cosmic ray anisotropy in interplanetary …1.6 cosmic rays in interplanetary space 06 1.6.1 short...
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COSMIC RAY ANISOTROPY I N INTERPLANETARY SPACE"
SUBWTTeb FOR THE AWARD EC Of
Under the Supervision of
DR. BADRUD0IN
DEPARTMENT OF PHYSICS ALI6ARH MUSLIM UNIVERSITY
ALIGARH ( INDIA)
June, 2005
'p^^^-"G *f!sri
^'T FB^ «^«^
969esa
Dr. Badruddin Reader
Department of Physics Aligarh Muslim University, Aligarh-202002
Phone:0571-2701001(O) :0571-2720162(R)
Fax : 0571-2700093 : 0571-2701001
e-mail: badr phvsfgivahoo.co.in
Dated: /7/V-'^'^^'
CERTIFICATE
I certify that the M. Phil, dissertation titled "Cosmic ray
anisotropy in interplanetary space" is based on the original
research work carried out by Mr. Munendra Singh under my
supervision.
Supervisor
(Dr. Badruddin)
Acknowledgement
I express my sincere gratitude to my supervisor, Dr. Badruddin, for providing his able guidance, kind support and blessings: all the ingredients necessary for this work.
I am grateful to Indian Space Research Organization (I.S.R.O.) for providing all the necessary monetary help through their RESPOND program.
I also want to thank all of my fr iends/ colleagues who helped me directly or indirectly \r\ the accomplishment of this work. May god help them.
-Munendra Singh ([email protected])
Contents
1. The cosmic radiation^ Reviewing the present and future 01
1.1 Cosmic rays within the atmosphere 01
1.2 The elemental composition 02
1.3 Energies and intensities 04
1.4 The stable and radioactive isotopes 05
1.5 The highest energy cosmic rays 05
1.6 Cosmic rays in interplanetary space 06
1.6.1 Short term cosmic ray intensity decreases 06 1.6.2 Long term variations 07 1.6.3 Daily variations 07
2. The interplanetary medium 09
2.1 Solar wind and interplanetary magnetic field 09
2.2 Impacts of solar and interplanetary phenomena at the E a r t h 11
2.3 Magnetic domain of the interplanetary space- The Heliosphere 15
2.3.1 Size of Heliosphere 17 2.3.2 Hehospheric neutral sheet 18
3. Solar modulation of galactic cosmic rays 21
3.1 Solar modulation: Basic processes 21
3.1.1 Diffusion 21 3.1.2 Effects due to the large scale magnetic field 22 3.1.3 Convection 23 3.1.4 Energy change 23
3.2 Solar modulation^ Theoretical models 23
3.2.1 Predictions of models 26
4. Anisotropic cosmic ray modulation 28
4.1 Diurnal anisotropy: basic concepts and its importance 28
4.2 Harmonic analysis 33
4.3 Data analysis 34
4.4 Results 35
4.5 Discussion 60
4.6 Conclusions 60
References 62
CHAPTER - 1
The cosmic radiation: Reviewing the present and future
CHAPTER-1
THE COSMIC RADIATION: REVIEWING THE PRESENT AND FUTURE
Victor Hess discovered a penetrating extraterrestrial radiation in
1911, later called cosmic rays. The search for the origin of cosmic rays
gave birth to many new scientific disciplines, each evolving into a life of
its own. Examples include the discoveries of new elementary particles,
high-energy physics, radioactive particle dating, dating geological
formations and establishing the age of galactic cosmic rays. Cosmic ray
research has become an important part of astrophysics, especially
gamma ray and radio astrophysics.
Starting with balloons and then aircrafts, cosmic ray study has
come into the era of satellites. Scientists design and build instruments to
be carried by satellites and deep space probes - now the magnetospheres
of planets and the heliosphere has become the laboratory in space.
Through experiment and theory we now have a remarkable, but terribly
incomplete, understanding of the origins and physical mechanisms of the
cosmic rays. A brief discussion of cosmic rays and related facts is
discussed below (for more details, see Dorman, 2004).
1.1 Cosmic rays within the atmosphere
Atmospheric gases are a target for the arriving primary cosmic ray
nuclei. Figure 1.1 shows this interaction and the resulting products
(divided in three groups: electromagnetic, hard and nucleonic
components). The external geomagnetic field determines the latitude of
access to the atmosphere by the charged cosmic ray nuclei. For example,
only the cosmic ray nuclei with energies > 12 GeV per nucleon enter at
the geomagnetic equator, whereas all but the lowest energy nuclei have
access over the polar regions and produce a nucleonic cascade that can be
detected by neutron monitors. Thus, the latitude effect was used both to
prove that the cosmic rays were mostly positively charged particles and
to show they had a broad energy distribution.
Incident Primary Particle
Low energy rsucleonic component (disintegration product neutrons
•^degenerate to "slow" neutrons)
Electromagnetic or "soft" corriponenf
Meson or "hard" component
Energy feeds across from nuclear to electromognetic interociions
Nucleonic component N,P=High energy nucleons
n,p = Disintegration 1 Product
. 1 - . - . . •—m-
1 Small energy feedback nucieons 1 from meson to nucteonic Jt>. = Nuclear 1 tO'^Ponent disintegrotion
Fig. l.i: Schematic of secondary radiation production. Ionization chambers mainly monitor the meson and soft component, whereas neutron monitors measure exclusively the nucleonic component.
1.2 The elemental composition
The cosmic rays contain all the nuclei, from Hydrogen to
Uranium. During their acceleration and propagation in the interstellar
medium of our galaxy, these elements have been totally stripped of all
their electrons so that they arrive in the solar system as the bare nuclei.
The cosmic rays represent the only contemporary sample of the elements
from the galaxy that is directly accessible to the observer in the solar
system. Clearly, the cosmic rays are nuclear messengers from the galaxy
with unique information on their nuclear origin.
In Figure 1.2 the relative abundances of nuclei in the cosmic rays
are compared with abundances of elements in the solar system.
- a
DC
10
hHe
iO
S' ! * r-II ^ ? S
Fe
CaTi Cr
1 Na
\ F
II ?/ ' -11 V i ( . , 1
P,?, ClK
f-i w -,Mnj,' -
' Co H
10
1 • w
r Sc
• Satellite
o Solar system
Be i l l I I I I I ! i I l,J,..l, I .1, 1 1.,.1,-L.
0 4 8 12 16 20 24 28 Nuclear Chorge Number
Fig. 1.2: Elemental composition from hydrogen to Nickel in the cosmic rays arriving near the top of Earth's atmosphere. The solar system relative abundances are shown normalized to the cosmic ray Carbon abundances.
The overall similarity between them is apparent with two
exceptions"- Lithium (Li), Beryllium (Be) and Boron (B) and e lements
from Chlorine (CI) to Manganese (Mn). The anomalously high
abundance of these elements is due to the fact tha t as the abundant high
energy Carbon, Oxygen and Iron nuclei propagate through, and collide
with, the gas atoms in the interstellar medium, they knock off fragments
at high energy (such as Li, Be, B) which then become a secondary
addition to the radiation measured by the investigator. These secondary
carry critical information concerning the accelerated cosmic ray nuclei
tha t are propagating through the interstel lar mat te r and magnetic fields
(see Figure 1.3).
o
o o
O
CC
o w —
o
i / i OJ
3 O
CO
ProDaaotion via aolactic disk -Energy loss by ionization -Spoliation. . -Escape . -Rodioactive decoy
Accelej;ation! OaloOic propagation in -*n infersiellor magnetic fields
-*-i
Solar modulation in interplonetary magnetic fields
Fig. I.3: Sketch of the hfe history of an accelerated cosmic ray nucleon.
1.3 Energies and intensities
Figure 1.4 shows a generic energy spectrum of cosmic rays.
2pro}ons per square centimeter per second
a few protons per square kifometer per century.
™C 108 iQio iot210^4 iQie jQie jo2o
Energy (electron volts)
Fig. 1.4: The approximate energy-intensity spectrum of cosmic ray protons in the solar system.
Over 99% of the nuclei are in the energy regions "A" and
measured by spacecraft and balloon instrumentation. For energies in the
region "B", space shuttle sized instruments are essential. Beyond the
energy range "B" the nuclei are probably of extragalactic origin. At the
highest energies (region "C") huge, ground based detector arrays are
required (Simpson, 1997).
1.4 The stable and radioactive isotopes
The isotropic composition of the stable primary, galactic source
nuclei, from Carbon to Iron and Nickel are surprisingly similar to the
corresponding relative abundances of solar system matter. Surprising
because cosmic ray matter is modern (not more than 10-20 million
years), whereas solar system matter was formed more than 4 billion
years ago. Thus, at present the cosmic ray analysis does not support a
dramatic elemental evolution of the interstellar medium over this wide
span of time.
Radioactive decay isotopes provide information on the time
between nucleosynthesis of cosmic ray nuclei and their initial
acceleration, or time of propagation in galactic magnetic fields (i.e.
cosmic ray age). For example, since Beryllium is rare in nature, its high
abundance in the cosmic rays is due to its secondary production in the
interstellar medium. The spallation processes produce known relative
abundances of stable ''Be and ^Be and of radioactive i*'Be with half-life of
1.6 million years. Thus, from the amount of ^"Be that has decayed
relative to the stable ^Be, we obtain an age for the galactic containment
of the high-energy radiation of 12 to 18 million years.
1.5 The highest energy cosmic rays
Arrays of ground-based detectors of continually increasing area
have been deployed (such as the MIT collaborations, the Leeds arrays
and the world's largest array in Akeno, Japan) to capture the shower
particles and deduce the energy of the incoming primary radiation. These
arrays have produced an energy spectrum, shown in generic form in
region "C", Figure 1.4, that extends to at least 3 x lO^^ electron volts -
the highest energy known for any particle in the universe. These
particles are certainly not containable in magnetic fields in our galaxy.
