COSMIC RAY ANISOTROPY AND INTERPLANETARY TRANSIENTS
DURING HIGH AMPLITUDE DAYS
RAJESH KUMAR MISHRA1, REKHA AGARWAL MISHRA2
1
Computer and I.T. Section, Tropical Forest Research Institute, P.O.: RFRC, Mandla Road, Jabalpur
(M.P.) India 482 021
2
Department of Physics, Govt. Model Science College (Autonomous),
Jabalpur (M.P.) 482 001, India
E-mail: [email protected] or [email protected]
Received January 14, 2008
Numerous studies dealt to find out the possible origin of the ‘high amplitude
wave trains’ of enhanced diurnal variation of cosmic rays and to develop a suitable
realistic theoretical model, which can explain the different harmonics in individual
days. The main objective of this work is to study the first three harmonics of high
amplitude wave trains of cosmic ray intensity over the period 1981–1994 for Deep
River neutron monitoring station and their association with different solar and
interplanetary transients. The amplitude of all the three harmonics (diurnal/semidiurnal/tri-diurnal) of HAE events significantly remains quite high and statistically
constant as compared to the annual average amplitude for majority of the events,
whereas the time of maximum significantly shifts towards earlier hours for first
harmonic and towards later hours for second and third harmonic as compared to the
co-rotational direction for majority of the events. The occurrence of HAE events is
dominant, when the value of interplanetary magnetic field (B) remains in the range
(4–10 nT); the product Ap × Dst remains negative only the ion density remains ≤ 20.
It is noteworthy that the occurrence of high amplitude day is dominant during solar
activity minimum years (1986–87) and solar activity maximum years (1991–92). The
amplitude as well as time of maximum of the cosmic ray diurnal anisotropy is
positively correlated to the sunspot numbers during HAEs.
Key words: cosmic ray, diurnal, semi-diurnal anisotropy, solar wind, interplanetary
magnetic field and geomagnetic activity.
1. INTRODUCTION
The various cosmic-ray intensity variations over different time-scales, the
modulation of the intensity by the evolving solar activity and the role of the
electromagnetic state of the interplanetary medium (otherwise called heliosphere)
can now be investigated as never before; these studies contribute immensely to
our knowledge of the solar neighborhood. An unusual class of consecutive days having
Rom. Journ. Phys., Vol. 54, Nos. 1–2, P. 165–185, Bucharest, 2009
166
Rajesh Kumar Mishra, Rekha Agarwal Mishra
2
abnormally high or low amplitudes in daily variation of cosmic rays have been
investigated several times earlier with explanation of sources and sinks in antigarden-hose and garden-hose directions [1–3]. The existence of high and low
amplitude anisotropic wave trains have been revealed through the long-term study
of cosmic ray intensity. Periods of unusually large amplitude often occur in trains
of several days. The average characteristics of cosmic-ray diurnal anisotropy are
adequately explained by the co-rotational concept [4–6]. This concept supports the
mean diurnal amplitude in space of 0.4% along the 1800 Hr direction using the
worldwide neutron monitor data. However, the observed day-to-day variation both in
amplitude and time of maximum, and the abnormally large amplitudes or abnormally
low amplitudes of consecutive days, cannot be explained in co-rotational terms.
Moreover, the maximum intensity of diurnal anisotropy has not appeared in the
direction of 1800 Hr, which is the nominal co-rotational phase [7–8].
The average daily variation of cosmic ray intensity generally consists of
diurnal variation, semi-diurnal variation and tri-diurnal variation. The amplitude of
the diurnal variation at a high / middle latitude station has been found to be of the
order of 0.3 to 0.4%, whereas the amplitudes of two higher harmonics is of the
order of 0.02% and 0.08% respectively [9]. The average characteristics have also
been found to vary with solar cycle, where the variation is much larger at higher
energies. A number of investigators have reported the short-term characteristics of
the daily variation, where they have selected continually occurring days of high
and low amplitudes of diurnal variation [3, 10, 11]. These results have pointed out
significant departures in the time of maximum as well as their association with
higher harmonics. Many workers [2, 12, 13] used a new concept for the
interpretation of the diurnal variation. McCracken et al. [14] first suggested the
extension of this new concept from the solar cosmic events to the observed diurnal
variation and theoretical formulation has provided by Forman and Gleeson [15].
