1259 1300
7.20
11.76
12.31
7.19
11.74
12.31
7.19
11.73
12.30
7.18
11.71
12.30
7.17
11.70
12.30
X
GSE
Y
GSE
Z
GSE
5
10
15
20
–15
–5
0
10
–15
–5
0
10
0
10
5
15
1
2
3
4
0
400
800
–1000
–500
0
500
1000
N
, cm
–3
V
par
, km/s
1996/03/14
10
–17
10
–18
10
–19
10
–20
10
–21
0
–10
–20
–30
–1000 –500 50001000
1255:12
1255:22
1255:33
1255:41
1255:52
1256:00
1256:11
1256:22
1256:30
1256:41
1256:48
1256:59
1257:10
1257:18
1257:29
1257:39
1257:48
1257:59
1258:07
1258:17
1258:28
1258:36
1258:47
1258:55
1259:06
1259:16
1259:24
1259:35
1259:43
1259:54
1300:05
1300:13
1300:24
1300:32
log(F)
V
par
, km/s
Fig. 11.
Left: from top to bottom: ion dynamic spectra for parallel and perpendicular velocity components, number density, three
components of magnetic field, magnitude of magnetic field. To the right—distributions of ions parallel velocities.

GEOMAGNETISM AND AERONOMY
Vol . 52
No. 1
2012
INVESTIGATION OF HOT FLOW ANOMALY STRUCTURE OBSERVED NEAR 27
wind that explains expansion of HFA. However since
frontal solar wind dynamic pressure significantly
exceeds internal HFA pressure we can conclude that
inside the formation we are dealing with convective
processes. Ion velocity distribution functions inside
the anomaly add to general picture of this phenome
non including formation of twobeam ion velocity dis
tribution inside HFA.
From plasma measurements we estimated velocity
and direction of HFA’s displacement along the bow
shock that is in agreement to the current sheet orien
tation relative to bow shock. From the value and direc
tion of HFA’s velocity and time of observation we also
estimated transverse size of formation. It turned out to
be about
2.5
R
E
.
Shocks were detected on both sides of HFA: quasi
parallel bow shock from side of the leading part and
quasiparallel one from side of trailing part of HFA.
Directions to normals to these shocks suggest that
HFA extends out of Earth’s bow shock.
Thus we showed that anomaly tends to expand.
A rough scenario of HFA’s behavior was offered.
This scenario characterizes anomaly qualitatively and
quantatively.
ACKNOWLEDGMENTS
Authors are grateful to Klimov S.I. for possibility to
use magnetic field data and Shahverdyan T.A. for
assistance in processing graphical data.
REFERENCES
Burgess, D., On the Effect of a Tangential Discontinuity on
Ions Specularly Reflected at an Oblique Shock,
J. Geo
phys. Res.
, 1989, vol. 94, no. A1, pp. 472–478.
Formisano, V., Orientation and Shape of the Earth’s Bow
Shock in Three Dimensions,
Planetary and Space Sci
ence
, Sept. 1979, vol. 27, pp. 1151–1161.
Klimov, S., Romanov, S., Amata, E., et al., ASPI Experi
ment: Measurements of Field and Waves Onboard
Interball Tail Mission, in: INTERBALL Mission and
Payl oad,
Ann. Geophys.
, 1997, vol. 15, no. 5, pp. 514–
527.
Sauvaud, J.A., Koperski, P., Beutier, T., et al., The ELEC
TRON Spectrometer Experiment: a Top Hat Spec
trometer for the Tail Probe in: Interball Mission and
Payl oad,
Ann. Geophys.
, 1997, vol. 15, no. 5, pp. 587–
595.
Schwartz, S.J., Paschmann, G., Sckopke, N., Bauer, T.M.,
Dunlop, M., Fazakerley, A.N., and Thomsen, M.F.,
Conditions for the Formation of Hot Flow Anomalies
at Earth’s Bow Shock,
J. Geophys. Res.
, 2000, vol. 105,
no. A6, pp. 12, 63912, 650.
Sibeck, D.G., Borodkova, N.L., Zastenker, G.N.,
Romanov, S.A., and Sauvaud, J.A., Gross Deforma
tion of the Dayside Magnetopause,
Geophys. Res. Lett.
,
1998, vol. 25, no. 4, pp. 453–456.
Sibeck, D.G., Borodkova, N.L., Schwartz, S.J., et al.,
Comprehensive Study of the Magnetospheric Response
to a Hot Flow Anomaly,
J. Geophys. Res.
, 1999, vol. 104,
no. A3, pp. 4577–4593.
Thomas, V.A., Winske, D., Thomsen, M.F., and Onsager, T.G.,
Hybrid Simulation of the Formation of a Hot Flow
Anomaly,
J. Geophys. Res.,
1991, vol. 96, no. A7, pp. 11,
62511, 632.
Vaisberg, O.L., Leibov, A.W., Avanov, L.A., et al., Complex
Plasma Analyzer SCA1, in
Interball Mission and Pay
load
,
RSAIKICNES, 1995, pp. 170–177.
Vaisberg. O.L., Waite. J.H., Avanov. L.A., Smirnov. V.N.,
Dempsey. D., Burch. J.L., and Skalsky. A.A., HFA
Like Signatures Observed with InterballTail Space
craft,
Proceeding of the Solar Wind 9 Conference
(Amer
ican Institute of Physics, Conference Proceedings),
1999, vol. 471, pp. 551–554.