On the other hand, in their intcrgalactic travel they collide with the
universal cosmic microwave background radiation and lose energy, which
results in their effective propagation distance being limited to less than
about 100 mega-parsecs, a short distance on the scale of the universe.
If they are nuclei of unknown composition or an unknown kind of
radiation and with uncertainties in their direction of arrival, these
highest energy primaries are one of the exciting areas for experimental
and theoretical research in the near future.
1.6 Cosmic rays in interplanetary space
Our Sun influences and shapes the region of the interplanetary
medium. In this region, renamed the Heliosphere, physical conditions are
established, modulated and governed by the Sun. When galactic cosmic
rays come in this region, they are influenced by the Sun's magnetic field
and they get modulated on various time scales. In subsequent sections,
the observed variations of cosmic ray intensity and the effects of solar
influence on these are discussed (see Venkatesan and Badruddin, 1990),
1.6.1 Short-term cosmic ray intensity decreases
Short-term decreases in cosmic ray intensity observed by ground-
based detectors are, in general, broadly classified into two categories:
1.6.1.1 Forbush decreases
Forbush decreases (generally non-recurrent) associated with
transients on the Sun are characterized by a rapid reduction (within a few
hours) in cosmic ray intensity followed by a slow recovery typically lasting
several days (Forbush, 1938). The study of Forbush decreases has
assumed considerable importance, particularly with the resurgence of an
earlier concept that the cumulative effect of Forbush decreases can
account for the - 1 1 year (long-term) variation of cosmic ray intensity
(Lockwood and Webber, 1984).
1.6.1.2 Recurrent cosmic ray intensity decreases
Generally, recurrent (corotating) decreases are associated with
corotating high-speed solar wind streams from coronal holes
(Venkatesan et al., 1982) and has a period of- 27 days.
1.6.2 Long-term variations
Solar wind expands and flows continuously from the Sun into
interplanetary medium; the magnetic field associated with it varies both
in time and space according to the solar conditions. The cosmic rays being
charged particles are affected by the magnetic field variations. On the
scale of years, two prominent variations in cosmic ray intensity are those
related to the - 1 1 year period of solar activity revealed by the sunspot
number and the - 22 year period of the solar magnetic polarity cycle.
1.6.3 Daily variation
Daily variations in cosmic ray intensity arise from spatial
anisotropies in interplanetary space. Ground based detectors record
these once every day as their asymptotic cone of acceptance sweep
through the direction containing the spatial anisotropy. Daily variations
can be studied by the use of harmonic analysis. First harmonic represent
the diurnal variation, second harmonic represent the semi diurnal
variation and so on.
1.6.3.1 Diurnal variation
The solar diurnal variation of the cosmic ray intensity was
interpreted initially on the basis of an outward radial convection and an
inward diffusion along the interplanetary magnetic field (IMF). The
balance between convection and diffusion generates an energy
independent anisotropic flow of cosmic ray particles from the 18-00 hour
CO rotational direction. However, this is a much simple picture. Many
observed features of the diurnal variation had provided an evidence for
additional effects contributing to the diurnal anisotropy (Ananth et al.,
1974; Kane, 1974, 1975; Agrawal and Singh, 1975; Yadav and
Badruddin, 1983a, 1983b; Ahluwalia and Riker, 1985). Theoretical
modelers have introduced a drift concept in the modulation theories to
make it adequate (see chapter 3).
1.6.3.2 Higher harmonics of daily variation
The higher harmonics of daily variation with periods of 12, 8 and 6
hours (semi-, t r i - and quart-diurnal) have also been investigated. The
existence of at least the second and the third harmonics has been
confirmed (Elliot and Dolbear, 1950; Sarabhai and Nerurker, 1956;
Katzman and Venkatesan, 1960). Abies et al. (1965) pointed out that the
direction of maximum of semi-diurnal component in free space (about
03^00 local time) was very nearly perpendicular to the average direction of
the IMF (09:00 or 21:00 local time). Subramanian and Sarabhai (1967)
and Quenby and Lietti (1968) have provided an explanation for the
observed semi-diurnal variation in terms of the cosmic ray gradient
perpendicular to the ecliptic plane.
CHAPTER - 2
The interplanetary medium
/•
/ > t
CHAPTER-2
THE INTERPLANETARY MEDIUM
2.1 Solar wind and Inteiplanetary magnetic field (IMF)
The solar wind is the continuous outflow of completely ionized gas
from the solar corona. It consists of protons and electrons, with an
admixture of a few percent alpha particles and much less abundant
heavy ions in different ionization stages. The hot corona typically has
(base) electron and proton temperatures of 1-2 million Kelvin and
expands radially outward into interplanetary space, with the flow
becoming supersonic within a few solar radii. Because the solar wind
plasma is highly electrically conductive, the solar magnetic field lines are
dragged away by the flow, and due to solar rotation are wound into
spirals. This magnetic field forms the interplanetary magnetic field
(IMF). The wind attains a constant terminal speed, and its density then
decreases radially in proportion to the square of the radial distance.
At 1 AU the average speed of the solar wind is about 400 km/s.
This speed is by no means constant. The solar wind can reach speeds in
excess of 900 km/s and can travel as slowly as 300 km/s. The average
density of the solar wind at 1 AU is about 7 protons/cm^ with large
variations. Flux of solar wind particles at 1 AU is 500 x 10^ particles per
square centimeter per second. At this distance, the thermal energy is
around 10 eV. Protons have kinetic energy 1000 eV and electrons have 10
eV. Magnetic field in the solar wind at 1 AU is around 5 x 10" ^ gauss.
The hot coronal plasma of the Sun (solar wind) has a high
electrical conductivity and, therefore, it carries the solar magnetic field
lines into the interplanetary space, but with the roots of the lines fixed
on the rotating Sun. The frozen-in magnetic field lines do not allow the
plasma to diffuse across them. They connect all plasma originated from
the same position on the Sun, and thus form an Archimedean spiral in
the interplanetary space (see Figures 3.1 and 4.1).
The equation of the Archimedean spiral can be derived (Kallenrode,
1998) from the displacements Ar and A^. If we assume as initial
conditions of the plasma parcel on the Sun a source longitude ^^ and a
source radius r^, at a time t the parcel can be found at the position
<PiO = ft>™„ .t + (PQ a n d r{t) = M „„, .t + r,.
Eliminating the time yields the equation for the Archimedean spiral:
^Zl^ + r n^
With y/ = oy,^„r Iu^^^^,^ , the path length s along the spiral is given as
1 u 2 CO,.,,
(^•V^' + 1 + In {/ + V^'+l}) (2)
The magnetic field in the equatorial plane can be expressed in
polar coordinates B = (B^,B^). The magnitude of B depends on the radial
distance only, thus it is \B\ = B(r). Gauss's law in spherical coordinates
yields
V j = 4 | - ( r ' 5 , ) = 0 (3) r •' dr
or r^B^ -r^oB^ . Thus the magnetic flux through spherical shells is
conserved and the radial component of the field decreases as
B.=B, 'o
V ' y
(4)
Since the Magnetic field is constant, it is dB/dt = 0. From the frozen-in
condition: — - V x (w x 5) = - ^ V 'S , (5) dt ATTG
(Equation (5) allows to determine how a given velocity field u deforms a
magnetic field B), we then get V x (M x 5) - 0 , or in spherical coordinates
- ^ ( K ^ 5 , - M , 5 ^ ) - 0 . (6) r or
Thus we have r{u^B^ -u^B^) = const. Assume ro to be at the source
surface. There B is radial and we get
ru^B^ - ru^B^ = r.u^^^B^ =r\co^^„B,. (7)
In the second step, the rotation speed of the Sun was used to describe the
azimuthal component of the solar wind speed at the source surface. From
the expression (7), the azimuthal component of the magnetic field is
2
This can be approximated as B^--rco^^„BJu^ for large distances
{rco^^^ >u^). The azimuthal component therefore decreases with 1/r while
the radial component decreases as l/r^. The field strength decreases with
r as
5(r)^^Jl V ". J
(9)
The angle y/ between the magnetic field direction and the radius vector
from the Sun is tan <p = B^ / B^. For large distances this reduces to
tan^ = a> .„„r/w . At the earth's orbit, tan ^ is about 1 for typical solar
wind conditions, and thus the field line is inclined by 450 with respect to
the radial direction. This is known as the garden-hose angle because the
similar effect can be observed with a rotating sprinkler; thus the
deformation of the field lines is also called the garden-hose effect.
2.2 Impacts of solar and interplanetary phenomena at the Earth
The Sun has very serious impacts on interplanetary space and the
environments of planets (Dwivedi, 2003).
Near the solar poles the magnetic field lines are open and solar
plasma flows continuously into space creating there the fast solar wind
11
blowing around the Earth deep into outer regions of the planetary
system. Some region of the corona appear dark where the coronal gas is
much less dense and less hot than usual; these regions are called coronal
holes (Figure 2.1) and are responsible for solar wind streams. At lower
latitudes, coronal helmet streamers and possibly active regions during
periods of field-line openings are sources oi slow solar W7i2<i (Figure 2.2).
Fig. 2.V- Coronal hole
Fig. 2.2- Schematic diagram showing region of fast and slow solar wind from the Sun and some other features of interplanetary medium.