Several workers have attempted to find the possible origin of the 'large amplitude
wave trains' of cosmic ray neutron intensity to develop a suitable realistic
theoretical model, which can explain the diurnal anisotropy in individual days.
Hashim and Thambyahpillai [16] and Rao et al. [2] have shown that the
enhanced diurnal variation of large amplitude events exhibits a maximum intensity
in space around the anti-garden-hose direction (2100 Hr) and a minimum intensity
in space around the garden-hose direction (0900 Hr). Kane [17] and Bussoletti [18]
have noticed that quite often an enhanced intensity is presented along the
corotational direction and it is not correlated with the garden-hose direction. The
diurnal anisotropy is well understood in terms of a convective-diffusive mechanism
[15]. Mavromichalaki [19] has observed that the enhanced diurnal variation was
caused by a source around 1600 Hr or by a sink at about 0400 Hr. It was pointed
out that this diurnal variation by the superposition of convection and field-aligned
diffusion due to an enhanced density gradient of ≈ 8% AU–1.
3
Cosmic ray anisotropy during high amplitude days
167
A systematic correlative study has been performed to establish the
relationship of cosmic ray anisotropy with solar activity parameters for low and
high cut-off rigidity neutron monitoring stations Kiel and Tokyo [20]. They
observed a positive correlation both for amplitude and phase of the diurnal
anisotropy with sunspot numbers. They also noticed that the semidiurnal phase is
positively correlated with sunspot numbers for both the stations, whereas,
semidiurnal amplitude shows small negative correlation with sunspot numbers.
Kane [21] reported that the recovery of cosmic ray intensity have followed two
distinct patterns, slow recovery during odd solar activity cycles 17, 19, 21 and fast
recovery during even solar activity cycles 18, 20. Kane [21] noticed that the
sunspot number pattern remains different in even cycles as compared to the odd
cycles in cycles 17–22, with step functions almost similar for sunspots and cosmic
rays in even cycles. According to Kane [21] the differential effects on cosmic rays
in alternate cycles could be related to sunspot activity.
2. DATA SOURCES AND ANALYSIS
The amplitude and phase of the harmonics of the daily variation in cosmic
ray intensity are derived by Fourier Analysis [22] by noting the hourly counting
rate of the observed cosmic ray intensity over a period of twenty-four hours.
The Fourier analysis yields reliable measures of the amplitude and phase on a
day-to-day basis, provided the time series is reasonably stationary. However, this
method cannot estimate the amplitude of the ambient anisotropy, which, for small
amplitudes, contributes to large uncertainties in the Fourier coefficients.
2.1. HARMONIC ANALYSIS
Time dependent harmonic function F(t) with 24 equidistant points in the
interval from t = 0 to t = 2π can be expressed in terms of Fourier series
24
F ( t ) = a0 + ∑ ( an cos ( nt ) + bn sin ( nt ) )
n =1
24
F ( t ) = a0 + ∑ rn cos ( nt − φn )
n =1
Where a0 is the mean value of F(t) for the time interval from t = 0 to 2π and an, bn
are the coefficients of nth harmonics, which can be expressed as follows:
a0 =
1 24
∑ ri
12 i =1
168
Rajesh Kumar Mishra, Rekha Agarwal Mishra
an =
bn =
4
1 24
∑ ri cos nt
12 i =1
1 24
∑ ri sin nt
12 i =1
The amplitude rn and phase φn of the nth harmonic are expressed as
rn = ( an2 + bn2 )
1/ 2
and
 an 

 bn 
φn = tan −1 
The daily variation of the cosmic ray intensity can be adequately represented
by the superposition of first, second, third and fourth harmonics as follows:
F(t) = a1 cos t + b1 sin t + a2 cos 2t + b2 sin 2t + a3 cos 3t + b3 sin 3t + a4 cos 4t + b4 cos 4t.
2.2. TREND CORRECTION
The daily variation in cosmic ray intensity is not strictly periodic. Thus, if the
number to be analysed represents bi-hourly (or hourly) means of cosmic ray intensity,
the mean for hour t0 (0th hour) will not, in general be the same as the mean for hour t24
(or 24th hour) this difference on account of secular changes, is allowed for in practice
by applying a correction known as trend correction, to each of the terms.
