Arab Journal of Nuclear Sciences and Applications16) 80 - 2017... · M. A. EL- Borie and A. Hamdy Arab J. Nucl. Sci. Appl, Vol 51, 1, 152-167 (2018) 152 A Correlative Study between

M. A. EL- Borie and A. Hamdy Arab J. Nucl. Sci. Appl, Vol 51, 1, 152-167 (2018)

152

A Correlative Study between Heliospheric Current Sheet Tilts,

Cosmic Ray Intensities and Solar Activity Parameters

M. A. EL- Borie1 and A. Hamdy2 (1) Physics Department, Faculty of Science, Alexandria University, Egypt

(2) Physics Department, Faculty of Science, Cairo University, Egypt

Received: 15/5/2017 Accepted: 16/7/2017

ABSTRACT

The correlations between the tilt angle (TA) of heliospheric current sheet

(HCS) and the cosmic ray intensity (CRI), strength (B) of the interplanetary

magnetic field (IMF), sunspot number (SSN), solar plasma speed (SWS) and density

( n ) have been studied before and after the reversal of IMF polarities. High

sensitivity of the CRI of different rigidities to changes in the TA of HCS is observed

during the qA < 0 epoch (when the IMF toward the Sun) as compared to the qA > 0

epoch (when IMF away from the Sun). The results of the present study are

consistent with the drift model of cosmic rays, showing that the spectra of drift

particles were harder after the reversal of IMF polarity state in (1999/2000).

The reversal of IMF polarity state from (qA > 0 state to qA < 0 state) has a

great effect on the rigidity-tilts dependence. The modulation of the lower energy

particles of (median rigidity Rm < 22 GV) is more pronounced throughout qA < 0

epoch than that of qA > 0 epoch. The rate of sensitivity/modulation of CRIs to the

HCS tilts is higher throughout the minimum solar activity years as compared to the

maximum solar activity period.

Keywords: Cosmic rays – Interplanetary magnetic field – Solar Activity – Solar wind –

Heliospheric current sheet

INTRODUCTION

The TA of the HCS plays a dominant role in the modulation of galactic cosmic rays.

The highly inverse correlation between the cosmic ray intensities and the HCS tilts was more

pronounced during the qA < 0 epochs as compared to the qA > 0 epochs (1 - 6).

In contrast, there is a highly positive correlation between the sunspot numbers and the tilts of

HCS (6 - 8). The polarity state of the solar magnetic field reverses at the solar maximum activity, nearly

every (11- year). The strength of the interplanetary magnetic field (IMF) and the sunspot number are

highly correlated (9). The behavior of the TA of HCS exhibits roughly the same variations over all

solar activity cycles in accord with idea of the cyclic behavior. This behavior depends only on the

phase of the solar activity cycle (SAC), not on its strength. Moreover the ascending and maximum

phases of the HCS TA cycle are shorter and faster than that during the descending phase (10 , 11).

The solar wind speed increases with distance from the HCS. When the HCS is inclined and the

spacecraft which are in the ecliptic plane spends a greater fraction of time away from the neutral sheet,

and then experiences higher solar wind speeds, this leads to observing the correlation between the

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Arab Journal of Nuclear Sciences and Applications

Vol 51, 1, (152-167) 2018


153

solar wind speed and the TA of HCS (12). During the time of minimum solar activity, the lines of solar

magnetic field are mostly of an open type and generate a fast solar wind. Therefore, the fast solar wind

is always associated with small proton density (13). On the other hand, during the period of maximum

solar activity, closed lines of solar magnetic field and slow solar wind dominate. Therefore, the slow

solar wind is associated with relatively high proton density (14, 15).

On the other hand, the solar minimum of solar activity cycle 23 (2006 - 2009) has been

unusually long and deep, in comparison with the previous three solar minima. The recent solar

minimum has the smallest sunspot number, as well as the lowest and the least dense solar wind and the

weakest IMF (16). Furthermore, high cosmic ray intensities were resulted from the reduction in IMF

rather than from the reduction in the TA of HCS in 2009 during the recent solar minimum (17).

The aim of the present work is to study the relationship between the TA of HCS and the CRIs,

as well as some solar parameters: (B of the IMF, SSN, SWS and n) for different geomagnetic epochs:

1981-1988 (qA < 0), 1991-1998 (qA > 0) and 2001-2008 (qA < 0).