Streams of accelerated particles, both electrons and atomic nuclei,
propagate at various places through interplanetary space. And in
addition to these streams of plasma and particles, coronal mass ejections
Fig. 2.3: Coronal mass ejection (CME)
(plasma ejection from the Sun? are main cause of geomagnetic storms on
Earth) send plasma clouds and shock waves in various directions
through interplanetary space and eventually cause other particle
accelerations there. All this creates highly variable and very complex
conditions in the space between the Sun and the Earth and in the last
decade people began to speak about, and regularly study, the space
weather.
Solar flare, a source of X-rays, influences Earth's ionosphere and
thus cause disturbances in radio communications around the Earth. A
major eruptive (long-decay) flare can disturb radio contacts for many
hours.
13
The most energetic flares emit protons with energy exceeding 500
MeV which arrive at the Earth some 15 minutes after the flare onset,
produce streams of neutrons in Earth's atmosphere, and cause the so-
called ground level effects (GLEs). Flares that produce protons of such
high energies are sometimes called cosmic—ray flares. Flares that emit
protons with energies higher than 10 MeV are often called proton flares.
Particles of lower energy are guided by the Earth magnetic field to the
polar regions and cause there absorption of radio waves (polar cap
absorption) and intense aurorae. All these effects are delayed by tens of
minutes to several hours after the flare onset, depending on the energy of
the propagating particles.
Before the discovery of coronal mass ejections (CMEs) in the
seventies, all effects of the Sun on the magnetosphere were ascribed to
major solar flares. Coronal mass ejection (Figure 2.3), often with a shock
wave, arrives at the Earth, if it propagates in the right direction toward
us. This arrival - two or three days after its origin on the Sun - has a
strong impact at the Earth's magnetosphere and causes a geomagnetic
storm which sometimes can last for several days and has serious impact
on communications all around the Earth. Now, it is known that the real
agent that causes geomagnetic storms are CMEs, which can originate
also in quiet parts of the Sun, without any observed chromospheric flare.
Flares are excellent indicators of coronal storms and actually indicate the
strongest, fastest, and most energetic disturbances coming from the Sun.
The largest geomagnetic storms are caused by fast CMEs, which usually
are associated with flares, while moderate or small storms mostly have
no association with flares (Webb, 1995). Flares are also sources of short
wave radiation that affects the ionosphere, and produce a significant
fraction of accelerated particles that cause disturbances in space and at
the Earth.
Active processes on the Sun also influence the weather at the
Earth, but these effects are indirect - depending on the behavior of the
magnetosphere and ionosphere and on the meteorological situation at the
time of the disturbance arrival - so that they are very complex.
14
2.3 Magnetic domain of the interplanetary space:
The Heliosphere
Heliosphere is the region of space where the solar wind's
momentum is sufficiently high that it excludes the interstellar medium.
The solar wind plasma thus dominates this region.
As the solar wind expands, its density decreases as the inverse of
the square of its distance from the Sun. At some large enough distance
from the Sun (in a region known as the heliopause), the solar wind can
no longer "push back" the fields and particles of the local interstellar
medium and the solar wind slows down from 400 km/s to perhaps 20
km/s. This transition region is known as heliospheric termination shock.
Beyond the termination shock, a pressure balance exists between the
Local Interstellar Medium (LISM) and the solar wind, through a surface
called the heliopause. It is possible (although not proven as yet) that the
interstellar wind (corresponding to the motion of the heliosphere through
the LISM) may be fast enough to generate a shock wave, the heliospheric
bow shock, upstream of the heliopause (Figure 2.4).
200 -250 AU
INTERSTELLAR WIND
TERMINATION
HELIOSPHERIC BOW SHOCK
Fig. 2.4: A schematic representation of various region of the heliosphere.
Actually, heliosphere extends from the solar corona to an outer
boundary where the solar wind encounters the interstellar medium
15
(Parker, 1958). The outer corona of the Sun consists of a fully ionized gas
threaded by magnetic fields rooted in the visible surface of the Sun, the
photosphere. The coronal plasma is very hot, with a temperature in
excess of a million degrees. It is still unclear just how the corona is
heated to such temperatures! the most likely explanation is that waves
from the lower layers of the solar atmosphere provide the necessary
energy to heat the corona. The energy deposited in the coronal plasma
appears also to be sufficient to accelerate it away from the Sun in the
form of the solar wind. The speed of the solar wind varies between about
300 km/s to more than 800 km/s. This speed is well in excess of the speed
of sound in the plasma.
Polarity of the heliosphere changes after every 11 years. The
approximately 11-year solar activity cycle is reflected in the strength of
the IMF, the frequency of coronal mass ejections (CMEs) and shocks
propagating outward, and the strength of those shocks. The solar
magnetic field reverses at each solar activity maximum, resulting in 22-
year cycles as well. The field orientation is known as its polarity and is
positive when the field is outward from the Sun in the northern
hemisphere (e.g. during the 1970s and 1990s) and negative when the
field is outward in the southern hemisphere (e.g. during the 1960s and
1980s). A positive polarity field is denoted by A > 0 and a negative field
by A < 0.
HELIOPAUSE
.•INTERSTELL ••• MEDIUM
POSSIBLE BOW SHOCK
INTERSTELLAR MEDIUM
MAGNETIC FIELD LINES
Fig. 2.5: Schematic diagram of heliosphere
Galactic cosmic rays beyond the Heliosphere are considered to be
temporally and spatially isotropic, at least over timescales of decades to
centuries. Galactic cosmic rays get modulated when they come in
Heliosphere. It is likely that the Heliosphere is not spherical but that it
interacts with the interstellar medium as shown schematically in Figure
2.5. Cosmic rays enter the Heliosphere due to random motions, and
diffuse inward toward the Sun, gyrating around the interplanetary
magnetic field (IMP) and scattering at irregularities in the field. They
will also experience gradient and curvature drifts (Isenberg and Jokipii,
1979) and will be convected back toward the boundary by the solar wind
and lose energy through adiabatic cooling, although the latter process is
only important below a few GeV and does not affect ground-based
observations. The combined effect of these processes is the modulation of
the cosmic ray distribution in the Heliosphere (Forman and Gleeson,
1975) (see details in Chapter 3).
2.3.1 Size of Heliosphere
Given the existence of the continuous flow of the solar wind, how is
the outer boundary of the Heliosphere determined? A simple sketch of
the Heliosphere and related phenomena in Figure 2.4 provides an outline
of the very complex answer to this question.
In the first place, the solar wind eventually slows down," this
occurs through a shock wave, the so-called termination shock, where the
solar wind speed falls below the sound speed. The location of this
transition region (called the heliospheric termination shock) is unknown
at the present time, but from direct spacecraft measurements, must be at
more than 50 AU. In fact, in 1993 observations of 3 kHz radiation in the
outer Heliosphere (Kurth et al., 1984) by plasma wave receivers on
Voyagers 1 and 2 have been interpreted as coming from a radio burst at
the termination shock. This burst is thought to have been triggered by an
event in the solar wind observed by Voyager 2. From the time delay
between this triggering event and the observation of the 3 kHz
radiations, the distance of the termination shock has been put between
130 and 170 AU.
17
•
. • • • . • * • ' ' .
rn (TJ . TBE I."?
C <B § J^ V » ^ - i / * ! _ . . W
§ . . - . - , » -.^---«- , •,-. Aatorold
B B K .
Heliosphere
..'~2 ~ 3 - i . ' . " ' i - ' 4 ., «5 " ^ ^ ^ , JL; 10 10 Ediii 1 0 •'0 10
^ g ^ ^ ^ ^ ^ ^ B • ^-^^ GCioud?
Interstellar Medium ^
Fig. 1.6: Size of heliosphere compared with various objects. Lengths are in AU.
No space probe has yet reached the termination shock, although
Voyager 1, now at some 80AU from the Sun is thought to be getting close
to it.
2.3.2 Heliospheric neutral sheet
The expanding solar wind plasma carries with it the interplanetary
magnetic field (IMF). A neutral sheet separates the field into two distinct
hemispheres, one above the sheet, with the field either emerging from or
returning to the Sun, and the other below the sheet, with the field in the
opposite sense.
The solar magnetic field is not aligned with the solar rotation axis and
is also more complex than a simple dipole. As a result, the neutral sheet is
not flat but wavy, rotating with the Sun every 27 days. At solar minimum,
the waviness of the sheet is limited to about 10° helio-latitude but near solar
maximum the extent of the sheet may almost reach the poles. With the
rotation of the sheet every 27 days, the Earth is alternately above and below
the sheet and thus in an alternating regime of magnetic field directed toward
or away from the Sun (but at an angle of 45° to the west of the Sun-Earth
line).
Fig. 1.7: Schematic diagram of neutral sheet
This alternating field orientation at the Earth's orbit is known as the
IMF sector structure. The neutral sheet structure is such that there are
usually two or four crossings per solar rotation.
An inclined current sheet has a significant effect on the global
heliospheric field and on the drift motions of the cosmic rays. These
implications were pointed out by Jokipii, who proceeded to include drift
effects in the basic transport equation (see chapter 3 for details) used to
describe the behavior of energetic particles (Jokipii et al., 1977). In
particular, the heliospheric current sheet (HCS) was shown to cause fast
drifts along it and to act as a major source or sink of cosmic rays in the
heliosphere (depending on the polarity of the fields above and below it, which
change sign from one sunspot cycle to the next). The influence of the HCS
was evident in the model as a correlation between cosmic ray intensity and
19
the changing inchnation of the current sheet. This aspect of the model was
shown to be consistent with observations (Smith, 1990). Other importance of
the HCS is its close relation with plasma parameters. Since the HCS serves
as a magnetic equator, many solar wind properties are organized with respect
to it. Studies of various plasma parameters, including solar wind speed,
density, temperature, and composition, show a close correlation with the
current sheet (see Smith, 2001 and references therein).
