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).