The sensitivity of CRI of different median rigidities (Rm: 16 GV - 33 GV) to changes in the TA

has been studied before and after the reversals of IMF polarity state during three considered epochs.

DATA RESOURCES

The 27-day measurements of solar/interplanetary parameters: sunspot number (RZ), solar wind

speed (SWS) , solar wind plasma density (n) and strength (B) of IMF have been obtained from the

Omni-web data explorer via <omniweb.gsfc.nassa.gov/from/dx1.htm>. The measurements of the

heliospheric current sheet tilts have been obtained via the website <Wso.stanford.edu/tilts.html>. In

addition, the 27-day counts of the CRIs with different median rigidities have been obtained via

<http://cr0.izmiran.rssi.ru/common/links.htm>.

The details of the cosmic ray stations are displayed in Table (1).

Table (1): Details of the selected NM stations ; cut-off (Ro) and median (Rm) rigidities, geographical

locations and the altitude from the sea level

Stations Of

Cosmic Rays

Rigidity Geographical Details

Alt.

(m)

Ro

(GV)

Rm

(GV)

Lat.

(deg.)

Long.

(deg.)

Apatity 0.57 16 67.55 33.33 177

Kiel 2.36 18 54.3 10.1 54

Hermanus 4.44 20 -34.43 19.23 26

Rome 6.32 22 41.9 12.52 60

Tbilisi 6.73 23 41.43 44.48 510

Potchefstroom 6.98 25 -26.7 27.09 1351

Tsumeb 9.12 27 -19.2 17.58 1240

Huancayo /

Haleakala

12.91 33 20.72

-12.03

-156.25

-75.33

3040

3400

http://cr0.izmiran.rssi.ru/common/links.htm


154

RESULTS AND DISCUSSION

1- Correlation between HCS Tilts and some solar parameters

According to the cosmic ray drift theory, when the polarity state of the heliospher is (qA > 0),

charged particles are drifted inward from the polar regions to the equatorial plane and out along the

heliospheric current sheet HCS. So charged particles are less affected by the drifts associated with the

changes in the TA of HCS. On the other side, when the polarity state of the heliospher is (qA < 0), the

charged particles reach the inner heliosphere by drifting in along the sheet with a maximum intensity.

The intensity of the particles decreases with distance away from the sheet leading to cosmic ray

maxima. Therefore, the charged particles are more affected by the drifts associated with the changes

in the TA of HCS (18). It is well now know that, during the positive polarity state of solar magnetic

field (qA > 0), the IMF directs away from the Sun’s north (above the HCS) toward the Sun’s south

(below the HCS). In contrast, the IMF directs away from the Sun’s south below the HCS toward the

Sun’s north above the HCS During the negative polarity state of solar magnetic field (qA < 0) (19).

Near the solar maximum activity, the polarity state of the heliosphere is reversed when the HCS

tilts become greater than 70o (closer to 90o). The charged particles can encounter the fields in polar

regions of both positive and negative polarities. So, the charged particles drift sometimes inward and

sometimes outward and there is no response to changes in the tilt angle of HCS (20). Therefore, these

years have omitted from the present study because there is no regular pattern can describe the

complex structure of HCS around the years of IMF polarity reversal.

The relative sunspot number (Rz) is an index of solar activity of the entire visible disk of the

Sun. It is computed by equation (I). Where G is the number of sunspot groups on the solar disk, S is

the total number of individual spots in all the sunspot groups and K is the variable scaling factor

(usually < 1) which accounts for observing conditions (21). On the other hand, there is a highly negative

correlation between SSN and CRI (22).

Rz = K (10 G + S) (I)

The solar wind (SW) is divided into two components, slow and fast solar wind. A slow solar

wind is originated from a region around the Sun's equatorial belt and its velocity is about (400

km/sec). In addition, a fast solar wind is originated from coronal holes which are funnel-like regions of

open field lines in the sun's magnetic field and the range of its velocity is about (750 - 1800 km/sec) (23). The fast solar wind is always associated with small plasma density while the slow solar wind is

associated with relatively high plasma density (13 - 15). On the other hand, the dynamic pressure (P) of

the solar wind is a function of solar wind speed (v) in km/sec and its density (n) in particles/cm3 (24).

The dynamic pressure of the solar wind is about (1 - 6) nPa , and can be computed by the equation (II).