20
CHAPTER - 3
Solar modulation of galactic cosmic rays
CHAPTER-3
SOLAR MODULATION OF GALACTIC COSMIC RAYS
3.1 Solar modulation: Basic processes
In the local interstellar region, outside the heliosphere, the
distribution of galactic particles is considered almost isotropic in space
and time. Due to random motion and collisions these particles cross the
boundary and enter the Heliosphere. They gyrate around the IMF but
due to small-scale irregularities in the IMF the particles are scattered
from their gyro-orbits. The overall motion of the particles will be seen as
diffusion from the boundary towards the Sun. Along their diffusive
journey the particles will also undergo gradient and curvature drifts in
the IMF (Isenberg and Jokipii, 1979). The solar wind, with the IMF
frozen into it, also convects particles back towards the heliospheric
boundary. The overall result of these processes is solar modulation
within the Heliosphere of the galactic distribution of cosmic-ray particles
(Forman and Gleeson, 1975).
In this way, there are four physical processes, which are believed
to be important for modulation: diffusion, effects associated with the
large-scale magnetic field, convection, and energy change (adiabatic
cooling). They are discussed below in brief.
3.1.1 Diffusion
The magnetic field in the solar wind contains small-scale
irregularities. There are Alfven waves, perhaps some magetosonic waves,
and other fluctuations. In some cases these irregularities have scale sizes
comparable to the gyroradii of the cosmic rays, with the result that the
cosmic rays are scattered. Their pitch angle or equivalently their velocity
parallel to the mean magnetic field changes randomly with time. It is
also possible for the particles to be scattered or to propagate by other
means, in a random fashion, in a direction normal to the mean magnetic
field (Jokipii and Parker, 1969).
21
3.1.2 Effects due to the large-scale magnetic field
Due to the rotation of Sun, its field is spiral. The spiral is tightest in the
equatorial plane of the Sun where the rotation effects are most important
(see Fig. 3.1). However, as we increase in latitude the spiral becomes less
Fig.3.1: A schematic drawing of the pattern of the mean magnetic field in the Heliosphere.
tightly wound, and, in fact, the field becomes radial over the solar poles.
The orientation, then, and also the magnitude of the magnetic field in the
heliosphere vary systematically with radial distance and latitude. Hence
cosmic rays have an easier access to the inner Heliosphere over the solar
poles than they do near the equatorial plane.
Another important effect associated with the large-scale field is
gradient and curvature drift. The orientation and magnitude of the
magnetic field varies with radial distance and latitude. Thus, particles
may undergo systematic drifts in this field, which among other effects
should result in a significant transport of particles in latitude (Isenberg
and Jokipii, 1979 and Jokipii et al., 1977). The direction in which
particles drift depends on the polarity of the magnetic field (see section
3.2.1).
22
3.1.3 Convection
The speeds of the waves, which scatter the particles and cause
them to diffuse, are very much less than the solar wind speed. The waves
are thus convected outward with the solar wind, and in turn tend to
convect the cosmic rays out of the Heliosphere. Indeed, it is the effect
which gives rise to the modulation. Neither of the two previous effects,
diffusion or drift, would by themselves cause a reduction in the galactic
cosmic-ray intensity in the inner Heliosphere.
3.1.4 Energy change
The cosmic rays, as for as the solar wind is concerned, are a highly
mobile gas which exerts a pressure. And since there are more cosmic rays
in the interstellar medium than in the inner Heliosphere, this pressure
has a positive gradient. The solar wind, then, which blows outward, does
work against this pressure gradient and imparts energy to the cosmic
rays. However, as for as the cosmic rays are concerned, they find
themselves in an expanding medium. The solar wind blows radially from
the Sun, and thus diverges or expands as it goes outward. The cosmic
rays, which are rattling around in the wind, expand along with it, and are
adiabatically cooled (Parker, 1965).
3.2 Solar modulation^ Theoretical models
As already described, four processes together are responsible for
the modulation of cosmic rays in the Heliosphere. However, adiabatic
cooling is effective only for particles having energy less than few GeV,
hence this effect can be neglected for ground level studies. Irregularities
in IMF make particles to diffuse (towards Sun) parallel and normal to the
field. The same scattering mechanism is partly responsible for the
convection of particles outwards from the Sun by the solar wind.
The curvature of the IMF lines and the gradient in field intensity
leads to drift velocities of the cosmic-ray particles in the interplanetary
23
medium. All these mechanisms combine to produce the solar modulation
of galactic cosmic rays.
Modulation theories attempt to model the effect of Sun's IMF on
the distribution of the galactic cosmic rays in the Heliosphere. The
theoretical basis of modulation was formalized by Forman and Gleeson
(1975). The treatment of the distribution function of cosmic rays from
which the theory is derived was given by Isenberg and Jokipii (1979). A
brief description (Hall et al., 1996) is as follows^
If F(x, j j , t) is a distribution function of particles such that
p2F(je, ^ , t )d3xdpdQ
is the number of particles in a volume d^x with momentum p to p + dp
centered in the solid angle dQ then it can be shown (Isenberg and jokipii,
1979) that
^ + V.5 = 0, (1) dt
where
U(x,p,t) = p^ JF{x,p,t)dQ. 4)!
and S is the streaming vector:
1 + (COT) \ + (a)T)
and CO, gyro-frequency of the particle's orbit; x, mean time between
scattering; K, (isotropic) diffusion coefficient; C, Compton-Getting
coefficient (Compton and Getting, 1935 and Forman, 1970); B, unit
vector in the direction of the IMF; r, the radial direction of a coordinate
24
system centered on the Sun! V, solar wind velocity; and U, number
density of particles.
Adiabatic cooling has not been included in Equation (l) as it is
relatively unimportant above a few GeV. The first te rm of Equation (2)
n tiai-»T»i n o c f n o r m f \ n r a v r i nri-n\7Cini-irfn riT f n o rvQT ' f i r ' l oG K\r -i-ViO o r i l o -p ^xnr»r] fV to
second term describes parallel diffusion, the third describes
perpendicular diffusion and the fourth involves the gradient and
curvature drifts. Writing Equation (2) in te rms of a diffusion tensor
S = CUV-i£.{VU), K =
K , K-r J.
0 0
0 ^
0
K
(3)
IIJ
where KJ^ , ic,j, are respectively the perpendicular and parallel diffusion
coefficients and the off-diagonal elements, /c,,, are related to gradient and
curvature drifts (see Isenberg and Jokipii, 1979, and Equation (5) below),
then
— = -V.(CUV-ic.'^U). dt =
(4)
Equation (4) is a s tandard time dependent diffusion equation. It is
commonly called the transport equation because if we note t ha t
[dt)
= V.{>c'\VU) + {V.ic'){VU) (5)
V.(/c^V[/) + F^.V/7
25
where {dU/ dtY refers to only the non-convective terms in Equation (4)
and K and K^ refer to i£ being split into symmetric and anti-symmetric
tensors, one finds that V.K^ is the drift velocity (F^,) of a charged particle
in a magnetic field which has a gradient and curvature. Equation (4) is an
equation explicitly representing the transport of cosmic rays in the
heliosphere by convection, diffusion and drifts as mentioned earlier.
3.2.1 Predictions of models
Jokipii and co-workers presented some results by numerically
solving the transport equation (equation (4)) for U(x,p,t).
Jokipii et al. (1977) and Isenberg and jokipii (1978) showed that
because the IMF is characterized by the two distinct polarity
configurations over 22 years the drifts would have opposite effects on
modulation in these two states while diffusion mechanisms do not depend
on the IMF polarity. In A > 0 IMF polarity states particles will essentially
flow into the Heliosphere from the high latitudes and travel out of the
Heliosphere along the heliospheric equator (see Figure 3.2).
A<0
highly irregular, B field
Ttrmination /shock
palhs
enhanced scattering
iSM FLOW
Fig. 3.2: Cosmic ray drift patterns during two polarity epochs.
26
During the A < 0 IMF polarity states the net effect of drifts is to cause
particles to travel from the outer regions of the Heliosphere along the
helio-equator towards the Sun and exit the heliosphere via the polar
regions.
Jokipii and Kopriva (1979) predicted that these drift effects
(coupled with the diffusion of particles) would lead to a larger radial
gradient of particles during A < 0 epochs than in A > 0 epochs. The model
also suggested that the general route traveled by cosmic rays during the
A > 0 magnetic polarity states would cause a minimum in number
density at the neutral sheet for these epochs while the transport of cosmic
rays during the A < 0 magnetic polarity states would result in the density
of particles being a local maximum at the equator and a minimum at
some higher heliolatitude. They predicted that this would be observable
as a bi-directional (symmetric about the helio-equator) latitudinal
gradient, which reverses direction after every IMF polarity reversal.
27
CHAPTER - 4
* Anisotropic cosmic * ray modulation
/> t
CHAPTER-4
ANISOTROPIC COSMIC RAY MODULATION
In Chapter-1, a brief description of cosmic ray modulations on
various time scales has been given: Short-term Forbush decreases,
recurrent decreases and long-term variations are isotropic while diurnal,
semi-diurnal variations are anisotropic. Out of these only Forbush
decreases are non-periodic while others are periodic variations.
4.1 Diurnal Anisotropy: Basic concepts and its importance
The average hourly count rate of a cosmic-ray detecting
instrument from a series of complete solar days shows an approximately
sinusoidal variation with a period of 24 hours. Harmonic (Fourier)
analysis of the data will yield the time of maximum (phase) and
amplitude of the variation, with the amplitude usually being expressed
in terms of a percentage deviation from the mean hourly - count rate.