If y0 is the value of the ordinate at x = 0 (0th hour) and y12 is the value of the
ordinate at x = 2π (24th hour) then the trend corrected value for any hour is given
by the equation
( ±δ y ×k )
yk =yk
12
where k = 0, 1, 2, 3,…………………, 12
yk = uncorrected value
±δy = secular changes i.e. ±δy = y12 − y0
2.3. MODE OF ANALYSIS
The pressure corrected data of Deep River Neutron Monitor (NM) station has
been subjected to Fourier analysis for the period 1991–94 after applying the trend
correction. While performing the analysis of the data all those days are discarded
having more than three continuous hourly data missing.
5
Cosmic ray anisotropy during high amplitude days
169
2.4. CRITERIA FOR SELECTION OF EVENTS
Using the long-term plots of the cosmic ray intensity data as well as the
amplitude observed from the cosmic ray pressure corrected hourly neutron monitor
data using harmonic analysis the High amplitude wave train events (HAE) have
been selected on the basis of following criteria:
• High amplitude wave train events of continuous days have been selected when
the amplitude of diurnal anisotropy remains higher than 0.4% on each day of
the event for at least five or more days.
• In the selection of these types of events, special care has been taken, i.e. if
there occurred and pre-Forbush decreases or post-Forbush decrease before or
after the event or the event is in recovery phase or declining phase are not
considered.
On the basis of above selection criteria we have selected 38 high amplitude
wave train events during the period 1981–94. The hourly cosmic ray intensity data
for Deep River neutron monitoring station [Geog. Lat. 46.10 (Deg.), Geog. Long.
282.50 (Deg.), Vertical cut off rigidity 1.02 (GV)] has been investigated in the
present study.
Annual average values have been taken as a reference line for all the
respective HAE events.
3. RESULTS AND DISCUSSION
The amplitude (%) and Phase (Hr) of cosmic ray diurnal anisotropy of some
of the HAE events (July 17–21 1983 and Nov. 22–26 1989) for Deep River neutron
monitoring station along with the annual average value and the respective
statistical error bars (Ι) is shown in Fig. 1 (a, b). The diurnal amplitude A1 for HAE
as depicted in the upper panel remains significantly high and constant (∼0.6%) as
compared to the annual average diurnal amplitude (0.25%) and the direction of the
anisotropy i.e. phase (φ1) significantly remains in the direction of annual average
value (∼ 1600 Hr). It is also evident that the direction of diurnal anisotropy for both
HAE as well as annual average value found to shift towards earlier hours as
compared to the corotational direction (1800 Hr) throughout the event. However as
depicted in the lower panel the diurnal amplitude A1 for HAE again significantly
remains high (≥ 0.6%) as compared to the annual average diurnal amplitude
(0.37%) and the direction of the anisotropy i.e. phase (φ1) found to remains in the
corotational direction (∼ 1800 Hr), whereas it shifts towards later hours as
compared to the annual average anisotropy (1581 Hr) throughout the event.
The amplitude (%) and Phase (Hr) of cosmic ray semi-diurnal anisotropy of
some of the HAE events (July 17–21 1983 and Nov. 22–26 1989) for Deep River
neutron monitoring station along with the annual average value and the respective
Rajesh Kumar Mishra, Rekha Agarwal Mishra
170
6
statistical error bars (Ι) is shown in Fig. 2 (a, b). The semidiurnal amplitude (A2) as
shown in the upper panel for HAE remains high (≥0.8%) as compared to the annual
average amplitude (0.39%) throughout the event, whereas the phase (φ2) shifts
towards earlier hours for the earlier days of the event then it shifts towards later
hours as compared to the annual average phase. As seen in the lower panel the
semi-diurnal amplitude remains significantly high (≥0.2%) as compared to the
annual average amplitude (0.04%), whereas the semi-diurnal phase has no
significant trend as it frequently deviates towards earlier and later hours as
compared to the annual average phase (0575 Hr).
24
0.9
0.6
1(Hr)
A1 (%)
a
0.3
0.0
18
12
6
17 18 19 20 21
17
18
19
20
21
1.8
1.2
0.6
0.0
1(Hr)
A1 (%)
b
24
18
12
6
22 23 24 25 26
22 23 24 25 26
DAYS OF EVENT
DAYS OF EVENT
Fig. 1. – The amplitude (%) and phase (Hr) of diurnal anisotropy of HAE for the event of (a) July
17–21, 1983 and (b) Nov. 22–26, 1989 along with statistical error bars (I).