P = 1.6726 × 10 - 6

nv2 (II)

The linear correlations between tilt angle (TA) of the HCS and sunspot number (Rz), strength

(B) of the interplanetary magnetic field (IMF), solar wind speed (SWS) and density (n) are displayed

in Figures (1, 2, 3 and 4), respectively. This analysis is applied to three considered periods; 1981-

1988 (qA < 0), 1991-1998 (qA > 0) and 2001-2008 (qA < 0) and the correlation coefficient ( r ) is

added calculated for each epoch.

Figure (1) shows a highly positive correlation between the TA of HCS and the sunspot number

(SSN). The correlation coefficients are (87.1% , 85.6% and 77.8%) during three periods; 1981-1988

(qA < 0),1991-1998 (qA > 0) and 2001-2008 (qA < 0), respectively. Therefore, the correlation between

the TA of HCS and the SSN is nearly independent on the IMF polarity state. The slope of fitted line

(i.e. the sensitivity of Rz to the TA of HCS) throughout the period 2001-2008 ( 4.1791) is greater

than that of other periods. Therefore, the correlation between the TA of HCS and the SSN became

more pronounced in period 2001-2008.

http://en.wikipedia.org/wiki/Coronal_hole

http://en.wikipedia.org/wiki/Magnetic_field

http://en.wikipedia.org/wiki/Dynamic_pressure

http://en.wikipedia.org/wiki/Function_%28mathematics%29




155

The weak correlation between the TA of HCS and the strength (B) of IMF is presented in Figure

(2). The correlation coefficients have fairly small values (- 24.6 % , 11.3 % and 25.7 %) during three

periods; 1981-1988 (qA < 0), 1991-1998 (qA > 0) and 2001-2008 (qA < 0), respectively. Therefore,

the correlation between the TA of HCS and the strength of IMF is greater in the qA < 0 epochs as

compared to the qA > 0 epochs and depends on the IMF polarity state.

Fig. (1): The TA of HCS versus the sunspot number throughout three IMF polarity epochs; 1981-

1988 (qA < 0) , 1991-1998 (qA > 0) and 2001-2008 (qA < 0). Carrington rotation

numbers (CNs) are noted for each epoch

1981 - 1988 ( qA < 0 ) , CNs : 1704 - 1810

y = 3.6882 x - 41.833

r = 0.871

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70

TA of HCS ( Degree )

Su

nsp

ot

Nu

mb

er

1991 - 1998 ( qA > 0 ) , CNs : 1838 - 1944

y = 3.7176 x - 45.764

r = 0.856

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70


Su

nsp

ot

Nu

mb

er

2001 - 2008 ( qA < 0 ) , CNs : 1972 - 2078

y = 4.1791 x - 113.93

r = 0.778

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70


Su

nsp

ot

Nu

mb

er


156

Fig. (2): The TA of HCS versus the strength (B) of the IMF throughout three IMF polarity epochs;

1981-1988 (qA < 0) , 1991-1998 (qA > 0) and 2001-2008 (qA < 0). Carrington rotation

numbers (CNs) are noted for each epoch

Figure (3) displays a moderate correlation between the TA of HCS and the SWS. Moreover, the

regression coefficients were positives (25.1% and 35.6%) during the two periods; 1991-1998 (qA > 0)

and 2001-2008 (qA < 0), respectively, as well as a negative one (- 32.3 %) in the period 1981-1984

(qA < 0). The slope for the period 2001-2008 ( 1.56) was greater than other periods. Therefore, the

correlation between the TA of HCS and the SWS depends on the IMF polarity state. The SWS

decreased from ( 520 km/sec) to ( 420 km/sec) throughout the descending phase of SAC 21 (1981

- 1984). In addition, the TA of HCS increased from 30o to 60o during the same period (7).