Following the discovery that the solar diurnal variation in cosmic-
ray data was related to a spatial anisotropy in the primary cosmic-ray
distribution (Elliot and Dolbear, 1951) this anisotropy has continued to
be vigorously studied. By the mid-1960s 30 years of ionization chamber
data in 2- and 1-hour intervals had been collected and a concentrated
effort to understand the solar diurnal variation and the processes
responsible for producing the associated anisotropy in galactic cosmic
rays had begun.
Figure 4.1 gives a basic idea of the diurnal anisotropy. Earth's
rotation causes the asymptotic cone of view of an instrument to sweep
through the anisotropy once a day. This gives rise to a diurnal variation
in count rate data with a time of maximum around 18^00 local time.
Rao et al. (1963) defined the asymptotic cone of acceptance as 'the
solid angle' containing the asymptotic directions of approach (The
asymptotic direction of approach is the direction that a cosmic-ray
particle is traveling (in free space) before it is deflected by the Earth's
28
magnetic field) that significantly contributes to the counting rate of a
detector. It had been realized that the acceptance cone of a recording
instrument depends on its physical dimensions, position on the Earth
and the geomagnetic field. The asymptotic cone of a detector is never
immediately along the axis, which the instrument is aligned and this
causes the recorded phase of the diurnal variation to vary from station to
station. By taking account of the asymptotic cones of acceptance of
individual instruments, Rao et al. concluded from two years of neutron
monitor data that the solar diurnal anisotropy had an invariant
amplitude and phase in free space and was caused by an anisotropic
streaming of particles coming from somewhere close to 90" east of the
Earth-Sun line.
Fig. 4.1: Solar diurnal anisotropy in the local time-coordinate system.
Early modelers recognized that by neglecting drift terms and other
effects such as perpendicular diffusion, vector addition of the remaining
streaming components would lead to an overall streaming of particles in
a direction parallel to the Earth's orbit around the Sun. The particles
29
would seem to corotate with the Sun. This corotating streaming (or
anisotropic flow) of particles could be observed as a diurnal variation in
the count rate of a cosmic-ray detector as the detector's viewing cone
rotated through 360^ of space in one day. The anisotropy is the solar
diurnal anisotropy. The anisotropy, manifested as a diurnal variation,
would have the time of maximum count rate outside the magnetosphere
(phase) at 18-00 local solar time (streaming along the tangent to the
Earth's orbit; see Figure 4.1).
Parker (1964) proposed that corotation was a combination of the
random walk (scattering by magnetic irregularities) of particles in the
IMF and an electric field drift velocity. Forman and Gleeson (1975) built
on this model and produced the present theory (Equation (2), Chapter-3).
They showed that pure corotation would arise if there were no net radial
streaming (and drifts are considered negligible). Their model implied
that the magnitude of the solar diurnal anisotropy is 0.6% of the average
isotropic background flux of cosmic rays. If perpendicular diffusion is not
neglected the amplitude of the anisotropy will be less than 0.6% and will
be a function of the relative importance of perpendicular and parallel
diffusion.
Levy (1976) included the curvature and gradient drifts in a model,
which showed that these drifts could be responsible for changing the
direction of the anisotropy in alternate solar cycles. This could explain
the observed 22-year cycle in the anisotropy. A similar result was
obtained by the model of Erdos and Kota (1979). Their model predicted
that the direction of streaming during A < 0 IMF polarity states should
be along the direction of the Earth's orbit. Drifts included in this model
were considered responsible for the model indicating that the streaming
should change direction during the next IMF polarity state and this
streaming would be observed as a diurnal variation with a phase around
15:00 in local solar time. This model predicted that the anisotropy's
amplitude and phase would be insensitive to rigidity but the amplitude
would be sensitive to the neutral sheet warp.
If ^ symbols the anisotropy of cosmic rays in the heliosphere,
35* ^ = — (Gleeson, 1969), and defining i a n d i i n the ecliptic plane with
vU
z along the direction of the IMF away from the Sun, it can be shown
30
(Bieber and Chen, 1991) that transforming the gradient vector into a
spherical coordinate system centered on the Sun the component of ^ in
the coordinate system are^
x = 4 sin X - KGr sin X + pGe sgn(5)
^ =sgn(5)pG,sinj + /l G, •I'-'o (1)
4 =4cos;r-/l;/G,cos;!r
where ^ ,, Compton-Getting anisotropy (3CV/v) (Compton and Getting,
1935); X, angle of the IMF with the Earth-Sun line; 0, unit vector in the
direction of increasing solar co-latitude; p, gyro-radii of the particles; Gr,
radial gradient of cosmic-ray density; Ge, latitudinal gradient of cosmic-
ray density; V, solar wind speed; and v, speed of the cosmic-ray particles.
Sgn (B) represents the effects of drifts on anisotropy. Its value is 1
if the position of Earth in the neutral sheet is such that the IMF is
directed away from the Sun; otherwise is - 1 .
Equation (l) describes the anisotropy of cosmic rays in the three-
dimensional heliosphere. In that coordinate system, components in
ecliptic plane ( x, z) are the components of the anisotropy of cosmic rays
responsible for the solar diurnal anisotropy (£,SD).
In the absence of other anisotropies, the space distribution F(x) of
the solar diurnal anisotropy can be represented as the first order
ordinary Legendre polynomials (Nagashima, 1971):
F{x) = risDPxi.^^^X\ (2)
where
^so - F(X)G{P)
and
G{P) =
r DV
V i u y
p<p.. 10.
0, P>P.
(3)
31
Here, P is the rigidity and Pu is the rigidity where the anisotropy ceases
to be significant.
After further corrections (Nagashima and Ueno, 1971), the form of
space distribution F becomes-
where {6j^,aj^) are the co-declination and right-ascension of the reference
axis of the anisotropy (in the azimuthal direction around the Sun in the
ecHptic plane), {Oj,aj) are the co-declination and right-ascension of the
particles' arrival direction and
f"{ej,,a^,ej,a,) = P^J c o s | L „(cos^^)cosw(«^ -«^) (5)
where Pn,m(x) are the associated Legendre polynomials.
The space distribution F(x) will produce two space harmonic
components (zeroth and first orders). The zeroth order space harmonic
component is along the rotation axis of the Earth and is constant. The
first order space harmonic component (SsoCt)) is directed parallel to the
Earth's equator:
^nsijoos—itj-t^) (6)
ITT . In = x.-n COS—t. + y,.„ sm — /,
where
VsD =i(XsDf+(ySDf
24 t^ = —arctan
a = — 24
^X. ^ SD
V ^ . s v j ;
(7)
32
The free-space harmonic component SsD(t) will produce the solar
diurnal variation D(t) in an instrument's count rate at Earth. Fourier
analysis can be used to derive the components of this variation.
We have discussed that how the solar diurnal anisotropy is caused
by solar modulation of the galactic cosmic rays in the heliosphere.
Long-term averages of the solar diurnal variation provide information
about the average behavior of cosmic rays in the vicinity of the Earth.
Since the diurnal anisotropy is caused by solar modulation, one can use
the effect to derive information about the underlying modulation
processes (e.g. see Hall et al., 1996 and Venkatesan and Badruddin,
1990). Following the discovery that solar diurnal variation in cosmic ray
data was related to spatial anisotropy in primary cosmic ray distribution
(Elliot and Dolbear, 1951), this anisotropy has continued to be studied
(Rao et al., 1972; Forbush, 1973; Agrawal and Singh, 1975; Duggal et al.,
1979; Yadav and Badruddin, 1983a; Badruddin et al., 1985; Bieber and
Chen, 1991; Ahluwalia and Sabbah, 1993; Ananth et al., 1993; Swinson,
1993; Hall et al. 1997; Munakata et al., 1997; Sabbah, 1999).
In this study, a detailed investigation of the solar activity and
solar magnetic cycle dependence of the diurnal anisotropy over the period
of almost five solar cycles (19-23) has been done and the behavior of
diurnal anisotropy in the light of simulations of modulation including
drift effects and tilt of heliospheric current sheet has been interpreted.
4.2 Harmonic Analysis
Harmonic (Fourier) analysis has been done to derive the vector of
diurnal anisotropy because a periodic variation can always be studied by
means of it. In many cases, particularly in cosmic rays, the phenomenon
whose variation is to be studied is not strictly periodic. Thus if the
numbers to be analyzed represent hourly mean of cosmic ray intensity,
the mean for 0** hour will not, in general, be the same as the means for
24*'' hour. This difference is (which on account of secular changes etc.)
allowed for in practice by applying a correction (known as Trend
Correction) to each of the terms (i.e. 24 ordinates).
33
Let V, be the trend corrected value at x = — * 12
and y^. be the uncorrected value
'±Sy then, y, = y. •xk
24 J
where ±5y is the secular change (i.e., ±3\> = y.^^ - y^).
Formulism of Harmonic analysis is given below in brief
Any 2-71 - periodic function f(x) is the sum
CO
OQ + ^ ( a i coskx + bj^ sin Ax)
of its Fourier series. The coefficients ao, ak and bk are calculated by
OQ = — \f{x)dx, a,^-— \f{x)cos{kx)dx, b,^=— \ f {x) sin{kx)dx
The amplitude rk and phase (()k of the k'*' harmonic are expressed as
^k = V K ' + ^ t ' ) ' <l>k =tan' \^kj
Where r gives the amplitude of the anisotropy vector and (|) gives its
phase. Phase represents the time of the maximum of anisotropy.
Although it is a local time variation, the daily variation ought to be
referred to universal time to simplify comparisons between points of
observation with big differences in longitude.