The amplitude (%) and Phase (Hr) of cosmic ray tri-diurnal anisotropy of
some of the HAE events (July 17–21, 1983 and Nov. 22–26, 1989) for Deep River
neutron monitoring station along with the annual average value and the respective
statistical error bars (Ι) is shown in Fig. 3 (a, b). The amplitude A3 of tri-diurnal
anisotropy as seen in the upper panel of HAE remains high (≥0.06%) as compared
to the annual average amplitude (0.02%) and the phase (φ3) has no definite trend as
it shifts towards earlier as well as later hours as compared to the annual average
phase. One can see from the lower panel that the amplitude A3 of tri-diurnal
anisotropy remains significantly high (≥0.06%) as compared to the annual average
amplitude (0.01%). The phase (φ3) significantly shifts towards earlier hours as
compared to the annual average phase (0716 Hr) throughout the event.
7
a
Cosmic ray anisotropy during12
high amplitude days
φ 2(Hr)
A2 (%)
0.2
0.1
0.0
171
6
0
17
18
19
20
21
17
18
19
20
21
b
12
φ 2(Hr)
A2 (%)
0.4
0.2
6
0.0
0
22
23
24
25
26
22
DAYS OF EVENT
23
24
25
26
DAYS OF EVENT
Fig. 2. – The amplitude (%) and phase (Hr) of semi-diurnal anisotropy of HAE for the event of (a)
July 17–21 and (b) Nov. 22–26, 1989 along with statistical error bars (I).
a
6
φ 3(Hr)
A3 (%)
0.2
0.1
4
2
0
0.0
17
18
19
20
21
17
18
19
20
21
22
23
24
25
26
b
12
0.2
φ 3(Hr)
A3(%)
0.3
0.1
6
0
0.0
22
23
24
25
DAYS OF EVENT
26
DAYS OF EVENT
Fig. 3. – The amplitude (%) and phase (Hr) of semi-diurnal anisotropy of HAE for the event of (a)
July 17–21 and (b) Nov. 22–26, 1989 along with statistical error bars (I).
172
Rajesh Kumar Mishra, Rekha Agarwal Mishra
8
We have rigorously studied all the 38 HAE events and found similar trends
as discussed above. From these findings it is found that amplitude A1 of the diurnal
anisotropy for HAE events significantly remains quite high and statistically
constant as compared to the annual average amplitude for majority of the events.
The time of maximum φ1 of the diurnal anisotropy of HAE significantly shifts
towards earlier hours as compared to the co-rotational direction and remains in the
direction of annual average anisotropy for majority of the events. However,
sometimes the diurnal phase φ1 remains in the corotational direction and shifts
towards earlier hours as compared to the annual average phase. These results are in
good agreement with the earlier trends reported by Mishra and Agrawal [23] for
highly enhanced daily variation. Using the CR intensity data for a period of over a
decade (i.e. 1980–1990) from various neutron-monitoring stations; located at
different latitudes for high amplitude anisotropic wave train events, Dubey et al.
[24] observed that the diurnal phase of CR anisotropy appears to be independent of
amplitude, as no synchronization in variations is seen between them for majority of
the HAE cases.
Further, the amplitude A2 of the semi-diurnal anisotropy of HAE events
significantly remains high and statistically constant as compared to the annual
average amplitude for majority of the events. The phase φ2 of semi-diurnal
component of HAE found to shifts towards later hours for majority of the events
either, or changing abruptly for rest of the events; whereas, Jadhav et al. [1] have
observed that the semi-diurnal component of phase has remained in a direction
normally expected during the period of 1966–73 for HAE. The long-term variation
in the amplitude and phase of the semi-diurnal anisotropy has been studied for the
epochs 1964–76 [25], 1968–79 [26] and 1968–84 [27]. All the three studies have
found an increase in the amplitude of the anisotropy during the years 1973–74,
when high-speed streams were frequent; the phase remained constant throughout
the epoch of study. Dubey et al. [24] pointed out that the phase of the semi-diurnal
anisotropy for HAE has been found to shift towards later hours for all the events
during 1980–90; which is in good agreement with our findings. Furthermore, the
amplitude A3 of the tri-diurnal anisotropy for HAE events remains significantly
high and constant as compared to the annual average amplitude.
The time of maximum φ3 of the tri-diurnal component of HAE has
significantly shifted to later hours as compared to the annual average anisotropy for
majority of the events either, or changing abruptly for rest of the events. According
to Kumar et al. [28], phase of tri-diurnal anisotropy is distributed evenly for high
amplitude events.