1981 - 1988 ( qA < 0 ) , CNs : 1704 - 1810

y = - 0.0109 x + 1.7693

r = - 0.246

0

1

2

3

4

5

0 10 20 30 40 50 60 70


B (

n T

)

1991 - 1998 ( qA > 0 ) , CNs : 1838 - 1944

y = 0.0053 x + 1.1014

r = 0.113

0

1

2

3

4

5

0 10 20 30 40 50 60 70


B (

n T

)

2001 - 2008 ( qA < 0 ) , CNs : 1972 - 2078

y = 0.0098 x + 0.0659

r = 0.257

0

1

2

3

4

5

0 10 20 30 40 50 60 70


B (

n T

)


157

Figure (4) shows a negative and weak correlation between the TA of HCS and the solar plasma

density. The correlation coefficients have small values (- 9.20 % and - 4.60 %) during the two periods;

1991-1998 (qA > 0) and 2001-2008 (qA < 0), respectively. The magnitude of regression coefficient

was greater (r = - 25.2 %) during the period 1981-1988 (qA < 0). The slope of the fitted line for three

periods; 1981-1989, 1991-1998 and 2001-2008 has small magnitudes (- 0.029, - 0.010 and - 0.004)

respectively.

Fig. (3): The TA of HCS versus the solar wind speed throughout three IMF polarity epochs; 1981-

1984 (qA < 0) , 1991-1998 (qA > 0) and 2001-2008 (qA < 0). Carrington rotation numbers

(CNs) are noted for each epoch

1981 - 1984 ( qA < 0 ) , CNs : 1704 - 1756

y = -1.2705 x + 523.02

r = - 0.323

300

350

400

450

500

550

600

650

700

0 10 20 30 40 50 60 70


So

lar W

ind

Sp

eed

( K

m /

sec

)

1991 - 1998 ( qA > 0 ) , CNs : 1838 - 1944

y = 0.9411 x + 407.67

r = 0.251

300

350

400

450

500

550

600

650

700

0 10 20 30 40 50 60 70


So

lar W

ind

Sp

eed

( K

m /

sec

)

2001 - 2008 ( qA < 0 ) , CNs : 1972 - 2078

y = 1.5589 x + 388.31

r = 0.356

300

350

400

450

500

550

600

650

700

0 10 20 30 40 50 60 70


Sola

r W

ind

Sp

eed

( K

m /

sec

)


158

Fig.(4) The TA of HCS versus the proton density throughout three IMF polarity epochs; 1981-1988

(qA < 0) , 1991-1998 (qA > 0) and 2001-2008 (qA < 0). Carrington rotation numbers (CNs) are noted

for each epoch

1981 - 1988 ( qA < 0 ) , CNs : 1704 - 1810

y = - 0.0295 x + 9.3795

r = - 0.252

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70


Pro

ton

Den

sity

( c

m -3

)

1991 - 1998 ( qA > 0 ) , CNs : 1838 - 1944

y = - 0.0102 x + 8.7769

r = - 0.092

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70


Pro

ton

Den

sity

( c

m -3

)

2001 - 2008 ( qA > 0 ) , CNs : 1972 - 2078

y = -0.004 x + 6.0488

r = 0.046

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70


Proto

n D

en

sity

( c

m -3

)


159

2 - Correlation between HCS Tilts and CRIs with different rigidities

In this part, the regression analysis between the HCS tilts and cosmic ray intensities CRIs of

different median rigidities (Rm : 16 - 33 GV) has been studied. Scatter plots for the HCS tilts versus

the CRIs have been done. Top plots (4a and 4b) display the sensitivity correlation of the CRIs detected

at Apatity, Hermanus, Tsumeb and Potchefstroom with HCS inclinations for the period 1981-1988 (qA

< 0). The middle plots show the correlation for the period 1991-1998 (qA > 0), while the bottom plots

indicate the correlation for the period 2001-2008 (qA < 0). On the other hand, the slope of straight

line of the best-fit obtained from the regression analysis is considered as a measure for the sensitivity of

CRIs to the observed changes in the HCS tilts. The anatomized periods, Carrington rotation numbers

(CNs), the regression coefficient (r) and the sensitivity ( a ) of CRIs to changes in HCS tilts are noted

in each plot. The average value of r was found to be( - 0.86 and - 0.89) for the two periods 1981-

1988 and 2001-2008, respectively, however in the period 1991-1998, the average value was found to

be(r - 0.76) .