4.3 Data analysis
The pressure corrected hourly neutron monitor data of Oulu, Deep
River, Climax and Huancayo with different cut-off rigidities (Table-l),
have been subjected to harmonic analysis to derive the amplitude (in
percent) and time of maximum (in hours), for nearly 50 years during the
period 1955-2003. These neutron monitor stations are so selected that it
covers a major part of the Earth location (in latitude); polar stations are
34
not suitable for study of diurnal anisotropy. Further, care has been taken
that the data of at least two stations is available for every year. The days
associated with large transient cosmic ray intensity variations, Forbush
decreases and ground level enhancements (GLEs) have been removed
fi-om the data analyzed. Then the average amplitude and phase is
obtained for each year of available data and for each station. Further, the
diurnal anisotropy vectors have been examined by plotting them on
harmonic dial after classifying and averaging them into (different)
appropriate groups according to solar cycles, 1955-64 (19), 1965-75 (20),
1976-85 (21), 1986-96 (22) and 1997-2003 (23), and polarity state of the
heliosphere, 1961-70 (A < O), 1971-80 (A > O), 1981-90 (A < O) and 1991-
1999 (A > O). To obtain an insight of the whole spectrum of distribution of
amplitudes and time of maxima on day-to-day basis in different groups,
histogram of respective group of vectors has also been plotted.
Table-1: Summary of the data
Neutron
Monitor
Station
Oulu
Deep River
Climax
Huancayo
Latitude
(degrees)
65.02
46.10
39.37
-12.03
East
Longitude
(degrees)
25.50
-77.50
-106.18
-75.33
Threshold
Rigidity
(GV)
0.78
1.07
2.99
12.91
Data Period
1964-2003
1964-1992
1955-2002
1955-1992
4.4 Results
Figure 4.2 shows the yearly average diurnal amplitudes at Oulu
from 1964 to 2003, Deep River from 1964 to 1992, Climax from 1955 to
2002, and Huancayo from 1955 to 1992. In this figure, solid vertical lines
represent the years of solar activity minima and the period between two
dashed lines around each solar maximum represents the epoch of solar
polar field reversal. It is seen from this figure that the amplitude of the
diurnal anisotropy show an 11-year variations with the lowest values
35
occurring at solar minima and the highest values near solar maxima.
Enhanced amplitudes for one/two years during the declining phase of
each solar cycle are additional noticeable features of long-term plot
shown in Figure 4.2. Specifically, the near periodic enhanced amplitudes
are noticed in the periods 1962-63, 1973-74, 1984-85, 1994 and 2002-03;
periods in the declining phase of solar cycle 19, 20, 21, and 22
respectively. These are the periods when high-speed solar wind streams
from coronal holes are prevalent. Thus it is likely that the enhancements
in average solar wind speed during declining phases of solar cycle are
responsible to increase in amplitudes of diurnal anisotropy.
Enhancements in amplitudes of semi-diurnal and tri-diurnal anisotropy
with increase in solar wind velocity have been reported by Agrawal
(1981).
19 6 0 19 7 0 1 9 8 0
Y E A R 19 9 0 2 0 0 0 2 0 1 0
Fig. 4.2: Yearly mean cosmic ray diurnal anisotropy amplitudes obtained using Neutron Monitor data at four stations, Oulu, Deep River, Climax and Huancayo. Solid vertical lines indicate the years of solar minimum and the periods between two-dashed lines in each solar cycle indicate the epoch of solar polar field reversal.
36
Thus amplitude of the diurnal anisotropy is a clear 11-year solar
cycle variation with minima at or near sunspot minimum. From these
figures it is also evident (see also Table-2) that the diurnal amplitude is
almost independent of cut-off rigidity of the observing station. These
observations indicate that the amplitude of diurnal anisotropy is affected
both by changes in solar activity as well as by co-rotating high-speed
solar wind streams.
Table-2: Diurnal Amplitude (Ai) and Phase (91) during solar minima
Years
1955
1965
1976
1986
1996
Polarity Stat e
A>0
A<0
A>0
A<0
A>0
Oulu
Ai (%) *
0.219
0.228
0.176
0.137
(pi (hrs) -
14.98
12.90
14.62
12.89
Deep River
Ai (%) •
0.218
0.253
0.21
"
(91) (hrs) "
14.80
12.58
14.89
" •
Climax
Ai (%) 0.137
0.179
0.198
0.207
0.212
(cpi) (hrs) 14.66
15.29
12.56
15.20
13.01
Huancayo
Ai (%) 0.153
0.115
0.177
0.1
'
(91) (hrs) 11.48
11.61
7.57
9.44
~
The long-term variations in the phase (time of maximum) of the
average diurnal anisotropy for the years 1955 to 2003 are shown in
Figure 4.3. It is seen from the figure that local time of maximum of the
diurnal anisotropy at each location shows a prominent ~ 22-year
variation with minimum occurring in 1955, 1976 and 1997. The phase
shift to earlier hours starts after the solar polarity reverses from
negative (A < O) to positive (A > O) states (e.g. in 1971). This shift to
earlier hours continues till the subsequent solar minimum (1976),
reaching minimum phase at or near solar minimum and then starts
recovering towards the pre-reversal level. Again after ~ 22 years, after
1990 polarity reversal, when the Heliosphere comes to same polarity
37
C/3
X
LL O UJ
I I i I r I I I I I I I i I I I I I I I I I I 1 I I I ( 1 I I I I r I I I [ I I I I I I I I I I' I r I
1950 1960 1970 1980
YEAR
1990 2000 2010
Fig. 4.3: Yearly mean cosmic ray diurnal anisotropy phase (time of maximum) obtained using Neutron Monitor data at four stations, Oulu, Deep River, Climax and Huancayo. Solid vertical lines indicate the years of solar minimum and the periods between two-dashed hnes in each solar cycle indicate the epoch of solar polar field reversal.
s tate (A > O), phase shift to earlier hours s tar ts , reaches its minimum
value near solar minimum (in 1997) and then recovering to pre-reversal
level. These observations clearly indicate tha t the t ime of maximum is
influenced by the orientation of solar magnetic field ra the r t han by solar
activity and/or co rotating high-speed streams. The t ime of maximum
shows some rigidity dependence, as can be seen in Figure 4.3, (see also
Table-2), lowest value of phase (earliest time of maximum) of the diurnal
anisotropy is observed at Huancayo, with highest threshold rigidity
among all the four locations.
To provide the average perspective of the diurnal anisotropy, on
the scale of a solar cycle and over a polarity s tate of the Heliosphere, I
have plotted, in Figures 4.4 (a and b), the vector diagrams over harmonic
dial for complete solar cycles 19 (1955-1964), 20 (1966-1975), 21 (1976-
38
1985), 22 (1986-1996) and incomplete cycle 23 (1997-2003) as well as (in
Figures 4.5) for each A < 0 (1961-1970, 1981-1990) and A > 0 (1971-1980,
1991-1999) polarity epoch.
Although the amplitude of diurnal anisotropy displays a clear 11-
year sunspot cycle, when averaged over a complete cycle, no significant
and/or systematic difference in solar cycle averaged amplitudes from one
cycle to the other or between even and odd cycles is observed. Similarly
phase too, when averaged over a complete solar cycle, does not show any
significant and/or systematic shift from one cycle to the other or between
even and odd solar cycles. When averaged over a polarity state of the
heliospheric magnetic field (A < 0 & A > O), the amplitudes are nearly
same for both the polarity states. But the phase shift to earlier hours
during seventies and nineties (A > 0) is clearly evident even in the
average vectors (Figures 4.5, a and b).
Figures 4.6 shows the frequency distributions of the amplitude
of diurnal anisotropy for days of solar cycles 19, 20, 21, 22, and 23.
Amplitudes calculated for each day of a solar cycle and plotted in a
histogram, show almost similar distribution for all the cycles. Moreover,
the frequency distributions of the time of maximum for days of various
solar cycles, plotted in Figures 4.7, is also similar and no phase shift from
one solar cycle to other is seen in the average phase values.
In Figures 4.8 I have shown the frequency distribution of diurnal
amplitudes for days in different polarity states of the Heliosphere (A>0
and A<0). No significant difference in the amplitudes distribution is seen
in these histogram plots. However, the frequency distributions of the
time of maximum (Figures 4.9) clearly indicate the shifting of the diurnal
phase towards earlier hours during seventies (1971-1979) and nineties
(1991-1999). Thus frequency distribution plots with complete spectrum
shown in Figure 4.6, 4.7 and Figure 4.8, 4.9 complement the conclusions
drawn from average vector diagrams plotted in Figure 4.4 and 4.5
respectively.
39
00 h
HI Q
:D
_ i Q.
<
12 h
OOh
12h
06 h
06h
Fig. 4.4 a: Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over complete solar activity cycles for stations Oulu and Deep River.
40
OOh
LU Q =3 H _l Q.
<
02
0.0
0,2
0.0
12h
OOh
12 h
06h
06 h
Fig. 4.4 b: Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over complete solar activity cycles for stations Climax and Huancayo.
41
00 h
Q 3
Q.
<
0.2
12 h
OOh
06 h
06h
12h
Fig. 4.5 a: Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over solar polarity epochs (A > 0 and A < 0), for stations Oulu and deep River.
42
OOh
0.2
06h
LU Q 3
Q.
<
0.0
12h
OOh
12 h
06 h
Fig. 4.5 b- Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over solar polarity epochs (A > 0 and A < O), for s tat ions Climax and Huancayo.
43
20
I I 1 1 1
18
16 j i
14
i '2 1
'°! 1
8 •
6 j
4
2
-• 1
i
1 1 1 1
OULU 1965-75
i r-- .
TM-,.