To study the overall behaviour of all the HAE events and annual average of
all days we have plotted the Figs. 4–6. The amplitude (%) and phase (Hr) of cosmic
ray diurnal/semi-diurnal/tri-diurnal anisotropy for all the HAEs along with the
respective yearly annual average value for all days and statistical error bars (І) is
plotted and shown in Fig. 4. As depicted in Fig. 4, amplitude (A1) of diurnal anisotropy
9
Cosmic ray anisotropy during high amplitude days
173
Event Av.
All Days Ann. Av.
1.2
A1 (%)
0.9
0.6
0.3
0
20
φ 1 (Hr)
16
12
8
4
0
81
83
84
85
88
90
92
92
93
94
Year
Fig. 4. – Amplitude and Phase of diurnal anisotropy for HAE along with all days annual average
values during 1981–94.
significantly remains high as compared to the annual average value for all days
throughout all the HAE events, whereas, the phase φ1 shifts towards earlier hours
as compared to the all days annual average value for majority of the HAE (for
24 out of 38 HAE). It is further noted that the direction of the diurnal anisotropy for both
Rajesh Kumar Mishra, Rekha Agarwal Mishra
174
10
Event Av.
All Days Ann. Av.
A2 (%)
0.3
0.2
0.1
0
φ 2 (Hr)
9
6
3
0
81
83
84
85
88
90
92
92
93
94
Year
Fig. 5. – Amplitude and Phase of semi-diurnal anisotropy for HAE along with all days annual average
values during 1981–94.
HAE and all days significantly shifts towards earlier hours as compared to the corotational/18-Hr direction throughout the period except for one event where it
shifts towards later hours. The amplitude A2 of the semi-diurnal anisotropy remains
significantly higher as compared to the all days annual average values for majority of
11
Cosmic ray anisotropy during high amplitude days
175
Event Av.
All Days Ann. Av.
0.08
A3 (%)
0.06
0.04
0.02
0.00
10
φ 3 (Hr)
8
6
4
2
0
81
83
84
85
88
90
92
92
93
94
Year
Fig. 6. – Amplitude and Phase of tri-diurnal anisotropy for HAE along with all days annual average
values during 1981–94.
the events (for 33 out of 38 HAE); whereas, the phase φ2 shifts towards later hours as
compared to the all days annual average value for majority of the HAE (for 23 out
of 38 HAE). The amplitude A3 of the tri-diurnal anisotropy remains significantly
higher for all HAEs as compared to the all day annual average value throughout the
176
Rajesh Kumar Mishra, Rekha Agarwal Mishra
12
period and the tri-diurnal time of maximum φ3 has a tendency to shifts towards
later hours as compared to all day annual average value for majority of the events
(for 25 out of 38 HAE). This shows that the amplitude of HAE for all the three
harmonics (diurnal/semi-diurnal/tri-diurnal) significantly remains high as compared to
the all day annual average amplitude, whereas the phase shifts towards earlier
hours for diurnal component and towards later hours for semi and tri-diurnal
component of HAE as compared to the all day annual average values.
The dependence of the IMF sense on solar diurnal variation has been studied
by many workers [29]. Annual mean amplitudes of the diurnal anisotropy observed
with Deep River NM for ‘away’ and ‘towards’ polarity of IMF for the period
1965–93, the amplitude for the ‘away’ group exceeds that for the ‘toward’ group
for the period 1965–68 and from 1969–73, the amplitude for the ‘toward’ group
exceeds that for the away group [30]. The effect of interplanetary magnetic field B
and its Bz component on cosmic ray intensity and geomagnetic field variations
have been examined by Singh et al. [31]. They observed that (1) B not less than
10 gamma (magnetic blobs) is a pre-requisite in producing cosmic ray intensity and
geomagnetic field variations of varying magnitudes; (2) the longer existence of
magnetic blobs on successive days produces larger decreases in cosmic ray
intensity and geomagnetic field; (3) the southward component (Bz) of IMF
generally gives rise to large Ap changes, though it is not effective in producing
cosmic ray intensity decreases. Alania et al. [37] studied the effects of the sector
structure of the IMF on the Galactic cosmic ray (GCR) anisotropy at solar
minimum by using Global Network neutron monitor data. They noticed that the
magnitude of the GCR anisotropy vector is larger in the positive IMF sector and
that the phase shifts towards early hours.