Table (2): The correlations between CRIs of different median rigidities (Rm) with the tilt angles of the

warped HCS throughout the three periods of different IMF polarity states: 1981-1988 (qA

< 0), 1991-1998 (qA > 0) and 2001-2008 (qA < 0), respectively

NM Stations

Median

rigidities

Rm (GV)

Correlation between CRI and TA of HCS

1981- 1988

qA < 0

1991 - 1998

qA > 0

2001 - 2008

qA < 0

Apatity 16 - 0.88 - 0.72 - 0.91

Kiel 18 - 0.88 - 0.87 - 0.91

Hermanus 20 - 0.82 - 0.78 - 0.90

Rome 22 - 0.86 - 0.77 - 0.90

Tbilisi 23 - 0.82 - 0.73 - 0.80

Potchefstroom 25 - 0.88 - 0.74 - 0.91

Tsumeb 27 - 0.85 - 0.74 - 0.91

Huancayo / Haleakala 33 - 0.85 - 0.74 - 0.87


160

Fig.( 4.a): Scatter plots and best fit lines, between HCS tilts and GCRIs detected at Hermanus NM in

(left panels) and Apatity NM in (right panels) throughout the three periods of the different

IMF polarity states: 1981-1988 (qA < 0), 1991-1998 (qA > 0) and 2001-2008 (qA < 0),

respectively

y = -9.2012x + 4539.9

3500

3750

4000

4250

4500

4750

5000

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

10

0 )

r = - 0.82

a = - 0.203 % / deg

Hermanus NM 1981 - 1988 (CNs: 1704 - 1810)

Ro = 4.44 GV qA < 0

y = -21.371x + 8019.9

6000

6500

7000

7500

8000

8500

9000

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

12

8 )

r = - 0.88

a = - 0.266 % / deg

Apatity NM 1981 - 1988 (CNs: 1704 - 1810)

Ro = 0.57 GV qA < 0

y = -9.4679x + 4565.3

3500

3750

4000

4250

4500

4750

5000

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

10

0 )

r = - 0.78

a = - 0.207 % / deg

Hermanus NM 1991 - 1998 (CNs: 1838 - 1944)

Ro = 4.44 GV qA > 0

y = -23.742x + 8217.1

6000

6500

7000

7500

8000

8500

9000

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

12

8 )

r = - 0.75

a = - 0.289 % / deg

Apatity NM 1991 - 1998 (CNs: 1838 - 1944)

Ro = 0.57 GV qA > 0

y = -14.756x + 4883.6

R2 = 0.82

3500

3750

4000

4250

4500

4750

5000

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

10

0 )

r = - 0.90

a = - 0.302 % / deg

Hermanus NM 2001 - 2008 (CNs: 1972 - 2078)

Ro = 4.44 GV qA < 0

y = -35.317x + 8948.1

6000

6500

7000

7500

8000

8500

9000

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

12

8 )

r = - 0.91

a = - 0.395 % / deg

Apatity NM 2001 - 2008 (CNs: 1972 - 2078)

Ro = 0.57 GV qA < 0


161

`

Fig. (4b): Scatter plots and best fit lines, between HCS tilts and CRIs detected at Tsumeb NM in (left

panels) and Potchefstroom NM in (right panels) throughout three periods of the different

IMF polarity states: 1981-1988 (qA < 0), 1991-1998 (qA > 0) and 2001-2008 (qA < 0),

respectively. Carrington rotation numbers (CNs) are noted for each epoch

y = -17.599x + 12254

10000

10500

11000

11500

12000

12500

13000

0 10 20 30 40 50 60 70


CR

I (

Co

un

ts /

hr

/ 1

00

)

r = - 0.85

a = - 0.151 % / deg

Tsumeb NM 1981 - 1988 (CNs: 1704 - 1810)

Ro = 9.12 GV qA < 0

y = -3.5416x + 2119.4

1700

1800

1900

2000

2100

2200

0 10 20 30 40 50 60 70


CR

I

( C

ou

nts

/ h

r /

10

0 )

r = - 0.88

a = - 0.167 % / deg

Potch NM 1981 - 1988 (CNs: 1704 - 1810)

Ro = 6.98 GV qA < 0

y = -15.568x + 12160

10000

10500

11000

11500

12000

12500

13000

0 10 20 30 40 50 60 70


CR

I (

Co

un

ts /

hr

/ 1

00

)

r = - 0.74

a = - 0.128 % / deg

Tsumeb NM 1991 - 1998 (CNs: 1838 - 1944)