. -
-
-
-
-
-
-
-
-
HUUl.,l o o o o o o o o o
AMPLITUDE (%) AMPLITUDE {%)
d b o d b o o o
20
? ' UJ
LU
tc cc ID 12 O o o u. 10 o >-" n Ui ID O „ UJ 6 a:
4
2
Q
n 1
• ~
- OULU
1997-2003
-
1
! .
-;
-•
o o o o
AMPLITUDE (%) AMPLITUDE (%)
Fig. 4.6 a'- Amplitude distribution of diurnal vectors for days of various solar cycles at station Oulu.
44
IT D O
O > O Z UJ
O
1 ' I • I ' I ' 1 ' 1 ' 1 ' I ' I
DEEP RIVER 1965-1975
_1_1_
O O O O O O O C J i ^ r -
o u o u_ o
a
20
i a . 1 ! ,
16 -
' i 12 -
1
-H °n 11
- i
i
1 DEEP RIVER 1976-1985
j , 1
,
', i
i
n 1 1
1 '
i 1 ! ^.
I ' I
-
-
-
-
-
-
-_
AMPLITUDE (%)
^ ifi A -i lA
AMPLITUDE (%)
3 o o o
§
r : l lT-T- t -^
nunun AMPLITUDE (%)
Fig. 4.6 b: Amplitude distribution of diurnal vectors for days of various solar cycles at station Deep River.
45
o
-T—!—1—1—1—r—1—I—r—I—I—I—r
CLIMAX 1954-64
• : !
1-1
c m U.i II-ir -> r -1
C)
o
22
20
(8
16
14
10
o
T — 1 — r — I — t — ; — 1 "
n
CLIMAX 1966-75
: I
AMPLITUDE (%)
rf. 6 ^ r
AMPLITUDE (%)
2 2 l ^ - T -
n O uj a:
CLIMAX 1976-85 £ 18
^ 16 l i i t r M ac d 12 o o 10
" « >-o 2 6 UJ
o •* Ol CC 2
0
-1—J—1— (— 1 p I I 1 1 1 1 1 1 -l 1- • 1 1
f ' CLIMAX 1986-96
' i ; 1 1 t
1 ' \
, 1 1 • 1 1 '
1
' 1 1
, !
" , 1 1
i—T
....,
^ ,1 . ...Orir-te-,,™-,™--.^
-•
--
-•
rS 4 -ri. ri C O O
AMPLITUDE (%} L. CJ o o — " '
AMPLITUDE {%)
20
t i s UJ
z ^^ m
B 12 O o 10
o Z 6
g 4 ^ 2
0
FT" 1—r ' > ) 1 ,_.,.,. . , ,. ., ,, ,. r
1 1
j 1 ! 1
1 1 1
• 1 1 • l „ ,
1 1 1
1 1 i 1 i
i!
lixi-IIil:.
CLIMAX 1997-2003
' --'
-
-
AMPLITUDE (%)
Fig. 4.6 c" Amplitude distribution of diurnal vectors for days of various solar cycles at station Climax.
46
' ' ' ' ' ' ' ' 20 1 1
' i i -
t ' 1 1 T' 1
HUANCAYO 1954-1965
'- i . ^^i '
12 i-1 '
10 p j
\" 1
I 1
el' 1
^ ^ i 2 -
' i 1
1 .1 ;
-; 1
1 1
1 , 1
1 tl+TI-n—i—
-
-
-
-
-
-
-
-
-
20
18
16
14
12
10
8
6
4
2
1
1
! i
- 1 •- I
1
! i 1
HUANCAYO 1965-1975
: i . 1
!
''
1
1
1 — 1 —
-
-
-
-
-
-
-
-
-
s ^ i AMPLITUDE (%) AMPLITUDE (%)
^r
HUANCAYO 1976-1985
O O O O O O O O O r ^ T -
20
18
^ 16
UJ
z " a: cr =) 12 o o o u_ 10
o >-Lll 3 LU 6 Q: LL
4
2
r~ " 1
1
• |
. 1 1
.1 1
"
-
HUANCAYO 1986-1996
-
•
-1
-1
1 1
1
1 : 1
1 ! • . ~h-v_,—,
»- CM I'l ^ tn (O t oi a> o I-o o o d o o d o o ' - ' -
AMPLITUDE (%) AMPLITUDE (%)
Fig. 4.6 d: Amplitude distribution of diurnal vectors for days of various solar cycles at station Huancayo.
47
TIME OF MAXIMUM (HRS.) TIME OF MAXIMUM (HRS )
O O
f? 4 -
- T — I — I — I — I — r -
OULU 1986-96
r
n r 1
11 (TTf
ih
1 'T in (O r~~ •:
TIME OF MAXIMUM (HRS.)
i S S S F
OULU 1997-2003
Xlilll f t -
J_L 1 ta I-
TIME OF MAXIMUM (HRS)
Fig. 4.7 a- Phase distribution of diurnal vectors for days of various solar cycles at station Oulu.
48
D O O o
DEEP RIVER 1965-1975
[THl J-X ,Etd PHASE (HOUR)
o o O
o
t "
-1—I—I—I—I—1—I—I—!—I—I—1—I—
DEEP RIVER 1976-1985
nxdl-
i
PHASE (HOUR)
!:tn:
D O
DEEP RIVER 1986-1996
''"f''"i"'"i"'"i' * I ' I ' * 'I""I'"'!'"'I'' I ' I M PHASE (HOUR)
Fig. 4.7 b: Phase distribution of diurnal vectors for days of various solar cycles at station Deep River.
49
— I — I — I — J — I — f — T "
CLIMAX 1954-64
HfflMCi
CLIMAX 1965-75
I ,
J ,
I i1 d) cfi ' - (N f^ *? lA '
PHASE (HOUR)
" cfi 6 ^ c o ^ lA «
PHASE (HOUR)
O O O
-
T
CLIMAX 1976-85
TRT
- 1 I -T 1 T i )—( i—r I -I—(
-
i j 1 j i
1 1
t£' .1
i : • '
ii l i f
lu 12 a a; 3 '»
CLIMAX 1986-96
tomsl ' i <
: 2 S 3 ;
PHASE (HOUR)
d) -^ (N (^ i i lA <ib (
PHASE (HOUR)
?, 10-
-1—r~t—I—r—I—I—I—I—r—T—r-
CUMAX 1997-2003
n :3xtcnfXLU JXtO
PHASE (HOUR)
Fig. 4.7 c: Phase distribution of diurnal vectors for days of various solar cycles at station Climax.
50
o o o
HUANCAYO 1954-1964
r • ' • ' I ' I ' 'f ' '"i ^ I 'T
) O •- Ol m TT j ^ (O '^ i
PHASE (HOUR)
o
o >-o z
^ <
HUANCAYO 1965-1975
r i 1 1
I !• I I
I ' - K i r t ' i ' u ' j t i i ' l c i i T ' T T
PHASE (HOUR)
I " I • ' I •'•'!"
CC
o o o o >-o z
HUANCAYO 1976-1985
n o i .
r
r 1
m , „ , . „ . . ) O T- (N to •
) d) d T^ CN r • " - CM tN Nl f
PHASE (HOUR)
O O O
3
o
HUANCAYO 1986-1996
r" • ' ' r ! 7 CN <^ <f uj n> h
I I [—I * I ' I
S S !
PHASE (HOUR)
Fig. 4.7 d: Phase distribution of diurnal vectors for days of various solar cycles at station Huancayo.
51
S i 16 LU
o a: a:
o o u. 10
o
3
o
~T I 1—I—I—T"
OULU 1961-70
Idi o d d d o d o ' o d ' ^ ' - ' T -
in (O r- oo oi
^ u") (D r i CO
AMPLITUDE (%)
Si 16 LU O g 14
3 ^ o £ 10 o > O 8
z LU 3
6 LU
~\ I ! I I—1 1 T"
a
OULU 1971-80
1— ( S f O ^ m t D r ^ o o C T O i - C N M ' V t D t D f ^ e o o ) d d d d d c > d d d ^ ^ T ^ » 7 » 7 ' 7 - ^ V ' 7 - ^ d i - t N r o T i - i o u l i t - ^ c o d d T ^
d d o d d d o d d ' < - ^ ' < - ^ TT LO (O r-- CO
AMPLITUDE (%)
>-o z LU
O
-1—I—I—I—I—I—1—1—I—I—I—I—I—r
OULU 1981-90
" - f s l f O ' ^ i O c p h - c o o i O ' - t N c o ^ m t D r - o o o i d d d d d d d d d ' - ^ ' - ' ' - ^ ' - ^ T - ' i - ^ T - ; . r ^ - ^ ' - r -
22
20
en O o o
>-o z LU 3 a
1 1 1 1 1 1 1 1 1 1 -T—r
• h
1 1 1 1 I I r
OULU 1991-2003
:
~1
' - ( N r o ' v i n ( £ ) r - - ( o o j O ' ~ r - i c o T r m < D d d d d d d d d d ' r ^ ' - T - - ^ ' - ^ ' ^ T -O T ^ r N i c o - ^ u i t p r ^ c o d d r ^ f s i i r i T r i n
d d d d d d o d d ' - ^ ' - - ^ ^ ^ ' -
AMPLITUDE (%) AMPLITUDE (%)
Fig. 4.8 a- Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Oulu.
52
a. X a o o
3
a
20
)S
16
14
i: 1 \
1, 1
•
.
' 1
1
1
1
1 : 1
' 1
1 1 i_...
' ' 1
1
1
' ' DEEP RIVER
1961-1970
"!
1
1 i
i 1
1 1 1
... _.!.,
- 1
1 I- 1 1
-
-
-
-
.