The amplitude (%) and phase (Hr) of cosmic ray diurnal/semi-diurnal/tridiurnal anisotropy along with the variation in associated value of interplanetary
magnetic field (B) and the regression line is plotted and shown in Figs. 7–9 for
all the HAE events. The amplitude A1 of the diurnal anisotropy is found to
slightly increase with the increase of B shows some positive correlation
(r = 0.17); whereas, the phase φ1 is to remain in a direction earlier then corotational/18-Hr direction statistically and found to slightly increase with the
increase of B showing a positive correlation (r = 0.25) as depicted in Fig. 7. The
amplitude A2 of semi-diurnal anisotropy increase with the increase of IMF B shows
positive correlation (0.35). The direction of the semi-diurnal anisotropy φ2 do not
show any significant trend due to large scattering of points and shows a very weal
positive correlation with B i.e. (r = 0.07) as depicted in the Fig. 8. The amplitude
A3 of tri-diurnal anisotropy for HAE events is observed to increase as the IMF B
increases showing a positive correlation (r = 0.27). The phase φ3 of the tri-diurnal
anisotropy found to slightly decrease with the increase of IMF B and shows weak
negative correlation (r = – 0.14) as shown in Fig. 8. Thus from the above findings
13
Cosmic ray anisotropy during high amplitude days
A1 (%)
0.8
177
r = 0.17
0.6
0.4
0.2
0
2
4
6
8
10
12
14
8
10
12
14
B
φ1
(Hr)
21
r = 0.25
18
15
12
0
2
4
6
B
Fig. 7. – Amplitude and phase of diurnal anisotropy along with the variation in associated value of
interplanetary magnetic field (B) and the regression line.
we can say that the amplitude of second and third harmonics and the direction of
first harmonics deviates with the increase of interplanetary magnetic field (B) and
shows positively correlates with B. It is also observed from these plots that the
occurrence of HAE events is dominant, when the value of IMF (B) remains in the
range (4–10 nT).
The complex behaviour of the diurnal amplitude and time of maximum and
its association with the Ap index on a long term and day-to-day basis have been
studied [32]. They reported that the relationship between the Ap index and the
diurnal vector is out of phase during 1991–95. On a long-term basis, the correlation
of diurnal variation with Ap index has been found to vary during the solar cycle
whereas on a short-term basis, the high Ap days are usually associated with higher
amplitudes with phase shifted to earlier hours.
Rajesh Kumar Mishra, Rekha Agarwal Mishra
178
A1 (%)
0.8
14
r = 0.17
0.6
0.4
0.2
0
2
4
6
8
10
12
14
8
10
12
14
B
φ1
(Hr)
21
r = 0.25
18
15
12
0
2
4
6
B
Fig. 8. – Amplitude and phase of semi-diurnal anisotropy along with the variation in associated value
of interplanetary magnetic field (B) and the regression line.
The amplitude (%) and phase (Hr) of cosmic ray diurnal/semi-diurnal/tridiurnal anisotropy along with the variation in associated value of (Ap × Dst) index
and the regression line is plotted and shown in Fig. 10 (a, b, c) for all the HAE
events. The amplitude A1 of the diurnal anisotropy for HAE events is observed to
slightly increase with the increase of (Ap × Dst) index from negative to positive
values showing some positive correlation (r = 0.19). The amplitude A2 of the semidiurnal anisotropy is found to decrease with the increase in the value of (Ap × Dst)
index showing good positive correlation (r = 0.40). The amplitude A3 of the tridiurnal anisotropy is observed to slightly decrease with the increase in the value of
(Ap × Dst) index showing a weak negative correlation (r = –0.09).
15
Cosmic ray anisotropy during high amplitude days
A3 (%)
0.10
179
r = 0.27
0.05
0.00
0
2
4
6
8
10
12
14
10
12
14
B
r = - 0.14
φ 3 (Hr)
9
6
3
0
0
2
4
6
8
B
Fig. 9. – Amplitude and phase of tri-diurnal anisotropy along with the variation in associated value of
interplanetary magnetic field (B) and the regression line.