Ro = 9.12 GV qA > 0

y = -3.4141x + 2118

1600

1700

1800

1900

2000

2100

2200

0 10 20 30 40 50 60 70


CR

I (

Co

un

ts /

hr

/ 1

00

)

r = - 0.74

a = - 0.161 % / deg

Potch NM 1991 - 1998 (CNs: 1838 - 1944)

Ro = 6.98 GV qA > 0

y = -24.424x + 12762

10000

10500

11000

11500

12000

12500

13000

0 10 20 30 40 50 60 70


CR

I (

Co

un

ts /

hr

/ 1

00

)

r = - 0.91

a = - 0.191 % / deg

Tsumeb NM 2001 - 2008 (CNs: 1972 - 2078)

Ro = 9.12 GV qA < 0

y = -5.5053x + 2256.4

1600

1700

1800

1900

2000

2100

2200

0 10 20 30 40 50 60 70


CR

I (

Co

un

ts /

hr

/ 1

00

)

r = - 0.91

a = - 0.244 % / deg

Potch NM 2001 - 2008 (CNs: 1972 - 2078)

Ro = 6.98 GV qA < 0


162

3 - Particle Rigidities - HCS Tilts dependence during different IMF polarities (qA > 0 and

qA < 0)

High sensitivity of CRI to changes in the TA of HCS is observed during qA < 0 epochs as

compared to qA > 0 epochs (18). This sensitivity is rigidity-dependent and follows the power-type law.

The slope of the regression line is a measure of the sensitivity of CRIs to changes in the HCS tilts.

Table (3) shows the sensitivities CRIs of different median rigidities (Rm) to the HCS inclinations. The

value of Rm ranges from 16 GV for Apatity to 33 GV for Huancayo / Haleakala NMs.

Table (3): The sensitivities (% / deg) of CRIs of different median rigidities (Rm) to the tilt angles of

HCS throughout the three periods of different IMF polarity states: 1981-1988 (qA < 0),

1991-1998 (qA > 0) and 2001-2008 (qA < 0), respectively

Figure (5) displays the sensitivity of CRIs to the HCS tilt angles (TA 70°) versus the

median response rigidities (Rm). Plots show the power fit for the measurements during three considered

epochs gave ( R-1.00 , R-1.36 and R-1.49 ), respectively. The present results are in consistence with the drift

model of cosmic rays and indicated the spectra of particles drift were harder after the reversals of the

IMF polarity state in 1999/2000 than that before the reversal. Therefore, the reversal of IMF polarity

state from (qA > 0) to (qA < 0) has a great effect on the rigidity-tilts dependence.

a = 4.04 R

-

1.00

0.0

0.1

0.2

0.3

0.4

14 16 18 20 22 24 26 28 30 32 34

Median Rigidity ( GV )

Slo

pe

Of

Reg

ress

ion

Lin

e (

% /

deg

)

1981 - 1988 (qA < 0) , CNs : 1704 -1704 )

NM Stations

Median

rigidities

Rm (GV)

Sensitivities of CRIs to HCS Tilts (% / deg)

1981- 1988

qA < 0

1991 - 1998

qA > 0

2001 - 2008

qA < 0

Apatity 16 - 0.266 - 0.289 - 0.395

Kiel 18 - 0.242 - 0.253 - 0.343

Hermanus 20 - 0.203 - 0.207 - 0.302

Rome 22 - 0.153 - 0.179 - 0.216

Tbilisi 23 - 0.185 - 0.175 - 0.175

Potchefstroom 25 - 0.167 - 0.161 - 0.244

Tsumeb 27 - 0.144 - 0.127 - 0.191

Huancayo / Haleakala 33 - 0.134 - 0.114 - 0.131


163

Fig. (5): The sensitivities of CRIs with different Rm to HCS tilts throughout the three periods of

different IMF polarity states: 1981-1988 (qA < 0), 1991-1998 (qA > 0) and 2001-2008 (qA <

0), respectively

The sensitivity of CRs to the HCS tilts increased for particles of low energy and the rate of

increasing is more effective in qA < 0 epoch. This confirms that the modulation for lower energy

particles (Rm < 22 GV) is more pronounced during qA < 0 epoch than that of qA > 0.

