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Solar Modulation: A Theoretical PerspectiveModeling of cosmic ray charge-sign dependence in the heliosphere
Marius Potgieter
Unit for Space Physics North-West University
Potchefstroom, South Africa
PAMELA Workshop May 2009
Colaborators: Stefan Ferreira, Bernd HeberStudents: DuToit Strauss, Etienne Vos, Driaan Bisschoff,
Rex Manuel, Edwin Mogadimisha
Cosmic Rays from the Galaxy
Inside the heliosphere
Charged Particle Populations
Bow Shocks
500 AU
250 AU
Heliospace
The heliosphere
Voyager 1: Dec 2004
Voyager 2: Aug 2007
Cosmic ray transport partCosmic ray transport part
Hydrodynamic partHydrodynamic part
,
,
2
2,
( ) ,
( ) ( ) ,
2 1
,2 1
i i i i
i i i i i i m i
i ii
i
i i i ii i e i
i
Qt
P Qt
P
t
PQ
u
u u u I
u
uu u
> describe the balance of mass, momentum and > describe the balance of mass, momentum and energy of the protons in solar wind and LISM, neutral energy of the protons in solar wind and LISM, neutral hydrogen, pickup ions, and additional is GCR’s and hydrogen, pickup ions, and additional is GCR’s and ACR’sACR’s
> mass density > mass density , velocity , velocity u,u, pressure pressure P P and and QQ sources sources related to the interaction between the various species.related to the interaction between the various species.
A 5 fluid model based on the A 5 fluid model based on the Kausch (1998)Kausch (1998) model : model :
1( ) ( ) ( )
3 lns
f ff f
t R
Dvsw swV K V
> including all major modulation mechanisms : > including all major modulation mechanisms : diffusion, drifts, convection and energy changesdiffusion, drifts, convection and energy changes
Realistic heliospheric geometry Realistic heliospheric geometry andand solar wind flow profilesolar wind flow profile
Magnetic partMagnetic part
( ) 0t
B
u B
> Magnetized flow is calculated by solving Faraday’s law assuming ideal MHD> Magnetized flow is calculated by solving Faraday’s law assuming ideal MHD
Magnetic fieldMagnetic field
Cosmic ray transport and acceleration calculated by Cosmic ray transport and acceleration calculated by Parker (1965)Parker (1965) TPE : TPE :
How is the heliosphere formed ?
Allow the physics to tell us !
TS 93AU
HP 140 AU
TS 155 AU
HP 245 AU
TS 205 AUScherer, K., & Ferreira, S. E. S. 2005, ASTRA, 1, 17
Ferreira, S. E. S., & Scherer, K. 2004, ApJ, 616, 1215
Hydrodynamic modeling of major heliospheric structures
r
Predictions of TS crossing for V1 and V2
AU
Time (years)
Termination shock changes position over a solar cycle
V1 & V2 launched in 1977
V1 is presently at 107 AU, 34°N
V2 is presently at 86 AU, 28°S
V1 crossed the TS in Dec. 2004 at 94 AU
V2 crossed the TS end of Aug. 2007 at 84 AU
Cosmic rays are excellent indicators of solar cycle variations Modulation of galactic cosmic rays at Neutron Monitor energies
1
3 ln
Df f Q( r, p,f
f tt p
)f K VV v
Time-dependent, pitch-angle-averaged distribution functionDiffusion
Convection with solar windParticle Drifts
Adiabatic energy changesAny local source
Parker (Planet. Space Science, 13, 9,1965)
Transport equation for the modulation and acceleration of cosmic rays in the heliosphere
Modulation-Acceleration Model
Second order Fermi acceleration 2
2pp
1 f... ... p D
p pp
Heliospheric CR Modulation Processes
As for electrons
The wavy current sheet (HCS)
Heliosphere & Cosmic Ray Modulation Mechanisms
Tilt angle of the HCS: proxy for solar activity
L - values
Hoeksema's "Tilt Angles" (Averaged over one solar rotation)
Time (Years)
1975 1985 1995 2005
Tilt
Ang
le (
Deg
rees
)
0
10
20
30
40
50
60
70
80
Maximum solar activity
Minimum solar activity
The wavy heliospheric current sheet (HCS)
Moderate solar activity
Extreme solar activity
Galactic CR Spectra
Kinetic energy (GeV/nuc)
10-3 10-2 10-1 100 101
Diff
eren
tial i
nten
sity
(par
t.MeV
-1.m
-2.s
r-1.s
-1)
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
p
He
e+
C
e-
p-
B
Moskalenko and Strong, 2002. Langner, 2002, 2005;
Computed Galactic Spectra (LIS?)