The direction of the diurnal anisotropy φ1 found to remain in a direction
earlier than corotational direction for majority of the HAE events. The phase φ1
shows some positive correlation with (Ap × Dst) index (r = 0.19) as depicted in
Fig 10a. The semidiurnal phase of HAE φ2 found to slightly shifts towards earlier
hours with decrease of (Ap × Dst) index shows some negative correlation (r = –0.18),
whereas the tri-diurnal phase φ3 shows very weak negative correlation (r = –0.03) with
(Ap × Dst) index due to large scattering of points as seen in Fig. 10c. Thus it is noticed
that the amplitude of first and second harmonics and the direction of the first harmonic
varies with the variation in the value of (Ap × Dst) index, whereas the amplitude of the
second harmonic shows good negative correlation with (Ap × Dst) index. The third
harmonic (amplitude as well as direction) seems to remains unaffected with the
variation in the values of (Ap × Dst) index and shows very weak correlation. One
Rajesh Kumar Mishra, Rekha Agarwal Mishra
180
16
of the significant observations from these plots is that the (Ap × Dst) index
consistently remains negative for majority of the HAE events (for 26 out of
38 HAE). Thus we may conclude that the occurrence of HAE is dominant when
(Ap × Dst) index remains negative, which is never been reported earlier.
r = 0.19
1.2
DIU. PHASE (HR)
DIU. AMPLITUDE (%)
a
0.8
0.4
0.0
-400
-300
-200
-100
0
100
r = 0.19
24
18
12
6
-400
-300
Ap x Dst
-200
-100
0
100
0
100
0
100
Ap x Dst
0.3
r = – 0.40
0.2
0.1
0.0
-400
-300
-200
-100
0
100
SEMI-DIU. PHASE (Hr)
SEMI-DIU. AMP. (%)
b
r = – 0.18
12
6
0
-400
-300
-200
-100
Ap x Dst
Ap x Dst
r = – 0.09
TRI-DIU. PHASE (Hr)
TRI-DIU. AMPLITUDE (%)
c
0.08
0.04
0.00
-400
-300
-200
-100
Ap x Dst
0
100
r = – 0.02
8
4
0
-400
-300
-200
-100
Ap x Dst
Fig. 10. – Amplitude and Phase of the (a) diurnal, (b) semi-diurnal and (c) tri-diurnal anisotropy for
each HAE along with (Ap × Dst) index and regression line.
17
Cosmic ray anisotropy during high amplitude days
181
DIU. PHASE (Hr)
r = 0.14
1.2
0.8
0.4
0.0
0
10
SEMI-DIU. AMP. (%)
0.2
0.1
0.0
0
10
12
6
0
10
20
r = – 0.03
12
6
0
0
Ion density
TRI-DIU. PHASE (Hr)
TRI-DIU. AMPLITUDE
(%)
r = 0.13
0.04
0.00
0
10
Ion density
20
10
20
Ion density
c
0.08
20
Ion Density
b
r = 0.05
0.3
18
20
Ion density
r = 0.09
24
SEMI-DIU. PHASE (Hr)
DIU. AMPLITUDE (%)
a
r = – 0.34
8
4
0
0
10
20
Ion density
Fig. 11. – Amplitude and Phase of the (a) diurnal, (b) semi-diurnal and (c) tri-diurnal anisotropy for each
HAE along with ion density and regression line.
The amplitude (%) and phase (Hr) of cosmic ray diurnal/semi-diurnal/tridiurnal anisotropy along with the variation in associated value of ion density and
the regression line is plotted and shown in Fig. 11 (a, b, c) for all the HAE events.
One can see from these figures that the diurnal amplitude A1 is found to slightly
Rajesh Kumar Mishra, Rekha Agarwal Mishra
182
18
increase with the increase of ion density showing a positive correlation (r = 0.14).
The semi-diurnal amplitude A2 do not show significant trend and have a very weak
positive correlation with ion density (r = 0.05). The tri-diurnal amplitude A3 found
to slightly increase with the increase of ion density shows some positive correlation
(r = 0.13) with ion density.
The weak correlation has been observed with ion density for diurnal and semidiurnal phase (φ1 and φ2) of HAE events (0.09–0.03) as seen in Fig. 11a, b. However,
the tri-diurnal phase φ3 is found to decrease with the increase in the value of ion
density showing negative correlation (–0.34). It is also noticed that the direction of
the diurnal anisotropy φ1 found to remain in a direction earlier than corotational
direction for majority of the HAE events. Thus we observe that the amplitude as well
as direction of the first harmonic and amplitude of second harmonic shows
deviations with the increase of ion density. However the direction of the diurnal
anisotropy φ1 found to remain in a direction earlier than corotational direction for
majority of the HAE events. Neither the amplitude nor the direction of second
harmonic seems to depend upon the ion density and shows very weak correlation.