To study the variations of energy spectrum of CRIs caused by the change in HCS tilts, the tilts

of HCS have been divided into three groups based on the computed HCS tilts (the mean ). Group I

(low tilt angles; 0° < TA ≤ 30°), group II (medium tilts; 30° < TA ≤ 50°) and group III (high tilts; 50°

< TA ≤ 70°). Group I is consistent with the years of minimum solar activity, group II is in agreement

with the times of ascending and descending phases of the solar activity cycles, and group III refers to

the time near solar maximum activity. Figures (6) & (7) display the sensitivities of CRIs to the HCS

tilts versus the median particle rigidities for different IMF polarity epochs; 1991-1998 (qA > 0) and

2001-2008 (qA < 0). Top, middle and bottom panels of Figure (6) refer to (0° < TA ≤ 30°), (30° < TA

≤ 50°) and (50° < TA ≤ 70°), respectively. The obtained results indicate the following notes:

1) The top panel of Figure (6) shows that the power fit for periods of minimum solar activities during

qA > 0 and qA < 0 indicated R-1.81 and R-0.74, respectively. The rate of sensitivities of CRIs to the

HCS tilts for group I during qA > 0 minimum solar years 1991-1994 (CNs: 1884-1931) was higher

than that during qA < 0 minimum solar years 2007-2008 (CNs: 2052-2078). The spectrum

variation became softer after the reversal of IMF polarity state in 1999/2000.

a = 12.28 R

-

1.36

0.0

0.1

0.2

0.3

0.4

14 16 18 20 22 24 26 28 30 32 34


Slo

pe

Of

Reg

ress

ion

Lin

e (

% /

deg

)

1991 - 1998 (qA > 0) , CNs : 1838 - 1944

a = 24.08 R

-

1.49

0.0

0.1

0.2

0.3

0.4

0.5

14 16 18 20 22 24 26 28 30 32 34


Slo

pe

Of

Reg

ress

ion

Lin

e (

% /

deg

)

2001 - 2008 (qA < 0) , CNs : 1972 - 2078


164

2) The middle panel of Figure (6) shows that during the ascending and descending years of solar

activity, the rigidity changes for qA > 0 and qA < 0 epochs giving R-1.43 and R-1.55, respectively.

The rate of sensitivities of CRIs to HCS tilts for group II during the qA > 0 epoch was a little

smaller than that during the qA < 0 epoch. The spectrum variation became a little harder after the

reversal of IMF polarity state in 1999/2000.

3) The bottom panel of Figure (6) displays the periods of high solar activity, the power fit for qA > 0

and qA < 0 gave R-1.12 and R-0.21, respectively. These results confirm that there are variances in

energy spectrum for group III between qA > 0 and qA < 0 epochs.

Fig. (6): The sensitivities of CRIs with different Rm to HCS tilts throughout IMF polarity states;

1981-1988 (qA < 0) and 1991-1998 (qA > 0). The top, middle and bottom panels refer to (0°

< TA ≤ 30°), (30° < TA ≤ 50°) and (50° < TA ≤ 70°), respectively

a = 17.78 R -1.81

a = 1.80 R -0.74

0.0

0.1

0.2

0.3

0.4

0.5

15 16 17 18 19 20 21 22 23 24 25 26 27 28Slo

pe

Of

Reg

ress

ion

Lin

e (

% /

deg

)


1991-1998 (qA > 0) 2001-2008 (qA < 0) , 0 < TA ≤ 30

2001-2008 (qA < 0)

1991-1998 (qA > 0)

a = 12.25 R -1.43

a = 40.22 R -1.55

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

15 16 17 18 19 20 21 22 23 24 25 26 27 28Slop

e O

f R

egre

ssio

n L

ine

( %

/ de

g )


1991-1998 (qA > 0) 2001-2008 (qA < 0) , 30 < TA ≤ 50

2001-2008 (qA < 0)

1991-1998 (qA > 0)

a = 0.24 R -0.21

a = 9.15 R -1.12

0.0

0.1

0.2

0.3

0.4

0.5

0.6

15 16 17 18 19 20 21 22 23 24 25 26 27 28Slop

e O

f R

egre

ssio

n L

ine

( %

/ de

g )


1991-1998 (qA > 0) 2001-2008 (qA < 0) , 50 < TA ≤ 70

2001-2008 (qA < 0)

1991-1998 (qA > 0)


165

Fig. (7): The sensitivities of CRIs with different Rm to HCS tilts throughout IMF polarity states;

1981-1988 (qA < 0) and 1991-1998 (qA > 0). HCS tilts were divided in to three groups;