Webber et al. (AIP-IGPP-2006)
Solar modulation of galactic carbon
Major features of cosmic rays near Earth
Langner, Potgieter & Webber, JGR, 2003; ASR, 2004
Observed spectra crossings at Earth,from A > 0 and A < 0 solar minima polarity cycles…
Observed small latitudinal gradients, especially at low energies; compared to Ulysses-KET observations; for A > 0, solar minimum to maximum…
Effects of gradient and curvature drifts in the heliosheath-nose
Langner, Potgieter & Webber, JGR, 2003
200 MeV GCR protons
Solar minimum conditions
Conclusions:
GC&CS-drifts may play a significant role in the HS….?
Without drifts the TS seems insignificant for GCRs …
The HP is more important to GCR modulation than the TS
Drifts during a complete solar activity cycle
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
% d
rift
s in
mo
de
l
0
20
40
60
80
100
Time (Years)
Tilt
an
gle
(d
eg
r.)
0
20
40
60
Long term modulation: charge-sign dependence
Long-term modulation of 1.2 GV electrons and helium at Earth over 22 years.Electron measurements form ISEE/ICE (Clem et al., 1996; Evenson, 1998). He measurements form IMP (McDonald, 1998;
McDonald et al., 2001).
10-2 10-1 100 101
Gr (%
/AU
)
-1
0
1
2
3
4
5
A > 0A < 0
10-2 10-1 100 101
Gr (%
/AU
)
0
2
4
6
A > 0A < 0
Kinetic energy (GeV)
10-2 10-1 100 101
Gr (%
/AU
)
-8
-6
-4
-2
0
2
4
6
8
10
A > 0A < 0
Tilt = 10 degrees
equatorial plane
1 AU
50 AU
10-2 10-1 100 101
0
1
2
3
4
5
A > 0A < 0
10-2 10-1 100 101
0
1
2
3
4
5
6
7
A > 0A < 0
Kinetic energy (GeV)
10-2 10-1 100 101-8
-6
-4
-2
0
2
4
6
8
10
A > 0A < 0
Tilt = 10 degrees
= 550
1 AU
Tilt = 10 degrees
equatorial plane
Tilt = 10 degrees
= 550
50 AU
Tilt = 10 degrees
= 550
91 AU
Tilt = 10 degrees
equatorial plane
91 AU
Computed radial gradients for galactic protons
At Earth
50 AU
TS = 91 AU
During solar minimum modulation; A > 0; A < 0
10-2 10-1 100 101
rG
(%/d
eg
ree
)
-1.0
-0.5
0.0
0.5
1.0
10-2 10-1 100 101
rG
(%/d
eg
ree
)
-4
-3
-2
-1
0
1
2
Kinetic energy (GeV)
10-2 10-1 100 101
rG
(%/d
eg
ree
)
-4
-3
-2
-1
0
1
2
Tilt = 10 degrees
equatorial plane
1 AU
A < 0
A > 0
50 AU
91 AU
A > 0
A < 0
A > 0
A < 0
10-2 10-1 100 101-1.0
-0.5
0.0
0.5
1.0
10-2 10-1 100 101-4
-3
-2
-1
0
1
2
Kinetic energy (GeV)
10-2 10-1 100 101-4
-3
-2
-1
0
1
2
Tilt = 10 degrees
equatorial plane
Tilt = 10 degrees
equatorial plane
Tilt = 10 degrees
= 550
1 AU
Tilt = 10 degrees
= 550
50 AU
Tilt = 10 degrees
= 550
91 AU
A < 0
A > 0
A < 0
A > 0
A < 0
A > 0
Computed proton polar gradients
Earth
50 AU
91 AU
During solar minimum modulation; A > 0; A < 0
Modulation of galactic protons and anti-protonsat solar minimum
Modulation of galactic electrons and positrons at solar minimum
Ratio of Electrons to PositronsAt Earth
Solar minimum modulation Two concecutive magnetic field
polarities
Ratio of Electrons to PositronsAt Earth
Solar maximum modulation Two concecutive magnetic field
polarities
Ratio of Electrons to PositronsAt Earth vs. LIS
Solar minimum modulation
Two concecutive magnetic field polarities
Ratio of Protons to Anti-protonsAt Earth vs. LIS
Solar minimum modulation
Two concecutive magnetic field polarities
The Wonders of HeliospaceProfile of the Latitudinal Solar Wind
Contribution of Jovian Electrons
Electron Spectra at Earth and at increasing radial distances
Modulation of Jovian ElectronsJupiter is a strong source of low-energy electrons at 5 AU
Illustration of electrons following the HMF spiral structure; paralllel and perpendicular diffusion
Charged-sign Dependent Modulation over two Solar Maxima
Electron measurements form ISEE/ICE (Clem et al., 1996; Evenson, 1998) and KET (Heber et al, this conference). He measurements from IMP (McDonald, 1998; McDonald et al., 2001).