The direction of the third harmonic decreases gradually with the increase of ion
density and shows good negative correlation. It is also observed from these plots that
all the HAE events occurred when the ion density remains ≤ 20.
FREQUENCY OF OCCURRENCE (DAYS)
80
60
40
20
0
0-20 20-40 40-60 60-80
80100
100120
120140
140160
160180
180200
200220
220240
SUNSPOT NUMBERS
Fig. 12. – The frequency histogram of the solar wind velocity for all HAEs.
240260
19
Cosmic ray anisotropy during high amplitude days
183
The frequency histogram of sunspot numbers for all HAEs has been plotted
in Fig. 12. It is quite observable from the Fig that the majority of the HAE events
have occurred when the sunspot numbers lies in the interval 0–120. One can see
from the plot that very few events have occurred when the sunspot numbers
remains ≥ 200. The frequency distribution of high amplitude days for each year is
plotted in Fig. 13. The figure clearly illustrates that the distribution of high
amplitude days presents a very interesting picture. We observe that the occurrence
of high amplitude day is dominant during 1986–87 solar activity minimum year
and 1991–92 solar activity maximum year. We have also calculated the correlation
coefficients between the annual average amplitude and time of maximum of
cosmic ray diurnal anisotropy for HAEs and annual average sunspot numbers
during 1981–94. A good positive correlation is obtained for the diurnal amplitude
Vs sunspot numbers (i.e. 0.53) and time of maximum Vs sunspot numbers (i.e.
0.50). Thus we may conclude that the amplitude as well as time of maximum of the
cosmic ray diurnal anisotropy is positively correlated to the sunspot numbers
during HAEs. This significantly confirms the earlier results reported by Tiwari et
al. [20] where they observed a positive correlation both for amplitude and phase of
the diurnal anisotropy with sunspot numbers
1993
3%
1994
6%
1981 1983
3%
3%
1984
3%
1985
3%
1992
11%
1986
25%
1991
22%
1990
3%
1988
7%
1987
11%
Fig. 13. – The frequency distribution of high amplitude days during 1981–94.
184
Rajesh Kumar Mishra, Rekha Agarwal Mishra
20
4. CONCLUSIONS
On the basis of above investigations following important conclusions may
be drawn:
1. The amplitude of the diurnal anisotropy for HAE events significantly remains
quite high and statistically constant as compared to the annual average
amplitude for majority of the events, whereas the time of maximum
significantly shifts towards earlier hours as compared to the co-rotational
direction and remains in the direction of annual average anisotropy for majority
of the events. However, sometimes the diurnal phase remains in the
corotational direction and shifts towards earlier hours as compared to the
annual average phase.
2. The amplitude of the semi/tri-diurnal anisotropy of HAE events significantly
remains high and statistically constant as compared to the annual average
amplitude for majority of the events, whereas the phase found to shifts towards
later hours for majority of the events either, or changing abruptly for rest of the
events.
3. The amplitude of second and third harmonics and the direction of first
harmonics deviates with the increase of interplanetary magnetic field (B) and
shows positively correlated with B. It is also noteworthy that the occurrence of
HAE events is dominant, when the value of IMF (B) remains in the range (4–
10 nT).
4. The amplitude of first and second harmonics and the direction of the first
harmonic deviates with the increase in the value of (Ap × Dst) index, whereas
the amplitude of the second harmonic shows good negative correlation with
(Ap × Dst) index. The occurrence of HAE is dominant when (Ap × Dst) index
remains negative, which is never been reported earlier.
5. The amplitude as well as direction of the first harmonic and amplitude of
second harmonic shows deviations with the increase of ion density. The
direction of the third harmonic decreases gradually with the increase of ion
density and shows good negative correlation. It is also observed that all the
HAE events occurred when the ion density remains ≤ 20.
6. The occurrence of high amplitude day is dominant during 1986–87 solar
activity minimum year and 1991–92 solar activity maximum year. The
amplitude as well as time of maximum of the cosmic ray diurnal anisotropy is
positively correlated to the sunspot numbers during HAEs.
Acknowledgements. The authors are indebted to various experimental groups, in particular,
Prof. Margret D. Wilson, Prof. K. Nagashima, Miss. Aoi Inoue and Prof. J.H. King for providing the
data. We also acknowledge the use of NSSDC OMNI database and NGDC geophysical data.
21
Cosmic ray anisotropy during high amplitude days
185
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