(0° < TA ≤ 30°), (30° < TA ≤ 50°) and (50° < T A ≤ 70°)

4) From the top panel in Figure (7), it was observed that during the period 1991-1998 (qA > 0), the rate

of sensitivities of CRIs to the HCS tilts was R-1.81 around the minimum solar activity and R-1.12 near

high solar activity years. In addition, the bottom panel in Figure (7) displays the same for the period

2001-2008 (qA < 0), the rate of sensitivities of CRIs to the HCS tilts was R-0.74 around the minimum

solar activity and R-0.21 near high solar activity years. Therefore, the energy spectrum of the cosmic ray

modulations caused by the HCS tilts has different behaviors during the minimum and maximum solar

a = 17.78 R -1.81 a = 12.25 R -1.43 a = 9.15 R -1.12

0.0

0.1

0.2

0.3

0.4

0.5

14 16 18 20 22 24 26 28

Slo

pe

Of

Reg

ress

ion

L

ine

( %

/ d

eg )


0 < TA ≤ 30 30 < TA ≤ 50 50 < TA ≤ 70

1991 - 1998 (CNs : 1938 - 1944) , qA > 0

a = 1.80 R -0.74 a = 40.22 R -1.55 a = 0.241 R -0.21

0.0

0.1

0.2

0.3

0.4

0.5

0.6

14 16 18 20 22 24 26 28

Slo

pe

Of

Reg

ress

ion

L

ine

( %

/ d

eg )


0 < TA ≤ 30 30 < TA ≤ 50 50 < TA ≤ 70

2001- 2008 ( CNs: 1972 - 2078) , qA < 02001 - 2008 (CNs : 1972 - 2078) , qA < 0


166

activity periods. The rate of sensitivity/modulation of CRIs to the HCS tilts is higher throughout the

minimum solar activity years as compared to the maximum solar activity period.

CONCLUSIONS

It is well known that the polarity state of interplanetary magnetic field (IMF) changes during the

maximum phase of the solar activity cycle. We have omitted these years from our study because there

is no regular pattern can describe the complex structure of HCS around the years of IMF polarity

reversal.

In the present work, the linear correlations between tilt angle (TA) of the HCS and cosmic ray

intensity (CRI), strength (B) of the IMF, sunspot number (SSN), solar plasma speed (SWS) and

density (n) have been studied before and after the reversals of IMF polarity state. The sensitivities of

CRIs (Rm : 16 - 33 GV) to the tilts of HCS have been studied throughout three geomagnetic epochs:

1981-1988 (qA < 0) , 1991-1998 (qA > 0) and 2001-2008 (qA < 0). The obtained results display the

following:

1) The strength of IMF is much stronger during the minimum period of solar activity cycle than that

during the maximum period. The correlation between the TA of HCS and the strength of IMF is

greater during the qA < 0 epochs than that of the qA > 0 epochs.

2) There is a highly positive correlation between the TA of HCS and the sunspot number and it is

independent on the polarity state of the IMF. In addition, the TA of HCS changes systematically

over the solar activity cycles.

3) A moderate correlation between the TA of HCS and the solar wind speed (SWS) is observed while

a weak and negative correlation between the TA of HCS and solar plasma density (n) is noted

during the qA < 0 and qA > 0 epochs.

4) There is a highly negative correlation between the inclinations of HCS and the CRIs. The negative

correlation between the CRIs and the HCS tilts is more pronounced during the qA < 0 epochs as

compared to the qA > 0 epochs.

5) The sensitivity of CRI to changes in the TA of HCS is rigidity-dependent which follows the power-

type law. The power fitted of sensitivities throughout the three periods 1981-1988 , 1991-1998 and

2001-2008 gave R-1.01 , R-1.39and R-1.62, respectively.

6) The spectra of particles drift are harder after the reversal of IMF polarity state than before. In

addition, the modulation for lower energy particles is more pronounced during qA < 0 epochs than

that during qA > 0 epochs.

7) The rate of sensitivity/modulation of CRIs to the HCS inclinations is higher throughout the

minimum solar activity years as compared to the maximum solar activity period.

ACKNOWLEDGMENTS

The authors would like to thank Prof. Abdelallah Abdelsalam , Physics Department - Faculty of

Science - Cairo University, for his continuous support, suggestions, comments and discussions

throughout the present work.

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