_
C3 O d o o o cfi "- (^ (J) 4 uS CO '
ai o r-
AMPLITUDE (%)
o o O
' I • I • ) • I • I I I • I • I I
Ll ,
I • ) • 1 1 1 ' 1 1 1 1
D E E P R IVER
197M980
r-u-^ o c p o d d d d o o T - ^ T - ^
o d c i c i c i d o o o T - i - ^
AMPLITUDE (%)
20
. 6 r ' , 1
S' 16 L - 1 1 UJ
Z 1 4 -
8 1 s ° LU
a. 4
2
r
"1
DEEP RIVER 1981-1990
-
~i 1
-
" 1
"1
! rh—v->™
-
-
"
-•
--
0 0 0 0 0 0 0 0 0 1 -
O O
o
?n
18
16
14
12
10
8
6
4
2
.
•
" r i
" 1
• 1
-1 • 1
1
• i
1
) • I " 1 ' 1 ' 1
'—1
! 1 ^
"( 1
1 1 ! 1 ~1
1
1 , 1
1
1
ihr-r
DEEP RIVER 1991-2003
•
_
' -
-
-
--
--
O O G O O O O
O O O
AMPLITUDE (%) AMPLITUDE (%)
Fig. 4.8 b- Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Deep River.
53
20
--s;::, is
O 16
LU a: 14 Q;
7i .2 o O 10 u-^ a
>~ u Z 6 LU => ^ O " LU Cd 2
' ' -I—T'' r 1 1
1
• I 1 ,
1
~_
1 1 I
CUMAX 1951-60
. —
1
1 1
1
1
! 1 •- '^^^V-r^-^-,
T 1
-.
-.
--
•
9 9 9 ?
AMPLITUDE (%)
20
LU O 16 Z UJ Q: H a. H 12 O O 10 u. <-> « >-O Z 6 LU D , a " Lii
0
[ ^ . \"
-1 - 1
-
-T— - T - ~r- T r' 1" 1 1 1 1
1
'. I rrv-,
1 1 1
CLIMAX 1971-80
1 1
-. .
---
0 9 0 0 1 ^
d d o o d ^ " - ^
AMPLITUDE (%)
22
20
g 18 lU O 16
LU K 14
3 1 o O 10
o „
a
I ! -
I !
J L
20 L
£ 1 8 r 1
0 16 • Z
i r 14 -Q^ 1
5 - , 0 ' 0 10. ' ^ 1
0 8 '
> ; 0 1 Z 6 - , LU l ^ ^ L o "h LU I
° zt ot ! .
1
1
1
1 1 1
CLIMAX 1961-70
' 1 1 !
1 • -
1
1
'
1 1 1 1
1 I" I '. 1 i 1 nrrr-.--^
1
-
-_
-
HUUi AMPLITUDE (%)
3 O
20
18
14
12
10
8
6
4
2
- . CLIMAX 1981-90
' _
1
• 1
1
1
' 1
1
1 1
"1 1
1
r
1 1 1
1 1
! 1 " " . ^ - T — i — , . , - ™ , ^
-
' -------
5 2 3 3 3 3 3 d d d o d o
AMPLITUDE (%)
CUMAX 1991-2003
AMPLITUDE (%)
Fig. 4.8 c: Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Climax.
54
20
16
14
12
10
8
6
4
2
• • T ' •
' _|_ —r- ' '
~1
- !
- 1
1
- 1
i 1
r -
l _ ^
r - 1 1 1 • I
HUANCAYO 1951-1960
' '. "
1 1
"!
1
-
1- -
1
r-r-i_^ CN n ^ if) <o t 9 9 9 9 9 ' o o d o o d o o o
AMPLITUDE (%)
HUANCAYO 1961-1970
c j ) q ) 9 9 ^ 9 9 V ' d o o d d o o d '
AMPLITUDE (%)
20
in
16
14
12
10
8
6
4
2
1 1
1 ,
1 1
-
-
•
i HUANCAYO 1971-1980
-
1 '
1 1
-
-
"!
a_ o o q> OT o Q o 1^ o 1-
O O O O O O O G O
T — I — I — I — r -
r HUANCAYO 1981-1990
' I
AMPLITUDE (%) AMPLITUDE (%)
Fig. 4.8 d: Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Huancayo.
55 ->"V- . hV
'•n n . i v C ^
a: a. z> o o o u. O > o
a a:
I I I I I I ! I I I I
OULU 1971-80
r
ohrfTrf y CTJO'i—cNtO'j'ixiifjr^-roCTJCj'—c
TIME OF MAXIMUM (HRS.) TIME OF MAXIMUM (HRS.)
O 12
a: a: z> a o O
O > o
a UJ
n I I I I I r" I I I I I I I I I
OULU 1991-2003
tftQ Id TIME OF MAXIMUM (HRS.)
- o o o i O ' - c N r o ^ i j
( J i O T - r > j f O " « i O ( o r
TIME OF MAXIMUM (HRS.)
Fig. 4.9 a: Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Oulu.
56
O o o
DEEP RIVER 1961-1970
.i.u^.a
i !
..MJ
PHASE (HOUR)
~i—1—I—1—I—r
DEEP RIVER 1971-1980
, I
Illll tnttl 5 ^ ^ 3 '
PHASE (HOUR)
o o o
o
DEEP RIVER 1981-1990
imd
1
r ' I •••r*T' ' ' t " ' '
' - ( N f O ' j i n t o N - o p a i O T - c
M < D I ~ - c O O i O ' - C N r O '
PHASE (HOUR)
3 O o o
o
DEEP RIVER 1991-2003
1 5 2 3 3 4 S I
PHASE (HOUR)
Fig. 4.9 b- Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Deep River.
57
^ 2
CLIMAX 1951-60
IteMll Wn
PHASE (HOUR)
—I—\—1—1—1—r-
CLIMAX 1971-80
:TOxan. 11
''M. PHASE (HOUR)
CLIMAX 1961-70
cc 2-
IrTTTTT-TT m r^ ^ u i tp r^ C9 t
PHA'SE (HOUR)'
CLIMAX 1981-90
n
I^^TT^" y PHASE (HOUR)
O
>
"- 2
CLIMAX 1991-2003
TWfTfl inji PHASE (HOUR)
: s 8 E; !
Fig. 4.9 c: Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Climax.
58
cr D o o o
3 o ^ 4-u- '
HUANCAYO 1951-1960
, I
I
PHASE (HOUR)
HUANCAYO 1961-1970
PHASE (HOUR)
UJ O 12 z UJ
en 10-
o o o
o > o z LU D
o
HUANCAYO 1981-1990
affl PHASE (HOUR) PHASE (HOUR)
Fig. 4.9 d Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Huancayo.
59
4.5 Discussion
In model calculations (see chapter 3 for details and references)
including drift effects, cosmic ray trajectories were calculated for the two
IMF configurations corresponding to two orientations of Sun's polar
magnetic field. During 1960s and 1980s (for example), when the IMF was
inward (A < O) above the heliospheric current sheet, galactic cosmic rays
enter the Heliosphere mainly in the ecliptic plane. During the 1970s and
1990s when the IMF was outward above the current sheet (A > O), cosmic
ray particles penetrate the Heliosphere more easily from polar regions.
During 1960 and 1980 (A < O), the convection diffusion model adequately
describes the solar diurnal variation because the cosmic rays entering
the Heliosphere diffuse predominantly in the ecliptic plane, with the net
inflow in the ecliptic plane balancing the net outflow in the ecliptic plane
(the convective component), leading to an azimuthal cosmic ray diurnal
variation. During the 1970s and 1990s (A > 0), with cosmic rays entering
preferentially by way of the poles, there is a reduction in the inward
diffusive component in the ecliptic plane, leading to a net diurnal
variation that has its maximum at an earlier time. In this case the net
inflow of cosmic rays from the poles balances the net outflow in the
ecliptic plane, with a relative increase of the radial component of the
diurnal variation, and a shift in phase to earlier hours.
4.6 Conclusions
In this work, the cosmic ray diurnal anisotropy using data
over a period of about 50 years from four neutron monitors has been
determined. Following conclusions can be drawn from this study.
The amplitude of the cosmic ray diurnal anisotropy varies
with a period of one solar activity cycle (~ 11-years), while the phase of
the diurnal anisotropy varies with a period of one solar magnetic cycle (~
22-years) i.e. two solar cycles.
In each solar activity cycle, the amplitude is observed to be
enhanced for one/two years during declining phase when co-rotating
high-speed streams from coronal holes are prevalent.
60
Amplitude is influenced by solar activity and co rotating high
speed solar wind streams while the time of maximum is influenced by
the orientation of solar magnetic field,' the shift in phase appears to be
related to switch of the Heliosphere from one magnetic state to another
following polar field reversal and the consequent change in preferential
entry of cosmic ray particles into the Heliosphere.
The amplitude of diurnal anisotropy is independent of the
threshold rigidity of the cosmic ray particles. However, the time of
maximum depends upon the threshold rigidity of the observing station.
Time of maximum of the diurnal anisotropy is dependent on
the polarity state of the Heliosphere; it is influenced by the orientation of
the solar magnetic field rather than by solar activity and/or co rotating
high-speed solar wind streams. The phase shift to earlier hours in each
solar magnetic cycle starts after the solar polarity reverses from negative
(A < 0) to positive state (A > 0).
The solar cycle averaged diurnal amplitude is almost same for
different solar cycles and no significant change is observed from one cycle
to the other or between odd and even cycles. The average time of
maximum too does not change from one cycle to the other when averaged
over a solar activity cycle. However, the average phase during one
polarity state of the Heliosphere (e.g. A > O) is significantly different from
the other polarity state (A < O) and it is shifted to earlier hours during A
< 0 state as compared to A > 0 state.
61
REFERENCES
/« t
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